id	sid	tid	token	lemma	pos
ejde-388	1	1	electronic	electronic	ADJ
ejde-388	1	2	journal	journal	NOUN
ejde-388	1	3	of	of	ADP
ejde-388	1	4	differential	differential	ADJ
ejde-388	1	5	equations	equation	NOUN
ejde-388	1	6	,	,	PUNCT
ejde-388	1	7	vol	vol	NOUN
ejde-388	1	8	.	.	PUNCT
ejde-388	1	9	2020	2020	NUM
ejde-388	1	10	(	(	PUNCT
ejde-388	1	11	2020	2020	NUM
ejde-388	1	12	)	)	PUNCT
ejde-388	1	13	,	,	PUNCT
ejde-388	1	14	no	no	INTJ
ejde-388	1	15	.	.	NOUN
ejde-388	1	16	104	104	NUM
ejde-388	1	17	,	,	PUNCT
ejde-388	1	18	pp	pp	ADJ
ejde-388	1	19	.	.	PUNCT
ejde-388	2	1	1–21	1–21	PROPN
ejde-388	2	2	.	.	PUNCT
ejde-388	3	1	issn	issn	PROPN
ejde-388	3	2	:	:	PUNCT
ejde-388	3	3	1072	1072	NUM
ejde-388	3	4	-	-	SYM
ejde-388	3	5	6691	6691	NUM
ejde-388	3	6	.	.	PUNCT
ejde-388	4	1	url	url	PROPN
ejde-388	4	2	:	:	PUNCT
ejde-388	4	3	http://ejde.math.txstate.edu	http://ejde.math.txstate.edu	PROPN
ejde-388	4	4	or	or	CCONJ
ejde-388	4	5	http://ejde.math.unt.edu	http://ejde.math.unt.edu	VERB
ejde-388	4	6	short	short	ADJ
ejde-388	4	7	term	term	NOUN
ejde-388	4	8	unpredictability	unpredictability	NOUN
ejde-388	4	9	of	of	ADP
ejde-388	4	10	high	high	ADJ
ejde-388	4	11	reynolds	reynold	NOUN
ejde-388	4	12	number	number	NOUN
ejde-388	4	13	turbulence	turbulence	NOUN
ejde-388	4	14	–	–	PUNCT
ejde-388	4	15	rough	rough	ADJ
ejde-388	4	16	dependence	dependence	NOUN
ejde-388	4	17	on	on	ADP
ejde-388	4	18	initial	initial	ADJ
ejde-388	4	19	data	datum	NOUN
ejde-388	4	20	zaichun	zaichun	PROPN
ejde-388	4	21	feng	feng	PROPN
ejde-388	4	22	,	,	PUNCT
ejde-388	4	23	y.	y.	PROPN
ejde-388	4	24	charles	charles	PROPN
ejde-388	4	25	li	li	PROPN
ejde-388	4	26	abstract	abstract	PROPN
ejde-388	4	27	.	.	PUNCT
ejde-388	5	1	short	short	ADJ
ejde-388	5	2	term	term	NOUN
ejde-388	5	3	unpredictability	unpredictability	NOUN
ejde-388	5	4	is	be	AUX
ejde-388	5	5	discovered	discover	VERB
ejde-388	5	6	numerically	numerically	ADV
ejde-388	5	7	for	for	ADP
ejde-388	5	8	high	high	ADJ
ejde-388	5	9	reynolds	reynold	NOUN
ejde-388	5	10	number	number	NOUN
ejde-388	5	11	fluid	fluid	NOUN
ejde-388	5	12	flows	flow	NOUN
ejde-388	5	13	under	under	ADP
ejde-388	5	14	periodic	periodic	ADJ
ejde-388	5	15	boundary	boundary	ADJ
ejde-388	5	16	conditions	condition	NOUN
ejde-388	5	17	.	.	PUNCT
ejde-388	6	1	furthermore	furthermore	ADV
ejde-388	6	2	,	,	PUNCT
ejde-388	6	3	the	the	DET
ejde-388	6	4	abundance	abundance	NOUN
ejde-388	6	5	of	of	ADP
ejde-388	6	6	the	the	DET
ejde-388	6	7	short	short	ADJ
ejde-388	6	8	term	term	NOUN
ejde-388	6	9	unpredictability	unpredictability	NOUN
ejde-388	6	10	is	be	AUX
ejde-388	6	11	also	also	ADV
ejde-388	6	12	discovered	discover	VERB
ejde-388	6	13	.	.	PUNCT
ejde-388	7	1	these	these	DET
ejde-388	7	2	discoveries	discovery	NOUN
ejde-388	7	3	support	support	VERB
ejde-388	7	4	our	our	PRON
ejde-388	7	5	theory	theory	NOUN
ejde-388	7	6	that	that	SCONJ
ejde-388	7	7	fully	fully	ADV
ejde-388	7	8	developed	develop	VERB
ejde-388	7	9	turbulence	turbulence	NOUN
ejde-388	7	10	is	be	AUX
ejde-388	7	11	constantly	constantly	ADV
ejde-388	7	12	driven	drive	VERB
ejde-388	7	13	by	by	ADP
ejde-388	7	14	such	such	ADJ
ejde-388	7	15	short	short	ADJ
ejde-388	7	16	term	term	NOUN
ejde-388	7	17	unpredictability	unpredictability	NOUN
ejde-388	7	18	.	.	PUNCT
ejde-388	8	1	1	1	X
ejde-388	8	2	.	.	X
ejde-388	8	3	introduction	introduction	NOUN
ejde-388	8	4	turbulence	turbulence	NOUN
ejde-388	8	5	as	as	ADP
ejde-388	8	6	an	an	DET
ejde-388	8	7	open	open	ADJ
ejde-388	8	8	problem	problem	NOUN
ejde-388	8	9	has	have	VERB
ejde-388	8	10	two	two	NUM
ejde-388	8	11	aspects	aspect	NOUN
ejde-388	8	12	:	:	PUNCT
ejde-388	8	13	turbulence	turbulence	NOUN
ejde-388	8	14	engineering	engineering	NOUN
ejde-388	8	15	and	and	CCONJ
ejde-388	8	16	turbulence	turbulence	NOUN
ejde-388	8	17	physics	physics	NOUN
ejde-388	9	1	[	[	X
ejde-388	9	2	11	11	NUM
ejde-388	9	3	]	]	PUNCT
ejde-388	9	4	.	.	PUNCT
ejde-388	10	1	turbulence	turbulence	NOUN
ejde-388	10	2	engineering	engineering	NOUN
ejde-388	10	3	deals	deal	NOUN
ejde-388	10	4	with	with	ADP
ejde-388	10	5	how	how	SCONJ
ejde-388	10	6	to	to	PART
ejde-388	10	7	describe	describe	VERB
ejde-388	10	8	turbulence	turbulence	NOUN
ejde-388	10	9	in	in	ADP
ejde-388	10	10	engineering	engineering	NOUN
ejde-388	10	11	.	.	PUNCT
ejde-388	11	1	turbulence	turbulence	NOUN
ejde-388	11	2	physics	physics	NOUN
ejde-388	11	3	deals	deal	VERB
ejde-388	11	4	with	with	ADP
ejde-388	11	5	the	the	DET
ejde-388	11	6	physical	physical	ADJ
ejde-388	11	7	mechanism	mechanism	NOUN
ejde-388	11	8	of	of	ADP
ejde-388	11	9	turbulence	turbulence	NOUN
ejde-388	11	10	.	.	PUNCT
ejde-388	12	1	in	in	ADP
ejde-388	12	2	pursuit	pursuit	NOUN
ejde-388	12	3	of	of	ADP
ejde-388	12	4	understanding	understanding	NOUN
ejde-388	12	5	of	of	ADP
ejde-388	12	6	turbulence	turbulence	NOUN
ejde-388	12	7	physics	physic	NOUN
ejde-388	12	8	,	,	PUNCT
ejde-388	12	9	recently	recently	ADV
ejde-388	12	10	we	we	PRON
ejde-388	12	11	proposed	propose	VERB
ejde-388	12	12	the	the	DET
ejde-388	12	13	theory	theory	NOUN
ejde-388	12	14	that	that	SCONJ
ejde-388	12	15	fully	fully	ADV
ejde-388	12	16	developed	develop	VERB
ejde-388	12	17	turbulence	turbulence	NOUN
ejde-388	12	18	is	be	AUX
ejde-388	12	19	caused	cause	VERB
ejde-388	12	20	by	by	ADP
ejde-388	12	21	short	short	ADJ
ejde-388	12	22	term	term	NOUN
ejde-388	12	23	unpredictability	unpredictability	NOUN
ejde-388	12	24	due	due	ADP
ejde-388	12	25	to	to	ADP
ejde-388	12	26	rough	rough	ADJ
ejde-388	12	27	dependence	dependence	NOUN
ejde-388	12	28	upon	upon	SCONJ
ejde-388	12	29	initial	initial	ADJ
ejde-388	12	30	data	datum	NOUN
ejde-388	12	31	,	,	PUNCT
ejde-388	12	32	while	while	SCONJ
ejde-388	12	33	(	(	PUNCT
ejde-388	12	34	often	often	ADV
ejde-388	12	35	)	)	PUNCT
ejde-388	12	36	transient	transient	ADJ
ejde-388	12	37	turbulence	turbulence	NOUN
ejde-388	12	38	at	at	ADP
ejde-388	12	39	moderate	moderate	ADJ
ejde-388	12	40	reynolds	reynold	NOUN
ejde-388	12	41	number	number	NOUN
ejde-388	12	42	is	be	AUX
ejde-388	12	43	caused	cause	VERB
ejde-388	12	44	by	by	ADP
ejde-388	12	45	chaos	chaos	NOUN
ejde-388	12	46	(	(	PUNCT
ejde-388	12	47	long	long	ADJ
ejde-388	12	48	term	term	NOUN
ejde-388	12	49	unpredictability	unpredictability	NOUN
ejde-388	12	50	)	)	PUNCT
ejde-388	13	1	[	[	X
ejde-388	13	2	12	12	NUM
ejde-388	13	3	]	]	PUNCT
ejde-388	13	4	.	.	PUNCT
ejde-388	14	1	the	the	DET
ejde-388	14	2	main	main	ADJ
ejde-388	14	3	goal	goal	NOUN
ejde-388	14	4	of	of	ADP
ejde-388	14	5	this	this	DET
ejde-388	14	6	article	article	NOUN
ejde-388	14	7	is	be	AUX
ejde-388	14	8	to	to	PART
ejde-388	14	9	demonstrate	demonstrate	VERB
ejde-388	14	10	the	the	DET
ejde-388	14	11	short	short	ADJ
ejde-388	14	12	term	term	NOUN
ejde-388	14	13	unpredictability	unpredictability	NOUN
ejde-388	14	14	via	via	ADP
ejde-388	14	15	numerical	numerical	ADJ
ejde-388	14	16	simulations	simulation	NOUN
ejde-388	14	17	.	.	PUNCT
ejde-388	15	1	according	accord	VERB
ejde-388	15	2	to	to	ADP
ejde-388	15	3	our	our	PRON
ejde-388	15	4	analytical	analytical	ADJ
ejde-388	15	5	theory	theory	NOUN
ejde-388	15	6	[	[	X
ejde-388	15	7	12	12	NUM
ejde-388	15	8	]	]	PUNCT
ejde-388	15	9	,	,	PUNCT
ejde-388	15	10	perturbations	perturbation	NOUN
ejde-388	15	11	in	in	ADP
ejde-388	15	12	turbulence	turbulence	NOUN
ejde-388	15	13	can	can	AUX
ejde-388	15	14	amplify	amplify	VERB
ejde-388	15	15	in	in	ADP
ejde-388	15	16	time	time	NOUN
ejde-388	15	17	according	accord	VERB
ejde-388	15	18	to	to	ADP
ejde-388	15	19	exp(σ	exp(σ	PROPN
ejde-388	15	20	√	√	NUM
ejde-388	15	21	re	re	ADP
ejde-388	15	22	√	√	PROPN
ejde-388	15	23	t	t	PROPN
ejde-388	15	24	+	+	CCONJ
ejde-388	15	25	σ1	σ1	PROPN
ejde-388	15	26	t	t	PROPN
ejde-388	15	27	)	)	PUNCT
ejde-388	15	28	where	where	SCONJ
ejde-388	15	29	re	re	NOUN
ejde-388	15	30	is	be	AUX
ejde-388	15	31	the	the	DET
ejde-388	15	32	reynolds	reynolds	PROPN
ejde-388	15	33	number	number	PROPN
ejde-388	15	34	,	,	PUNCT
ejde-388	15	35	σ1	σ1	NOUN
ejde-388	15	36	=	=	SYM
ejde-388	15	37	σ	σ	PROPN
ejde-388	15	38	√	√	NUM
ejde-388	15	39	2e/2	2e/2	NUM
ejde-388	15	40	,	,	PUNCT
ejde-388	15	41	and	and	CCONJ
ejde-388	15	42	σ	σ	NOUN
ejde-388	15	43	depends	depend	VERB
ejde-388	15	44	only	only	ADV
ejde-388	15	45	on	on	ADP
ejde-388	15	46	the	the	DET
ejde-388	15	47	base	base	NOUN
ejde-388	15	48	solutions	solution	NOUN
ejde-388	15	49	on	on	ADP
ejde-388	15	50	which	which	PRON
ejde-388	15	51	the	the	DET
ejde-388	15	52	perturbations	perturbation	NOUN
ejde-388	15	53	are	be	AUX
ejde-388	15	54	introduced	introduce	VERB
ejde-388	15	55	,	,	PUNCT
ejde-388	15	56	the	the	DET
ejde-388	15	57	spatial	spatial	ADJ
ejde-388	15	58	domain	domain	NOUN
ejde-388	15	59	,	,	PUNCT
ejde-388	15	60	and	and	CCONJ
ejde-388	15	61	n	n	PROPN
ejde-388	15	62	of	of	ADP
ejde-388	15	63	the	the	DET
ejde-388	15	64	sobolev	sobolev	NOUN
ejde-388	15	65	space	space	NOUN
ejde-388	16	1	hn	hn	PROPN
ejde-388	16	2	.	.	PUNCT
ejde-388	17	1	when	when	SCONJ
ejde-388	17	2	the	the	DET
ejde-388	17	3	time	time	NOUN
ejde-388	17	4	is	be	AUX
ejde-388	17	5	small	small	ADJ
ejde-388	17	6	,	,	PUNCT
ejde-388	17	7	the	the	DET
ejde-388	17	8	first	first	ADJ
ejde-388	17	9	term	term	NOUN
ejde-388	17	10	in	in	ADP
ejde-388	17	11	the	the	DET
ejde-388	17	12	exponent	exponent	NOUN
ejde-388	17	13	dominates	dominate	VERB
ejde-388	17	14	,	,	PUNCT
ejde-388	17	15	and	and	CCONJ
ejde-388	17	16	this	this	DET
ejde-388	17	17	term	term	NOUN
ejde-388	17	18	can	can	AUX
ejde-388	17	19	cause	cause	VERB
ejde-388	17	20	the	the	DET
ejde-388	17	21	amplification	amplification	NOUN
ejde-388	17	22	to	to	PART
ejde-388	17	23	be	be	AUX
ejde-388	17	24	super	super	ADV
ejde-388	17	25	fast	fast	ADJ
ejde-388	17	26	when	when	SCONJ
ejde-388	17	27	the	the	DET
ejde-388	17	28	reynolds	reynolds	PROPN
ejde-388	17	29	number	number	NOUN
ejde-388	17	30	is	be	AUX
ejde-388	17	31	large	large	ADJ
ejde-388	17	32	.	.	PUNCT
ejde-388	18	1	by	by	ADP
ejde-388	18	2	the	the	DET
ejde-388	18	3	time	time	NOUN
ejde-388	18	4	t	t	PROPN
ejde-388	18	5	∼	∼	NOUN
ejde-388	18	6	re	re	ADP
ejde-388	18	7	,	,	PUNCT
ejde-388	18	8	the	the	DET
ejde-388	18	9	two	two	NUM
ejde-388	18	10	terms	term	NOUN
ejde-388	18	11	in	in	ADP
ejde-388	18	12	the	the	DET
ejde-388	18	13	exponent	exponent	NOUN
ejde-388	18	14	are	be	AUX
ejde-388	18	15	about	about	ADV
ejde-388	18	16	equal	equal	ADJ
ejde-388	18	17	.	.	PUNCT
ejde-388	19	1	after	after	ADP
ejde-388	19	2	the	the	DET
ejde-388	19	3	time	time	NOUN
ejde-388	19	4	t	t	PROPN
ejde-388	19	5	∼	∼	NOUN
ejde-388	19	6	re	re	ADP
ejde-388	19	7	,	,	PUNCT
ejde-388	19	8	the	the	DET
ejde-388	19	9	second	second	ADJ
ejde-388	19	10	term	term	NOUN
ejde-388	19	11	dominates	dominate	VERB
ejde-388	19	12	,	,	PUNCT
ejde-388	19	13	and	and	CCONJ
ejde-388	19	14	this	this	DET
ejde-388	19	15	term	term	NOUN
ejde-388	19	16	is	be	AUX
ejde-388	19	17	the	the	DET
ejde-388	19	18	classical	classical	ADJ
ejde-388	19	19	liapunov	liapunov	NOUN
ejde-388	19	20	exponent	exponent	NOUN
ejde-388	19	21	that	that	PRON
ejde-388	19	22	causes	cause	VERB
ejde-388	19	23	chaos	chaos	NOUN
ejde-388	19	24	(	(	PUNCT
ejde-388	19	25	long	long	ADJ
ejde-388	19	26	term	term	NOUN
ejde-388	19	27	unpredictability	unpredictability	NOUN
ejde-388	19	28	)	)	PUNCT
ejde-388	19	29	.	.	PUNCT
ejde-388	20	1	thus	thus	ADV
ejde-388	20	2	the	the	DET
ejde-388	20	3	time	time	NOUN
ejde-388	20	4	t	t	NOUN
ejde-388	20	5	∼	∼	NOUN
ejde-388	20	6	re	re	NOUN
ejde-388	20	7	is	be	AUX
ejde-388	20	8	the	the	DET
ejde-388	20	9	temporal	temporal	ADJ
ejde-388	20	10	separation	separation	NOUN
ejde-388	20	11	point	point	NOUN
ejde-388	20	12	between	between	ADP
ejde-388	20	13	short	short	ADJ
ejde-388	20	14	term	term	NOUN
ejde-388	20	15	unpredictability	unpredictability	NOUN
ejde-388	20	16	and	and	CCONJ
ejde-388	20	17	long	long	ADJ
ejde-388	20	18	term	term	NOUN
ejde-388	20	19	unpredictability	unpredictability	NOUN
ejde-388	20	20	.	.	PUNCT
ejde-388	21	1	when	when	SCONJ
ejde-388	21	2	the	the	DET
ejde-388	21	3	reynolds	reynolds	PROPN
ejde-388	21	4	number	number	NOUN
ejde-388	21	5	is	be	AUX
ejde-388	21	6	large	large	ADJ
ejde-388	21	7	,	,	PUNCT
ejde-388	21	8	long	long	ADV
ejde-388	21	9	before	before	SCONJ
ejde-388	21	10	the	the	DET
ejde-388	21	11	separation	separation	NOUN
ejde-388	21	12	point	point	NOUN
ejde-388	21	13	t	t	PROPN
ejde-388	21	14	∼	∼	NOUN
ejde-388	21	15	re	re	NOUN
ejde-388	21	16	,	,	PUNCT
ejde-388	21	17	the	the	DET
ejde-388	21	18	first	first	ADJ
ejde-388	21	19	term	term	NOUN
ejde-388	21	20	in	in	ADP
ejde-388	21	21	the	the	DET
ejde-388	21	22	exponent	exponent	NOUN
ejde-388	21	23	already	already	ADV
ejde-388	21	24	amplifies	amplify	VERB
ejde-388	21	25	the	the	DET
ejde-388	21	26	perturbation	perturbation	NOUN
ejde-388	21	27	to	to	ADP
ejde-388	21	28	substantial	substantial	ADJ
ejde-388	21	29	size	size	NOUN
ejde-388	21	30	so	so	SCONJ
ejde-388	21	31	that	that	SCONJ
ejde-388	21	32	the	the	DET
ejde-388	21	33	nonlinear	nonlinear	ADJ
ejde-388	21	34	effect	effect	NOUN
ejde-388	21	35	takes	take	VERB
ejde-388	21	36	over	over	ADP
ejde-388	21	37	,	,	PUNCT
ejde-388	21	38	and	and	CCONJ
ejde-388	21	39	the	the	DET
ejde-388	21	40	second	second	ADJ
ejde-388	21	41	term	term	NOUN
ejde-388	21	42	does	do	AUX
ejde-388	21	43	not	not	PART
ejde-388	21	44	get	get	VERB
ejde-388	21	45	a	a	DET
ejde-388	21	46	chance	chance	NOUN
ejde-388	21	47	to	to	PART
ejde-388	21	48	dominate	dominate	VERB
ejde-388	21	49	.	.	PUNCT
ejde-388	22	1	thus	thus	ADV
ejde-388	22	2	fully	fully	ADV
ejde-388	22	3	developed	develop	VERB
ejde-388	22	4	turbulence	turbulence	NOUN
ejde-388	22	5	is	be	AUX
ejde-388	22	6	dominated	dominate	VERB
ejde-388	22	7	by	by	ADP
ejde-388	22	8	such	such	ADJ
ejde-388	22	9	short	short	ADJ
ejde-388	22	10	term	term	NOUN
ejde-388	22	11	unpredictability	unpredictability	NOUN
ejde-388	22	12	.	.	PUNCT
ejde-388	23	1	when	when	SCONJ
ejde-388	23	2	the	the	DET
ejde-388	23	3	reynolds	reynolds	PROPN
ejde-388	23	4	number	number	NOUN
ejde-388	23	5	is	be	AUX
ejde-388	23	6	moderate	moderate	ADJ
ejde-388	23	7	,	,	PUNCT
ejde-388	23	8	both	both	DET
ejde-388	23	9	2010	2010	NUM
ejde-388	23	10	mathematics	mathematic	NOUN
ejde-388	23	11	subject	subject	NOUN
ejde-388	23	12	classification	classification	NOUN
ejde-388	23	13	.	.	PUNCT
ejde-388	24	1	76f02	76f02	NUM
ejde-388	24	2	,	,	PUNCT
ejde-388	24	3	76f06	76f06	NUM
ejde-388	24	4	,	,	PUNCT
ejde-388	24	5	76f20	76f20	NOUN
ejde-388	24	6	,	,	PUNCT
ejde-388	24	7	76f05	76f05	NUM
ejde-388	24	8	,	,	PUNCT
ejde-388	24	9	76f30	76f30	NUM
ejde-388	24	10	.	.	PUNCT
ejde-388	25	1	key	key	ADJ
ejde-388	25	2	words	word	NOUN
ejde-388	25	3	and	and	CCONJ
ejde-388	25	4	phrases	phrase	NOUN
ejde-388	25	5	.	.	PUNCT
ejde-388	26	1	short	short	ADJ
ejde-388	26	2	term	term	NOUN
ejde-388	26	3	unpredictability	unpredictability	NOUN
ejde-388	26	4	;	;	PUNCT
ejde-388	26	5	rough	rough	ADJ
ejde-388	26	6	dependence	dependence	NOUN
ejde-388	26	7	on	on	ADP
ejde-388	26	8	initial	initial	ADJ
ejde-388	26	9	data	datum	NOUN
ejde-388	26	10	;	;	PUNCT
ejde-388	26	11	turbulence	turbulence	NOUN
ejde-388	26	12	;	;	PUNCT
ejde-388	26	13	chaos	chaos	NOUN
ejde-388	26	14	;	;	PUNCT
ejde-388	26	15	sensitive	sensitive	ADJ
ejde-388	26	16	dependence	dependence	NOUN
ejde-388	26	17	on	on	ADP
ejde-388	26	18	initial	initial	ADJ
ejde-388	26	19	data	datum	NOUN
ejde-388	26	20	.	.	PUNCT
ejde-388	27	1	c	c	X
ejde-388	27	2	©	©	PROPN
ejde-388	27	3	2020	2020	NUM
ejde-388	27	4	texas	texas	PROPN
ejde-388	27	5	state	state	PROPN
ejde-388	27	6	university	university	PROPN
ejde-388	27	7	.	.	PUNCT
ejde-388	28	1	submitted	submit	VERB
ejde-388	28	2	january	january	PROPN
ejde-388	28	3	5	5	NUM
ejde-388	28	4	,	,	PUNCT
ejde-388	28	5	2020	2020	NUM
ejde-388	28	6	.	.	PUNCT
ejde-388	29	1	published	publish	VERB
ejde-388	29	2	october	october	PROPN
ejde-388	29	3	12	12	NUM
ejde-388	29	4	,	,	PUNCT
ejde-388	29	5	2020	2020	NUM
ejde-388	29	6	.	.	PUNCT
ejde-388	30	1	1	1	NUM
ejde-388	30	2	2	2	NUM
ejde-388	30	3	z.	z.	X
ejde-388	30	4	feng	feng	PROPN
ejde-388	30	5	,	,	PUNCT
ejde-388	30	6	y.	y.	PROPN
ejde-388	30	7	c.	c.	PROPN
ejde-388	30	8	li	li	PROPN
ejde-388	31	1	ejde-2020/104	ejde-2020/104	PROPN
ejde-388	31	2	terms	term	NOUN
ejde-388	31	3	in	in	ADP
ejde-388	31	4	the	the	DET
ejde-388	31	5	exponent	exponent	NOUN
ejde-388	31	6	have	have	VERB
ejde-388	31	7	a	a	DET
ejde-388	31	8	chance	chance	NOUN
ejde-388	31	9	to	to	PART
ejde-388	31	10	dominate	dominate	VERB
ejde-388	31	11	,	,	PUNCT
ejde-388	31	12	and	and	CCONJ
ejde-388	31	13	the	the	DET
ejde-388	31	14	corresponding	corresponding	ADJ
ejde-388	31	15	(	(	PUNCT
ejde-388	31	16	often	often	ADV
ejde-388	31	17	)	)	PUNCT
ejde-388	31	18	transient	transient	ADJ
ejde-388	31	19	turbulence	turbulence	NOUN
ejde-388	31	20	is	be	AUX
ejde-388	31	21	dominated	dominate	VERB
ejde-388	31	22	by	by	ADP
ejde-388	31	23	chaos	chaos	NOUN
ejde-388	31	24	in	in	ADP
ejde-388	31	25	long	long	ADJ
ejde-388	31	26	term	term	NOUN
ejde-388	31	27	.	.	PUNCT
ejde-388	32	1	long	long	ADJ
ejde-388	32	2	term	term	NOUN
ejde-388	32	3	unpredictability	unpredictability	NOUN
ejde-388	32	4	has	have	AUX
ejde-388	32	5	been	be	AUX
ejde-388	32	6	well	well	ADV
ejde-388	32	7	understood	understand	VERB
ejde-388	32	8	.	.	PUNCT
ejde-388	33	1	the	the	DET
ejde-388	33	2	main	main	ADJ
ejde-388	33	3	feature	feature	NOUN
ejde-388	33	4	of	of	ADP
ejde-388	33	5	chaos	chaos	NOUN
ejde-388	33	6	is	be	AUX
ejde-388	33	7	long	long	ADJ
ejde-388	33	8	term	term	NOUN
ejde-388	33	9	unpredictability	unpredictability	NOUN
ejde-388	33	10	led	lead	VERB
ejde-388	33	11	by	by	ADP
ejde-388	33	12	sensitive	sensitive	ADJ
ejde-388	33	13	dependence	dependence	NOUN
ejde-388	33	14	on	on	ADP
ejde-388	33	15	initial	initial	ADJ
ejde-388	33	16	data	datum	NOUN
ejde-388	33	17	.	.	PUNCT
ejde-388	34	1	on	on	ADP
ejde-388	34	2	the	the	DET
ejde-388	34	3	other	other	ADJ
ejde-388	34	4	hand	hand	NOUN
ejde-388	34	5	,	,	PUNCT
ejde-388	34	6	short	short	ADJ
ejde-388	34	7	term	term	NOUN
ejde-388	34	8	unpredictability	unpredictability	NOUN
ejde-388	34	9	is	be	AUX
ejde-388	34	10	led	lead	VERB
ejde-388	34	11	by	by	ADP
ejde-388	34	12	rough	rough	ADJ
ejde-388	34	13	dependence	dependence	NOUN
ejde-388	34	14	on	on	ADP
ejde-388	34	15	initial	initial	ADJ
ejde-388	34	16	data	datum	NOUN
ejde-388	34	17	.	.	PUNCT
ejde-388	35	1	if	if	SCONJ
ejde-388	35	2	the	the	DET
ejde-388	35	3	solutions	solution	NOUN
ejde-388	35	4	are	be	AUX
ejde-388	35	5	non	non	ADJ
ejde-388	35	6	-	-	ADJ
ejde-388	35	7	differentiable	differentiable	ADJ
ejde-388	35	8	in	in	ADP
ejde-388	35	9	their	their	PRON
ejde-388	35	10	initial	initial	ADJ
ejde-388	35	11	data	datum	NOUN
ejde-388	35	12	,	,	PUNCT
ejde-388	35	13	as	as	SCONJ
ejde-388	35	14	in	in	ADP
ejde-388	35	15	the	the	DET
ejde-388	35	16	case	case	NOUN
ejde-388	35	17	of	of	ADP
ejde-388	35	18	euler	euler	NOUN
ejde-388	35	19	equations	equation	NOUN
ejde-388	35	20	of	of	ADP
ejde-388	35	21	fluids	fluid	NOUN
ejde-388	35	22	[	[	X
ejde-388	35	23	3	3	NUM
ejde-388	35	24	]	]	PUNCT
ejde-388	35	25	,	,	PUNCT
ejde-388	35	26	then	then	ADV
ejde-388	35	27	any	any	DET
ejde-388	35	28	small	small	ADJ
ejde-388	35	29	initial	initial	ADJ
ejde-388	35	30	perturbation	perturbation	NOUN
ejde-388	35	31	will	will	AUX
ejde-388	35	32	be	be	AUX
ejde-388	35	33	amplified	amplify	VERB
ejde-388	35	34	to	to	PART
ejde-388	35	35	order	order	VERB
ejde-388	35	36	o(1	o(1	NOUN
ejde-388	35	37	)	)	PUNCT
ejde-388	35	38	instantly	instantly	ADV
ejde-388	35	39	.	.	PUNCT
ejde-388	36	1	such	such	DET
ejde-388	36	2	a	a	DET
ejde-388	36	3	short	short	ADJ
ejde-388	36	4	term	term	NOUN
ejde-388	36	5	unpredictability	unpredictability	NOUN
ejde-388	36	6	is	be	AUX
ejde-388	36	7	very	very	ADV
ejde-388	36	8	different	different	ADJ
ejde-388	36	9	from	from	ADP
ejde-388	36	10	the	the	DET
ejde-388	36	11	long	long	ADJ
ejde-388	36	12	term	term	NOUN
ejde-388	36	13	unpredictability	unpredictability	NOUN
ejde-388	36	14	of	of	ADP
ejde-388	36	15	chaos	chaos	NOUN
ejde-388	36	16	.	.	PUNCT
ejde-388	37	1	such	such	DET
ejde-388	37	2	a	a	DET
ejde-388	37	3	short	short	ADJ
ejde-388	37	4	term	term	NOUN
ejde-388	37	5	unpredictability	unpredictability	NOUN
ejde-388	37	6	is	be	AUX
ejde-388	37	7	closer	close	ADJ
ejde-388	37	8	to	to	PART
ejde-388	37	9	total	total	VERB
ejde-388	37	10	randomness	randomness	NOUN
ejde-388	37	11	than	than	ADP
ejde-388	37	12	the	the	DET
ejde-388	37	13	long	long	ADJ
ejde-388	37	14	term	term	NOUN
ejde-388	37	15	unpredictability	unpredictability	NOUN
ejde-388	37	16	of	of	ADP
ejde-388	37	17	chaos	chaos	NOUN
ejde-388	37	18	.	.	PUNCT
ejde-388	38	1	nevertheless	nevertheless	ADV
ejde-388	38	2	,	,	PUNCT
ejde-388	38	3	such	such	DET
ejde-388	38	4	a	a	DET
ejde-388	38	5	short	short	ADJ
ejde-388	38	6	term	term	NOUN
ejde-388	38	7	unpredictability	unpredictability	NOUN
ejde-388	38	8	is	be	AUX
ejde-388	38	9	still	still	ADV
ejde-388	38	10	not	not	PART
ejde-388	38	11	total	total	ADJ
ejde-388	38	12	randomness	randomness	NOUN
ejde-388	38	13	,	,	PUNCT
ejde-388	38	14	for	for	ADP
ejde-388	38	15	instance	instance	NOUN
ejde-388	38	16	the	the	DET
ejde-388	38	17	solutions	solution	NOUN
ejde-388	38	18	of	of	ADP
ejde-388	38	19	euler	euler	NOUN
ejde-388	38	20	equations	equation	NOUN
ejde-388	38	21	of	of	ADP
ejde-388	38	22	fluids	fluid	NOUN
ejde-388	38	23	are	be	AUX
ejde-388	38	24	still	still	ADV
ejde-388	38	25	continuous	continuous	ADJ
ejde-388	38	26	in	in	ADP
ejde-388	38	27	their	their	PRON
ejde-388	38	28	initial	initial	ADJ
ejde-388	38	29	data	datum	NOUN
ejde-388	38	30	,	,	PUNCT
ejde-388	38	31	and	and	CCONJ
ejde-388	38	32	the	the	DET
ejde-388	38	33	conserved	conserve	VERB
ejde-388	38	34	quantities	quantity	NOUN
ejde-388	38	35	do	do	AUX
ejde-388	38	36	not	not	PART
ejde-388	38	37	vary	vary	VERB
ejde-388	38	38	too	too	ADV
ejde-388	38	39	much	much	ADV
ejde-388	38	40	under	under	ADP
ejde-388	38	41	perturbations	perturbation	NOUN
ejde-388	38	42	.	.	PUNCT
ejde-388	39	1	such	such	DET
ejde-388	39	2	a	a	DET
ejde-388	39	3	short	short	ADJ
ejde-388	39	4	term	term	NOUN
ejde-388	39	5	unpredictability	unpredictability	NOUN
ejde-388	39	6	leads	lead	VERB
ejde-388	39	7	to	to	ADP
ejde-388	39	8	a	a	DET
ejde-388	39	9	peculiar	peculiar	ADJ
ejde-388	39	10	process	process	NOUN
ejde-388	39	11	that	that	PRON
ejde-388	39	12	is	be	AUX
ejde-388	39	13	very	very	ADV
ejde-388	39	14	close	close	ADJ
ejde-388	39	15	to	to	ADP
ejde-388	39	16	a	a	DET
ejde-388	39	17	random	random	ADJ
ejde-388	39	18	process	process	NOUN
ejde-388	39	19	but	but	CCONJ
ejde-388	39	20	still	still	ADV
ejde-388	39	21	constrained	constrain	VERB
ejde-388	39	22	.	.	PUNCT
ejde-388	40	1	when	when	SCONJ
ejde-388	40	2	the	the	DET
ejde-388	40	3	reynolds	reynolds	PROPN
ejde-388	40	4	number	number	NOUN
ejde-388	40	5	is	be	AUX
ejde-388	40	6	moderate	moderate	ADJ
ejde-388	40	7	,	,	PUNCT
ejde-388	40	8	dynamics	dynamic	NOUN
ejde-388	40	9	of	of	ADP
ejde-388	40	10	navierstokes	navierstoke	NOUN
ejde-388	40	11	equations	equation	NOUN
ejde-388	40	12	is	be	AUX
ejde-388	40	13	quite	quite	ADV
ejde-388	40	14	far	far	ADV
ejde-388	40	15	away	away	ADV
ejde-388	40	16	from	from	ADP
ejde-388	40	17	that	that	PRON
ejde-388	40	18	of	of	ADP
ejde-388	40	19	euler	euler	NOUN
ejde-388	40	20	equations	equation	NOUN
ejde-388	40	21	.	.	PUNCT
ejde-388	41	1	turbulence	turbulence	NOUN
ejde-388	41	2	at	at	ADP
ejde-388	41	3	such	such	DET
ejde-388	41	4	a	a	DET
ejde-388	41	5	stage	stage	NOUN
ejde-388	41	6	is	be	AUX
ejde-388	41	7	often	often	ADV
ejde-388	41	8	transient	transient	ADJ
ejde-388	41	9	,	,	PUNCT
ejde-388	41	10	and	and	CCONJ
ejde-388	41	11	bears	bear	VERB
ejde-388	41	12	clear	clear	ADJ
ejde-388	41	13	resemblance	resemblance	NOUN
ejde-388	41	14	to	to	PART
ejde-388	41	15	finite	finite	VERB
ejde-388	41	16	dimensional	dimensional	ADJ
ejde-388	41	17	chaos	chaos	NOUN
ejde-388	41	18	[	[	X
ejde-388	41	19	1	1	NUM
ejde-388	41	20	,	,	PUNCT
ejde-388	41	21	2	2	NUM
ejde-388	41	22	,	,	PUNCT
ejde-388	41	23	6	6	NUM
ejde-388	41	24	,	,	PUNCT
ejde-388	41	25	7	7	NUM
ejde-388	41	26	,	,	PUNCT
ejde-388	41	27	8	8	NUM
ejde-388	41	28	,	,	PUNCT
ejde-388	41	29	16	16	NUM
ejde-388	41	30	,	,	PUNCT
ejde-388	41	31	17	17	NUM
ejde-388	41	32	,	,	PUNCT
ejde-388	41	33	18	18	NUM
ejde-388	41	34	]	]	PUNCT
ejde-388	41	35	.	.	PUNCT
ejde-388	42	1	one	one	PRON
ejde-388	42	2	can	can	AUX
ejde-388	42	3	name	name	VERB
ejde-388	42	4	such	such	ADJ
ejde-388	42	5	turbulence	turbulence	NOUN
ejde-388	42	6	as	as	ADP
ejde-388	42	7	chaos	chaos	NOUN
ejde-388	42	8	in	in	ADP
ejde-388	42	9	navier	navier	NOUN
ejde-388	42	10	-	-	PUNCT
ejde-388	42	11	stokes	stoke	NOUN
ejde-388	42	12	equations	equation	NOUN
ejde-388	42	13	.	.	PUNCT
ejde-388	43	1	such	such	ADJ
ejde-388	43	2	turbulent	turbulent	ADJ
ejde-388	43	3	solutions	solution	NOUN
ejde-388	43	4	are	be	AUX
ejde-388	43	5	differentiable	differentiable	ADJ
ejde-388	43	6	in	in	ADP
ejde-388	43	7	their	their	PRON
ejde-388	43	8	initial	initial	ADJ
ejde-388	43	9	data	datum	NOUN
ejde-388	43	10	(	(	PUNCT
ejde-388	43	11	at	at	ADP
ejde-388	43	12	least	least	ADJ
ejde-388	43	13	during	during	ADP
ejde-388	43	14	the	the	DET
ejde-388	43	15	known	know	VERB
ejde-388	43	16	time	time	NOUN
ejde-388	43	17	interval	interval	NOUN
ejde-388	43	18	of	of	ADP
ejde-388	43	19	existence	existence	NOUN
ejde-388	43	20	)	)	PUNCT
ejde-388	43	21	,	,	PUNCT
ejde-388	43	22	and	and	CCONJ
ejde-388	43	23	the	the	DET
ejde-388	43	24	derivatives	derivative	NOUN
ejde-388	43	25	of	of	ADP
ejde-388	43	26	the	the	DET
ejde-388	43	27	solutions	solution	NOUN
ejde-388	43	28	in	in	ADP
ejde-388	43	29	initial	initial	ADJ
ejde-388	43	30	data	datum	NOUN
ejde-388	43	31	have	have	VERB
ejde-388	43	32	moderate	moderate	ADJ
ejde-388	43	33	norms	norm	NOUN
ejde-388	43	34	.	.	PUNCT
ejde-388	44	1	when	when	SCONJ
ejde-388	44	2	the	the	DET
ejde-388	44	3	reynolds	reynolds	PROPN
ejde-388	44	4	number	number	NOUN
ejde-388	44	5	is	be	AUX
ejde-388	44	6	very	very	ADV
ejde-388	44	7	high	high	ADJ
ejde-388	44	8	,	,	PUNCT
ejde-388	44	9	dynamics	dynamic	NOUN
ejde-388	44	10	of	of	ADP
ejde-388	44	11	navier	navier	NOUN
ejde-388	44	12	-	-	PUNCT
ejde-388	44	13	stokes	stoke	NOUN
ejde-388	44	14	equations	equation	NOUN
ejde-388	44	15	is	be	AUX
ejde-388	44	16	getting	get	VERB
ejde-388	44	17	closer	close	ADJ
ejde-388	44	18	to	to	ADP
ejde-388	44	19	that	that	PRON
ejde-388	44	20	of	of	ADP
ejde-388	44	21	euler	euler	PROPN
ejde-388	44	22	equations	equation	NOUN
ejde-388	44	23	.	.	PUNCT
ejde-388	45	1	high	high	ADJ
ejde-388	45	2	reynolds	reynolds	PROPN
ejde-388	45	3	number	number	NOUN
ejde-388	45	4	turbulence	turbulence	NOUN
ejde-388	45	5	is	be	AUX
ejde-388	45	6	fully	fully	ADV
ejde-388	45	7	developed	develop	VERB
ejde-388	45	8	,	,	PUNCT
ejde-388	45	9	and	and	CCONJ
ejde-388	45	10	has	have	VERB
ejde-388	45	11	no	no	DET
ejde-388	45	12	resemblance	resemblance	NOUN
ejde-388	45	13	to	to	PART
ejde-388	45	14	finite	finite	VERB
ejde-388	45	15	dimensional	dimensional	ADJ
ejde-388	45	16	chaos	chaos	NOUN
ejde-388	45	17	.	.	PUNCT
ejde-388	46	1	such	such	ADJ
ejde-388	46	2	turbulent	turbulent	ADJ
ejde-388	46	3	solutions	solution	NOUN
ejde-388	46	4	are	be	AUX
ejde-388	46	5	still	still	ADV
ejde-388	46	6	differentiable	differentiable	ADJ
ejde-388	46	7	in	in	ADP
ejde-388	46	8	their	their	PRON
ejde-388	46	9	initial	initial	ADJ
ejde-388	46	10	data	datum	NOUN
ejde-388	46	11	(	(	PUNCT
ejde-388	46	12	at	at	ADP
ejde-388	46	13	least	least	ADJ
ejde-388	46	14	during	during	ADP
ejde-388	46	15	the	the	DET
ejde-388	46	16	known	know	VERB
ejde-388	46	17	time	time	NOUN
ejde-388	46	18	interval	interval	NOUN
ejde-388	46	19	of	of	ADP
ejde-388	46	20	existence	existence	NOUN
ejde-388	46	21	)	)	PUNCT
ejde-388	46	22	,	,	PUNCT
ejde-388	46	23	but	but	CCONJ
ejde-388	46	24	the	the	DET
ejde-388	46	25	derivatives	derivative	NOUN
ejde-388	46	26	of	of	ADP
ejde-388	46	27	the	the	DET
ejde-388	46	28	solutions	solution	NOUN
ejde-388	46	29	in	in	ADP
ejde-388	46	30	initial	initial	ADJ
ejde-388	46	31	data	datum	NOUN
ejde-388	46	32	have	have	VERB
ejde-388	46	33	huge	huge	ADJ
ejde-388	46	34	norms	norm	NOUN
ejde-388	46	35	in	in	ADP
ejde-388	46	36	the	the	DET
ejde-388	46	37	order	order	NOUN
ejde-388	46	38	of	of	ADP
ejde-388	46	39	exp(σ	exp(σ	X
ejde-388	46	40	√	√	NUM
ejde-388	46	41	re	re	ADP
ejde-388	46	42	√	√	PROPN
ejde-388	46	43	t	t	PROPN
ejde-388	47	1	+	+	CCONJ
ejde-388	47	2	σ1	σ1	PROPN
ejde-388	47	3	t	t	PROPN
ejde-388	47	4	)	)	PUNCT
ejde-388	47	5	mentioned	mention	VERB
ejde-388	47	6	above	above	ADP
ejde-388	47	7	which	which	PRON
ejde-388	47	8	represent	represent	VERB
ejde-388	47	9	the	the	DET
ejde-388	47	10	growth	growth	NOUN
ejde-388	47	11	rate	rate	NOUN
ejde-388	47	12	of	of	ADP
ejde-388	47	13	the	the	DET
ejde-388	47	14	perturbations	perturbation	NOUN
ejde-388	47	15	.	.	PUNCT
ejde-388	48	1	thus	thus	ADV
ejde-388	48	2	initial	initial	ADJ
ejde-388	48	3	perturbations	perturbation	NOUN
ejde-388	48	4	are	be	AUX
ejde-388	48	5	amplified	amplify	VERB
ejde-388	48	6	super	super	ADV
ejde-388	48	7	fast	fast	ADV
ejde-388	48	8	even	even	ADV
ejde-388	48	9	in	in	ADP
ejde-388	48	10	short	short	ADJ
ejde-388	48	11	time	time	NOUN
ejde-388	48	12	.	.	PUNCT
ejde-388	49	1	we	we	PRON
ejde-388	49	2	believe	believe	VERB
ejde-388	49	3	that	that	SCONJ
ejde-388	49	4	this	this	PRON
ejde-388	49	5	causes	cause	VERB
ejde-388	49	6	the	the	DET
ejde-388	49	7	abrupt	abrupt	ADJ
ejde-388	49	8	nature	nature	NOUN
ejde-388	49	9	in	in	ADP
ejde-388	49	10	the	the	DET
ejde-388	49	11	development	development	NOUN
ejde-388	49	12	of	of	ADP
ejde-388	49	13	high	high	ADJ
ejde-388	49	14	reynolds	reynold	NOUN
ejde-388	49	15	number	number	NOUN
ejde-388	49	16	turbulence	turbulence	NOUN
ejde-388	49	17	.	.	PUNCT
ejde-388	50	1	since	since	SCONJ
ejde-388	50	2	perturbations	perturbation	NOUN
ejde-388	50	3	constantly	constantly	ADV
ejde-388	50	4	exist	exist	VERB
ejde-388	50	5	,	,	PUNCT
ejde-388	50	6	there	there	PRON
ejde-388	50	7	are	be	VERB
ejde-388	50	8	constantly	constantly	ADV
ejde-388	50	9	such	such	ADJ
ejde-388	50	10	super	super	ADJ
ejde-388	50	11	fast	fast	ADJ
ejde-388	50	12	amplifications	amplification	NOUN
ejde-388	50	13	of	of	ADP
ejde-388	50	14	perturbations	perturbation	NOUN
ejde-388	50	15	which	which	PRON
ejde-388	50	16	lead	lead	VERB
ejde-388	50	17	to	to	ADP
ejde-388	50	18	the	the	DET
ejde-388	50	19	persistence	persistence	NOUN
ejde-388	50	20	nature	nature	NOUN
ejde-388	50	21	of	of	ADP
ejde-388	50	22	high	high	ADJ
ejde-388	50	23	reynolds	reynold	NOUN
ejde-388	50	24	number	number	NOUN
ejde-388	50	25	turbulence	turbulence	NOUN
ejde-388	50	26	(	(	PUNCT
ejde-388	50	27	so	so	ADV
ejde-388	50	28	-	-	PUNCT
ejde-388	50	29	called	call	VERB
ejde-388	50	30	fully	fully	ADV
ejde-388	50	31	developed	develop	VERB
ejde-388	50	32	turbulence	turbulence	NOUN
ejde-388	50	33	)	)	PUNCT
ejde-388	50	34	in	in	ADP
ejde-388	50	35	contrast	contrast	NOUN
ejde-388	50	36	to	to	ADP
ejde-388	50	37	the	the	DET
ejde-388	50	38	transient	transient	ADJ
ejde-388	50	39	nature	nature	NOUN
ejde-388	50	40	of	of	ADP
ejde-388	50	41	moderate	moderate	ADJ
ejde-388	50	42	reynolds	reynold	NOUN
ejde-388	50	43	number	number	NOUN
ejde-388	50	44	turbulence	turbulence	NOUN
ejde-388	50	45	.	.	PUNCT
ejde-388	51	1	in	in	ADP
ejde-388	51	2	terms	term	NOUN
ejde-388	51	3	of	of	ADP
ejde-388	51	4	phase	phase	NOUN
ejde-388	51	5	space	space	NOUN
ejde-388	51	6	dynamics	dynamic	NOUN
ejde-388	51	7	of	of	ADP
ejde-388	51	8	dynamical	dynamical	ADJ
ejde-388	51	9	systems	system	NOUN
ejde-388	51	10	,	,	PUNCT
ejde-388	51	11	when	when	SCONJ
ejde-388	51	12	the	the	DET
ejde-388	51	13	reynolds	reynolds	PROPN
ejde-388	51	14	number	number	NOUN
ejde-388	51	15	is	be	AUX
ejde-388	51	16	very	very	ADV
ejde-388	51	17	high	high	ADJ
ejde-388	51	18	,	,	PUNCT
ejde-388	51	19	fully	fully	ADV
ejde-388	51	20	developed	develop	VERB
ejde-388	51	21	turbulence	turbulence	NOUN
ejde-388	51	22	is	be	AUX
ejde-388	51	23	not	not	PART
ejde-388	51	24	the	the	DET
ejde-388	51	25	result	result	NOUN
ejde-388	51	26	of	of	ADP
ejde-388	51	27	a	a	DET
ejde-388	51	28	strange	strange	ADJ
ejde-388	51	29	attractor	attractor	NOUN
ejde-388	51	30	,	,	PUNCT
ejde-388	51	31	rather	rather	ADV
ejde-388	51	32	a	a	DET
ejde-388	51	33	result	result	NOUN
ejde-388	51	34	of	of	ADP
ejde-388	51	35	super	super	ADJ
ejde-388	51	36	fast	fast	ADJ
ejde-388	51	37	amplifications	amplification	NOUN
ejde-388	51	38	of	of	ADP
ejde-388	51	39	ever	ever	ADV
ejde-388	51	40	present	present	ADJ
ejde-388	51	41	perturbations	perturbation	NOUN
ejde-388	51	42	.	.	PUNCT
ejde-388	52	1	strange	strange	ADJ
ejde-388	52	2	attractor	attractor	NOUN
ejde-388	52	3	is	be	AUX
ejde-388	52	4	a	a	DET
ejde-388	52	5	long	long	ADJ
ejde-388	52	6	time	time	NOUN
ejde-388	52	7	object	object	NOUN
ejde-388	52	8	,	,	PUNCT
ejde-388	52	9	while	while	SCONJ
ejde-388	52	10	the	the	DET
ejde-388	52	11	development	development	NOUN
ejde-388	52	12	of	of	ADP
ejde-388	52	13	such	such	ADJ
ejde-388	52	14	violent	violent	ADJ
ejde-388	52	15	turbulence	turbulence	NOUN
ejde-388	52	16	is	be	AUX
ejde-388	52	17	of	of	ADP
ejde-388	52	18	short	short	ADJ
ejde-388	52	19	time	time	NOUN
ejde-388	52	20	.	.	PUNCT
ejde-388	53	1	such	such	ADJ
ejde-388	53	2	fully	fully	ADV
ejde-388	53	3	developed	develop	VERB
ejde-388	53	4	turbulence	turbulence	NOUN
ejde-388	53	5	is	be	AUX
ejde-388	53	6	maintained	maintain	VERB
ejde-388	53	7	by	by	ADP
ejde-388	53	8	constantly	constantly	ADV
ejde-388	53	9	super	super	ADV
ejde-388	53	10	fast	fast	ADJ
ejde-388	53	11	perturbation	perturbation	NOUN
ejde-388	53	12	amplifications	amplification	NOUN
ejde-388	53	13	.	.	PUNCT
ejde-388	54	1	when	when	SCONJ
ejde-388	54	2	the	the	DET
ejde-388	54	3	reynolds	reynolds	PROPN
ejde-388	54	4	number	number	NOUN
ejde-388	54	5	is	be	AUX
ejde-388	54	6	set	set	VERB
ejde-388	54	7	to	to	ADP
ejde-388	54	8	infinity	infinity	NOUN
ejde-388	54	9	,	,	PUNCT
ejde-388	54	10	the	the	DET
ejde-388	54	11	perturbation	perturbation	NOUN
ejde-388	54	12	amplification	amplification	NOUN
ejde-388	54	13	rate	rate	NOUN
ejde-388	54	14	is	be	AUX
ejde-388	54	15	infinity	infinity	NOUN
ejde-388	54	16	.	.	PUNCT
ejde-388	55	1	so	so	ADV
ejde-388	55	2	the	the	DET
ejde-388	55	3	dynamics	dynamic	NOUN
ejde-388	55	4	of	of	ADP
ejde-388	55	5	euler	euler	NOUN
ejde-388	55	6	equations	equation	NOUN
ejde-388	55	7	is	be	AUX
ejde-388	55	8	very	very	ADV
ejde-388	55	9	close	close	ADJ
ejde-388	55	10	to	to	ADP
ejde-388	55	11	a	a	DET
ejde-388	55	12	random	random	ADJ
ejde-388	55	13	process	process	NOUN
ejde-388	55	14	.	.	PUNCT
ejde-388	56	1	in	in	ADP
ejde-388	56	2	contrast	contrast	NOUN
ejde-388	56	3	,	,	PUNCT
ejde-388	56	4	chaos	chaos	NOUN
ejde-388	56	5	in	in	ADP
ejde-388	56	6	finite	finite	ADJ
ejde-388	56	7	dimensional	dimensional	ADJ
ejde-388	56	8	conservative	conservative	ADJ
ejde-388	56	9	systems	system	NOUN
ejde-388	56	10	often	often	ADV
ejde-388	56	11	manifests	manifest	VERB
ejde-388	56	12	itself	itself	PRON
ejde-388	56	13	as	as	ADP
ejde-388	56	14	the	the	DET
ejde-388	56	15	so	so	ADV
ejde-388	56	16	-	-	PUNCT
ejde-388	56	17	called	call	VERB
ejde-388	56	18	stochastic	stochastic	ADJ
ejde-388	56	19	layers	layer	NOUN
ejde-388	56	20	.	.	PUNCT
ejde-388	57	1	dynamics	dynamic	NOUN
ejde-388	57	2	inside	inside	ADP
ejde-388	57	3	the	the	DET
ejde-388	57	4	stochastic	stochastic	ADJ
ejde-388	57	5	layers	layer	NOUN
ejde-388	57	6	has	have	VERB
ejde-388	57	7	the	the	DET
ejde-388	57	8	long	long	ADJ
ejde-388	57	9	term	term	NOUN
ejde-388	57	10	sensitive	sensitive	ADJ
ejde-388	57	11	dependence	dependence	NOUN
ejde-388	57	12	on	on	ADP
ejde-388	57	13	initial	initial	ADJ
ejde-388	57	14	data	datum	NOUN
ejde-388	57	15	.	.	PUNCT
ejde-388	58	1	when	when	SCONJ
ejde-388	58	2	the	the	DET
ejde-388	58	3	reynolds	reynolds	PROPN
ejde-388	58	4	number	number	NOUN
ejde-388	58	5	is	be	AUX
ejde-388	58	6	moderate	moderate	ADJ
ejde-388	58	7	,	,	PUNCT
ejde-388	58	8	viscous	viscous	ADJ
ejde-388	58	9	diffusive	diffusive	ADJ
ejde-388	58	10	term	term	NOUN
ejde-388	58	11	in	in	ADP
ejde-388	58	12	navier	navier	NOUN
ejde-388	58	13	-	-	PUNCT
ejde-388	58	14	stokes	stoke	NOUN
ejde-388	58	15	equations	equation	NOUN
ejde-388	58	16	is	be	AUX
ejde-388	58	17	stronger	strong	ADJ
ejde-388	58	18	,	,	PUNCT
ejde-388	58	19	perturbation	perturbation	NOUN
ejde-388	58	20	amplification	amplification	NOUN
ejde-388	58	21	rate	rate	NOUN
ejde-388	58	22	is	be	AUX
ejde-388	58	23	moderate	moderate	ADJ
ejde-388	58	24	.	.	PUNCT
ejde-388	59	1	at	at	ADP
ejde-388	59	2	this	this	DET
ejde-388	59	3	stage	stage	NOUN
ejde-388	59	4	,	,	PUNCT
ejde-388	59	5	turbulence	turbulence	NOUN
ejde-388	59	6	is	be	AUX
ejde-388	59	7	basically	basically	ADV
ejde-388	59	8	chaos	chaos	NOUN
ejde-388	59	9	in	in	ADP
ejde-388	59	10	navier	navier	NOUN
ejde-388	59	11	-	-	PUNCT
ejde-388	59	12	stokes	stoke	NOUN
ejde-388	59	13	equations	equation	NOUN
ejde-388	60	1	[	[	X
ejde-388	60	2	1	1	NUM
ejde-388	60	3	,	,	PUNCT
ejde-388	60	4	2	2	NUM
ejde-388	60	5	,	,	PUNCT
ejde-388	60	6	6	6	NUM
ejde-388	60	7	,	,	PUNCT
ejde-388	60	8	7	7	NUM
ejde-388	60	9	,	,	PUNCT
ejde-388	60	10	8	8	NUM
ejde-388	60	11	,	,	PUNCT
ejde-388	60	12	16	16	NUM
ejde-388	60	13	,	,	PUNCT
ejde-388	60	14	17	17	NUM
ejde-388	60	15	,	,	PUNCT
ejde-388	60	16	18	18	NUM
ejde-388	60	17	]	]	PUNCT
ejde-388	60	18	.	.	PUNCT
ejde-388	61	1	in	in	ADP
ejde-388	61	2	some	some	DET
ejde-388	61	3	cases	case	NOUN
ejde-388	61	4	,	,	PUNCT
ejde-388	61	5	strange	strange	ADJ
ejde-388	61	6	attractor	attractor	NOUN
ejde-388	61	7	can	can	AUX
ejde-388	61	8	be	be	AUX
ejde-388	61	9	observed	observe	VERB
ejde-388	61	10	[	[	X
ejde-388	61	11	17	17	NUM
ejde-388	61	12	]	]	PUNCT
ejde-388	61	13	.	.	PUNCT
ejde-388	62	1	ejde-2020/104	ejde-2020/104	PROPN
ejde-388	62	2	short	short	ADJ
ejde-388	62	3	term	term	NOUN
ejde-388	62	4	unpredictability	unpredictability	NOUN
ejde-388	62	5	3	3	NUM
ejde-388	62	6	the	the	DET
ejde-388	62	7	article	article	NOUN
ejde-388	62	8	is	be	AUX
ejde-388	62	9	organized	organize	VERB
ejde-388	62	10	as	as	SCONJ
ejde-388	62	11	follows	follow	VERB
ejde-388	62	12	:	:	PUNCT
ejde-388	62	13	in	in	ADP
ejde-388	62	14	section	section	NOUN
ejde-388	62	15	2	2	NUM
ejde-388	62	16	,	,	PUNCT
ejde-388	62	17	we	we	PRON
ejde-388	62	18	briefly	briefly	ADV
ejde-388	62	19	review	review	VERB
ejde-388	62	20	liapunov	liapunov	NOUN
ejde-388	62	21	exponent	exponent	NOUN
ejde-388	62	22	and	and	CCONJ
ejde-388	62	23	chaos	chaos	NOUN
ejde-388	62	24	.	.	PUNCT
ejde-388	63	1	in	in	ADP
ejde-388	63	2	section	section	NOUN
ejde-388	63	3	3	3	NUM
ejde-388	63	4	,	,	PUNCT
ejde-388	63	5	we	we	PRON
ejde-388	63	6	briefly	briefly	ADV
ejde-388	63	7	review	review	VERB
ejde-388	63	8	analytical	analytical	ADJ
ejde-388	63	9	results	result	NOUN
ejde-388	63	10	on	on	ADP
ejde-388	63	11	rough	rough	ADJ
ejde-388	63	12	dependence	dependence	NOUN
ejde-388	63	13	.	.	PUNCT
ejde-388	64	1	in	in	ADP
ejde-388	64	2	section	section	NOUN
ejde-388	64	3	4	4	NUM
ejde-388	64	4	,	,	PUNCT
ejde-388	64	5	we	we	PRON
ejde-388	64	6	are	be	AUX
ejde-388	64	7	going	go	VERB
ejde-388	64	8	to	to	PART
ejde-388	64	9	shed	shed	VERB
ejde-388	64	10	new	new	ADJ
ejde-388	64	11	light	light	NOUN
ejde-388	64	12	on	on	ADP
ejde-388	64	13	the	the	DET
ejde-388	64	14	classical	classical	ADJ
ejde-388	64	15	hydrodynamic	hydrodynamic	ADJ
ejde-388	64	16	instability	instability	NOUN
ejde-388	64	17	theory	theory	NOUN
ejde-388	64	18	from	from	ADP
ejde-388	64	19	a	a	DET
ejde-388	64	20	new	new	ADJ
ejde-388	64	21	perspective	perspective	NOUN
ejde-388	64	22	.	.	PUNCT
ejde-388	65	1	in	in	ADP
ejde-388	65	2	section	section	NOUN
ejde-388	65	3	5	5	NUM
ejde-388	65	4	,	,	PUNCT
ejde-388	65	5	2d	2d	NUM
ejde-388	65	6	numerical	numerical	ADJ
ejde-388	65	7	demonstration	demonstration	NOUN
ejde-388	65	8	on	on	ADP
ejde-388	65	9	rough	rough	ADJ
ejde-388	65	10	dependence	dependence	NOUN
ejde-388	65	11	is	be	AUX
ejde-388	65	12	presented	present	VERB
ejde-388	65	13	.	.	PUNCT
ejde-388	66	1	in	in	ADP
ejde-388	66	2	section	section	NOUN
ejde-388	66	3	6	6	NUM
ejde-388	66	4	,	,	PUNCT
ejde-388	66	5	3d	3d	PROPN
ejde-388	66	6	numerical	numerical	ADJ
ejde-388	66	7	demonstration	demonstration	NOUN
ejde-388	66	8	on	on	ADP
ejde-388	66	9	rough	rough	ADJ
ejde-388	66	10	dependence	dependence	NOUN
ejde-388	66	11	is	be	AUX
ejde-388	66	12	presented	present	VERB
ejde-388	66	13	.	.	PUNCT
ejde-388	67	1	2	2	X
ejde-388	67	2	.	.	X
ejde-388	67	3	chaos	chaos	NOUN
ejde-388	67	4	–	–	PUNCT
ejde-388	67	5	sensitive	sensitive	ADJ
ejde-388	67	6	dependence	dependence	NOUN
ejde-388	67	7	on	on	ADP
ejde-388	67	8	initial	initial	ADJ
ejde-388	67	9	data	datum	NOUN
ejde-388	67	10	there	there	PRON
ejde-388	67	11	are	be	VERB
ejde-388	67	12	many	many	ADJ
ejde-388	67	13	ways	way	NOUN
ejde-388	67	14	to	to	PART
ejde-388	67	15	characterize	characterize	VERB
ejde-388	67	16	chaos	chaos	NOUN
ejde-388	67	17	,	,	PUNCT
ejde-388	67	18	and	and	CCONJ
ejde-388	67	19	one	one	NUM
ejde-388	67	20	necessary	necessary	ADJ
ejde-388	67	21	ingredient	ingredient	NOUN
ejde-388	67	22	of	of	ADP
ejde-388	67	23	every	every	DET
ejde-388	67	24	characterization	characterization	NOUN
ejde-388	67	25	is	be	AUX
ejde-388	67	26	“	"	PUNCT
ejde-388	67	27	sensitive	sensitive	ADJ
ejde-388	67	28	dependence	dependence	NOUN
ejde-388	67	29	on	on	ADP
ejde-388	67	30	initial	initial	ADJ
ejde-388	67	31	data	datum	NOUN
ejde-388	67	32	”	"	PUNCT
ejde-388	67	33	.	.	PUNCT
ejde-388	68	1	for	for	ADP
ejde-388	68	2	solutions	solution	NOUN
ejde-388	68	3	that	that	PRON
ejde-388	68	4	exhibit	exhibit	VERB
ejde-388	68	5	sensitive	sensitive	ADJ
ejde-388	68	6	dependence	dependence	NOUN
ejde-388	68	7	on	on	ADP
ejde-388	68	8	initial	initial	ADJ
ejde-388	68	9	data	datum	NOUN
ejde-388	68	10	,	,	PUNCT
ejde-388	68	11	their	their	PRON
ejde-388	68	12	initial	initial	ADJ
ejde-388	68	13	small	small	ADJ
ejde-388	68	14	perturbations	perturbation	NOUN
ejde-388	68	15	are	be	AUX
ejde-388	68	16	usually	usually	ADV
ejde-388	68	17	amplified	amplify	VERB
ejde-388	68	18	exponentially	exponentially	ADV
ejde-388	68	19	(	(	PUNCT
ejde-388	68	20	with	with	ADP
ejde-388	68	21	an	an	DET
ejde-388	68	22	exponent	exponent	NOUN
ejde-388	68	23	named	name	VERB
ejde-388	68	24	liapunov	liapunov	NOUN
ejde-388	68	25	exponent	exponent	NOUN
ejde-388	68	26	)	)	PUNCT
ejde-388	68	27	,	,	PUNCT
ejde-388	68	28	and	and	CCONJ
ejde-388	68	29	it	it	PRON
ejde-388	68	30	takes	take	VERB
ejde-388	68	31	time	time	NOUN
ejde-388	68	32	for	for	SCONJ
ejde-388	68	33	the	the	DET
ejde-388	68	34	perturbations	perturbation	NOUN
ejde-388	68	35	to	to	PART
ejde-388	68	36	amplify	amplify	VERB
ejde-388	68	37	to	to	ADP
ejde-388	68	38	substantial	substantial	ADJ
ejde-388	68	39	size	size	NOUN
ejde-388	68	40	(	(	PUNCT
ejde-388	68	41	say	say	VERB
ejde-388	68	42	order	order	NOUN
ejde-388	68	43	o(1	o(1	NOUN
ejde-388	68	44	)	)	PUNCT
ejde-388	68	45	relative	relative	ADJ
ejde-388	68	46	to	to	ADP
ejde-388	68	47	the	the	DET
ejde-388	68	48	small	small	ADJ
ejde-388	68	49	initial	initial	ADJ
ejde-388	68	50	perturbations	perturbation	NOUN
ejde-388	68	51	)	)	PUNCT
ejde-388	68	52	.	.	PUNCT
ejde-388	69	1	if	if	SCONJ
ejde-388	69	2	ε	ε	PROPN
ejde-388	69	3	is	be	AUX
ejde-388	69	4	the	the	DET
ejde-388	69	5	initial	initial	ADJ
ejde-388	69	6	small	small	ADJ
ejde-388	69	7	perturbation	perturbation	NOUN
ejde-388	69	8	size	size	NOUN
ejde-388	69	9	,	,	PUNCT
ejde-388	69	10	and	and	CCONJ
ejde-388	69	11	σ	σ	PROPN
ejde-388	69	12	is	be	AUX
ejde-388	69	13	the	the	DET
ejde-388	69	14	liapunov	liapunov	NOUN
ejde-388	69	15	exponent	exponent	NOUN
ejde-388	69	16	,	,	PUNCT
ejde-388	69	17	then	then	ADV
ejde-388	69	18	the	the	DET
ejde-388	69	19	time	time	NOUN
ejde-388	69	20	for	for	SCONJ
ejde-388	69	21	the	the	DET
ejde-388	69	22	perturbation	perturbation	NOUN
ejde-388	69	23	to	to	PART
ejde-388	69	24	reach	reach	VERB
ejde-388	69	25	order	order	NOUN
ejde-388	69	26	o(1	o(1	NOUN
ejde-388	69	27	)	)	PUNCT
ejde-388	69	28	is	be	AUX
ejde-388	69	29	about	about	ADV
ejde-388	69	30	1	1	NUM
ejde-388	69	31	σ	σ	NOUN
ejde-388	69	32	ln	ln	ADJ
ejde-388	69	33	1	1	NUM
ejde-388	69	34	ε	ε	PROPN
ejde-388	69	35	.	.	PUNCT
ejde-388	70	1	the	the	DET
ejde-388	70	2	liapunov	liapunov	PROPN
ejde-388	70	3	exponent	exponent	PROPN
ejde-388	70	4	σ	σ	PROPN
ejde-388	70	5	is	be	AUX
ejde-388	70	6	a	a	DET
ejde-388	70	7	long	long	ADJ
ejde-388	70	8	term	term	NOUN
ejde-388	70	9	object	object	NOUN
ejde-388	70	10	defined	define	VERB
ejde-388	70	11	by	by	ADP
ejde-388	70	12	σ	σ	PROPN
ejde-388	70	13	=	=	PROPN
ejde-388	70	14	lim	lim	PROPN
ejde-388	70	15	t→+∞	t→+∞	PROPN
ejde-388	70	16	lim	lim	PROPN
ejde-388	70	17	du0→0	du0→0	PROPN
ejde-388	70	18	1	1	NUM
ejde-388	70	19	t	t	NOUN
ejde-388	70	20	ln	ln	ADJ
ejde-388	70	21	‖du(t)‖	‖du(t)‖	PROPN
ejde-388	70	22	‖du0‖	‖du0‖	NUM
ejde-388	70	23	,	,	PUNCT
ejde-388	70	24	where	where	SCONJ
ejde-388	70	25	du0	du0	NOUN
ejde-388	70	26	is	be	AUX
ejde-388	70	27	the	the	DET
ejde-388	70	28	initial	initial	ADJ
ejde-388	70	29	perturbation	perturbation	NOUN
ejde-388	70	30	,	,	PUNCT
ejde-388	70	31	and	and	CCONJ
ejde-388	70	32	‖	‖	PROPN
ejde-388	70	33	·	·	PUNCT
ejde-388	70	34	‖	‖	PROPN
ejde-388	70	35	is	be	AUX
ejde-388	70	36	certain	certain	ADJ
ejde-388	70	37	norm	norm	NOUN
ejde-388	70	38	.	.	PUNCT
ejde-388	71	1	positive	positive	ADJ
ejde-388	71	2	liapunov	liapunov	NOUN
ejde-388	71	3	exponent	exponent	NOUN
ejde-388	71	4	usually	usually	ADV
ejde-388	71	5	is	be	AUX
ejde-388	71	6	a	a	DET
ejde-388	71	7	good	good	ADJ
ejde-388	71	8	indicator	indicator	NOUN
ejde-388	71	9	of	of	ADP
ejde-388	71	10	chaos	chaos	NOUN
ejde-388	71	11	(	(	PUNCT
ejde-388	71	12	even	even	ADV
ejde-388	71	13	though	though	SCONJ
ejde-388	71	14	the	the	DET
ejde-388	71	15	matter	matter	NOUN
ejde-388	71	16	can	can	AUX
ejde-388	71	17	be	be	AUX
ejde-388	71	18	tricky	tricky	ADJ
ejde-388	71	19	sometimes	sometimes	ADV
ejde-388	72	1	[	[	X
ejde-388	72	2	9	9	NUM
ejde-388	72	3	]	]	SYM
ejde-388	72	4	)	)	PUNCT
ejde-388	72	5	.	.	PUNCT
ejde-388	73	1	in	in	ADP
ejde-388	73	2	the	the	DET
ejde-388	73	3	phase	phase	NOUN
ejde-388	73	4	space	space	NOUN
ejde-388	73	5	of	of	ADP
ejde-388	73	6	the	the	DET
ejde-388	73	7	dynamics	dynamic	NOUN
ejde-388	73	8	,	,	PUNCT
ejde-388	73	9	when	when	SCONJ
ejde-388	73	10	the	the	DET
ejde-388	73	11	liapunov	liapunov	NOUN
ejde-388	73	12	exponent	exponent	NOUN
ejde-388	73	13	is	be	AUX
ejde-388	73	14	positive	positive	ADJ
ejde-388	73	15	,	,	PUNCT
ejde-388	73	16	initially	initially	ADV
ejde-388	73	17	nearby	nearby	ADJ
ejde-388	73	18	orbits	orbit	NOUN
ejde-388	73	19	diverge	diverge	VERB
ejde-388	73	20	exponentially	exponentially	ADV
ejde-388	73	21	with	with	ADP
ejde-388	73	22	the	the	DET
ejde-388	73	23	exponential	exponential	ADJ
ejde-388	73	24	rate	rate	NOUN
ejde-388	73	25	being	be	AUX
ejde-388	73	26	the	the	DET
ejde-388	73	27	liapunov	liapunov	NOUN
ejde-388	73	28	exponent	exponent	NOUN
ejde-388	73	29	.	.	PUNCT
ejde-388	74	1	if	if	SCONJ
ejde-388	74	2	these	these	DET
ejde-388	74	3	orbits	orbit	NOUN
ejde-388	74	4	are	be	AUX
ejde-388	74	5	bounded	bound	VERB
ejde-388	74	6	in	in	ADP
ejde-388	74	7	the	the	DET
ejde-388	74	8	phase	phase	NOUN
ejde-388	74	9	space	space	NOUN
ejde-388	74	10	,	,	PUNCT
ejde-388	74	11	then	then	ADV
ejde-388	74	12	it	it	PRON
ejde-388	74	13	is	be	AUX
ejde-388	74	14	intuitively	intuitively	ADV
ejde-388	74	15	natural	natural	ADJ
ejde-388	74	16	to	to	PART
ejde-388	74	17	expect	expect	VERB
ejde-388	74	18	the	the	DET
ejde-388	74	19	dynamics	dynamic	NOUN
ejde-388	74	20	being	be	AUX
ejde-388	74	21	chaotic	chaotic	ADJ
ejde-388	74	22	.	.	PUNCT
ejde-388	75	1	there	there	PRON
ejde-388	75	2	are	be	VERB
ejde-388	75	3	of	of	ADP
ejde-388	75	4	course	course	NOUN
ejde-388	75	5	other	other	ADJ
ejde-388	75	6	ways	way	NOUN
ejde-388	75	7	for	for	SCONJ
ejde-388	75	8	solutions	solution	NOUN
ejde-388	75	9	of	of	ADP
ejde-388	75	10	deterministic	deterministic	ADJ
ejde-388	75	11	systems	system	NOUN
ejde-388	75	12	to	to	PART
ejde-388	75	13	be	be	AUX
ejde-388	75	14	“	"	PUNCT
ejde-388	75	15	irregular	irregular	ADJ
ejde-388	75	16	”	"	PUNCT
ejde-388	75	17	than	than	ADP
ejde-388	75	18	that	that	PRON
ejde-388	75	19	of	of	ADP
ejde-388	75	20	chaotic	chaotic	ADJ
ejde-388	75	21	solutions	solution	NOUN
ejde-388	75	22	.	.	PUNCT
ejde-388	76	1	next	next	ADV
ejde-388	76	2	we	we	PRON
ejde-388	76	3	will	will	AUX
ejde-388	76	4	describe	describe	VERB
ejde-388	76	5	another	another	DET
ejde-388	76	6	way	way	NOUN
ejde-388	76	7	:	:	PUNCT
ejde-388	76	8	rough	rough	ADJ
ejde-388	76	9	dependence	dependence	NOUN
ejde-388	76	10	on	on	ADP
ejde-388	76	11	initial	initial	ADJ
ejde-388	76	12	data	datum	NOUN
ejde-388	76	13	.	.	PUNCT
ejde-388	77	1	3	3	X
ejde-388	77	2	.	.	X
ejde-388	77	3	high	high	ADJ
ejde-388	77	4	reynolds	reynolds	PROPN
ejde-388	77	5	number	number	NOUN
ejde-388	77	6	turbulence	turbulence	NOUN
ejde-388	77	7	–	–	PUNCT
ejde-388	77	8	rough	rough	ADJ
ejde-388	77	9	dependence	dependence	NOUN
ejde-388	77	10	on	on	ADP
ejde-388	77	11	initial	initial	ADJ
ejde-388	77	12	data	datum	NOUN
ejde-388	77	13	turbulent	turbulent	ADJ
ejde-388	77	14	motion	motion	NOUN
ejde-388	77	15	of	of	ADP
ejde-388	77	16	fluids	fluid	NOUN
ejde-388	77	17	is	be	AUX
ejde-388	77	18	modeled	model	VERB
ejde-388	77	19	by	by	ADP
ejde-388	77	20	the	the	DET
ejde-388	77	21	so	so	ADV
ejde-388	77	22	-	-	PUNCT
ejde-388	77	23	called	call	VERB
ejde-388	77	24	navier	navier	NOUN
ejde-388	77	25	-	-	PUNCT
ejde-388	77	26	stokes	stoke	NOUN
ejde-388	77	27	equations	equation	NOUN
ejde-388	77	28	.	.	PUNCT
ejde-388	78	1	the	the	DET
ejde-388	78	2	phase	phase	NOUN
ejde-388	78	3	space	space	NOUN
ejde-388	78	4	of	of	ADP
ejde-388	78	5	the	the	DET
ejde-388	78	6	dynamics	dynamic	NOUN
ejde-388	78	7	of	of	ADP
ejde-388	78	8	navier	navier	NOUN
ejde-388	78	9	-	-	PUNCT
ejde-388	78	10	stokes	stoke	NOUN
ejde-388	78	11	equations	equation	NOUN
ejde-388	78	12	is	be	AUX
ejde-388	78	13	infinite	infinite	ADJ
ejde-388	78	14	dimensional	dimensional	ADJ
ejde-388	78	15	.	.	PUNCT
ejde-388	79	1	the	the	PRON
ejde-388	79	2	well	well	ADV
ejde-388	79	3	known	know	VERB
ejde-388	79	4	such	such	DET
ejde-388	79	5	a	a	DET
ejde-388	79	6	phase	phase	NOUN
ejde-388	79	7	space	space	NOUN
ejde-388	79	8	is	be	AUX
ejde-388	79	9	the	the	DET
ejde-388	79	10	sobolev	sobolev	ADJ
ejde-388	79	11	space	space	NOUN
ejde-388	79	12	of	of	ADP
ejde-388	79	13	divergence	divergence	NOUN
ejde-388	79	14	free	free	ADJ
ejde-388	79	15	fields	field	NOUN
ejde-388	79	16	,	,	PUNCT
ejde-388	79	17	hn(rd	hn(rd	NOUN
ejde-388	79	18	)	)	PUNCT
ejde-388	79	19	(	(	PUNCT
ejde-388	79	20	d	d	NOUN
ejde-388	79	21	=	=	SYM
ejde-388	79	22	2	2	NUM
ejde-388	79	23	,	,	PUNCT
ejde-388	79	24	3	3	NUM
ejde-388	79	25	)	)	PUNCT
ejde-388	79	26	which	which	PRON
ejde-388	79	27	contains	contain	VERB
ejde-388	79	28	functions	function	NOUN
ejde-388	79	29	that	that	PRON
ejde-388	79	30	are	be	AUX
ejde-388	79	31	square	square	ADJ
ejde-388	79	32	-	-	PUNCT
ejde-388	79	33	integrable	integrable	ADJ
ejde-388	79	34	and	and	CCONJ
ejde-388	79	35	so	so	ADV
ejde-388	79	36	are	be	AUX
ejde-388	79	37	their	their	PRON
ejde-388	79	38	derivatives	derivative	NOUN
ejde-388	79	39	up	up	ADP
ejde-388	79	40	to	to	ADP
ejde-388	79	41	n	n	ADV
ejde-388	79	42	-	-	PUNCT
ejde-388	79	43	th	th	VERB
ejde-388	79	44	order	order	NOUN
ejde-388	79	45	.	.	PUNCT
ejde-388	80	1	when	when	SCONJ
ejde-388	80	2	n	n	X
ejde-388	80	3	>	>	X
ejde-388	81	1	d	d	X
ejde-388	82	1	2	2	NUM
ejde-388	83	1	+	+	NUM
ejde-388	83	2	1	1	NUM
ejde-388	83	3	(	(	PUNCT
ejde-388	83	4	d	d	NOUN
ejde-388	83	5	=	=	SYM
ejde-388	83	6	2	2	NUM
ejde-388	83	7	,	,	PUNCT
ejde-388	83	8	3	3	NUM
ejde-388	83	9	)	)	PUNCT
ejde-388	83	10	,	,	PUNCT
ejde-388	83	11	for	for	ADP
ejde-388	83	12	any	any	DET
ejde-388	83	13	initial	initial	ADJ
ejde-388	83	14	condition	condition	NOUN
ejde-388	83	15	in	in	ADP
ejde-388	83	16	such	such	DET
ejde-388	83	17	a	a	DET
ejde-388	83	18	phase	phase	NOUN
ejde-388	83	19	space	space	NOUN
ejde-388	83	20	,	,	PUNCT
ejde-388	83	21	it	it	PRON
ejde-388	83	22	is	be	AUX
ejde-388	83	23	known	know	VERB
ejde-388	83	24	[	[	PUNCT
ejde-388	83	25	4	4	NUM
ejde-388	83	26	]	]	X
ejde-388	84	1	[	[	X
ejde-388	84	2	5	5	NUM
ejde-388	84	3	]	]	PUNCT
ejde-388	84	4	that	that	SCONJ
ejde-388	84	5	there	there	PRON
ejde-388	84	6	is	be	VERB
ejde-388	84	7	a	a	DET
ejde-388	84	8	(	(	PUNCT
ejde-388	84	9	short	short	ADJ
ejde-388	84	10	)	)	PUNCT
ejde-388	84	11	time	time	NOUN
ejde-388	84	12	t	t	PROPN
ejde-388	84	13	>	>	X
ejde-388	84	14	0	0	PUNCT
ejde-388	85	1	depending	depend	VERB
ejde-388	85	2	on	on	ADP
ejde-388	85	3	the	the	DET
ejde-388	85	4	norm	norm	NOUN
ejde-388	85	5	of	of	ADP
ejde-388	85	6	the	the	DET
ejde-388	85	7	initial	initial	ADJ
ejde-388	85	8	condition	condition	NOUN
ejde-388	85	9	,	,	PUNCT
ejde-388	85	10	such	such	ADJ
ejde-388	85	11	that	that	SCONJ
ejde-388	85	12	the	the	DET
ejde-388	85	13	corresponding	corresponding	ADJ
ejde-388	85	14	solution	solution	NOUN
ejde-388	85	15	(	(	PUNCT
ejde-388	85	16	orbit	orbit	NOUN
ejde-388	85	17	)	)	PUNCT
ejde-388	85	18	of	of	ADP
ejde-388	85	19	navier	navier	NOUN
ejde-388	85	20	-	-	PUNCT
ejde-388	85	21	stokes	stoke	NOUN
ejde-388	85	22	equations	equation	NOUN
ejde-388	85	23	(	(	PUNCT
ejde-388	85	24	and	and	CCONJ
ejde-388	85	25	euler	euler	PROPN
ejde-388	85	26	equations	equation	NOUN
ejde-388	85	27	)	)	PUNCT
ejde-388	85	28	exists	exist	VERB
ejde-388	85	29	on	on	ADP
ejde-388	85	30	[	[	X
ejde-388	85	31	0	0	NUM
ejde-388	85	32	,	,	PUNCT
ejde-388	85	33	t	t	X
ejde-388	85	34	]	]	PUNCT
ejde-388	85	35	.	.	PUNCT
ejde-388	86	1	such	such	DET
ejde-388	86	2	an	an	DET
ejde-388	86	3	orbit	orbit	NOUN
ejde-388	86	4	is	be	AUX
ejde-388	86	5	continuous	continuous	ADJ
ejde-388	86	6	in	in	ADP
ejde-388	86	7	time	time	NOUN
ejde-388	86	8	t	t	PROPN
ejde-388	86	9	and	and	CCONJ
ejde-388	86	10	its	its	PRON
ejde-388	86	11	initial	initial	ADJ
ejde-388	86	12	condition	condition	NOUN
ejde-388	86	13	.	.	PUNCT
ejde-388	87	1	as	as	ADP
ejde-388	87	2	the	the	DET
ejde-388	87	3	reynolds	reynolds	PROPN
ejde-388	87	4	number	number	NOUN
ejde-388	87	5	re→∞	re→∞	NUM
ejde-388	87	6	,	,	PUNCT
ejde-388	87	7	the	the	DET
ejde-388	87	8	solution	solution	NOUN
ejde-388	87	9	of	of	ADP
ejde-388	87	10	navier	navier	NOUN
ejde-388	87	11	-	-	PUNCT
ejde-388	87	12	stokes	stoke	NOUN
ejde-388	87	13	equations	equation	NOUN
ejde-388	87	14	converges	converge	VERB
ejde-388	87	15	to	to	ADP
ejde-388	87	16	that	that	PRON
ejde-388	87	17	of	of	ADP
ejde-388	87	18	the	the	DET
ejde-388	87	19	euler	euler	NOUN
ejde-388	87	20	equation	equation	NOUN
ejde-388	87	21	.	.	PUNCT
ejde-388	88	1	in	in	ADP
ejde-388	88	2	two	two	NUM
ejde-388	88	3	dimensions	dimension	NOUN
ejde-388	88	4	(	(	PUNCT
ejde-388	88	5	d	d	NOUN
ejde-388	88	6	=	=	SYM
ejde-388	88	7	2	2	NUM
ejde-388	88	8	)	)	PUNCT
ejde-388	88	9	,	,	PUNCT
ejde-388	88	10	the	the	DET
ejde-388	88	11	existence	existence	NOUN
ejde-388	88	12	time	time	NOUN
ejde-388	88	13	t	t	PROPN
ejde-388	88	14	is	be	AUX
ejde-388	88	15	infinite	infinite	ADJ
ejde-388	88	16	,	,	PUNCT
ejde-388	88	17	while	while	SCONJ
ejde-388	88	18	in	in	ADP
ejde-388	88	19	three	three	NUM
ejde-388	88	20	dimensions	dimension	NOUN
ejde-388	88	21	(	(	PUNCT
ejde-388	88	22	d	d	NOUN
ejde-388	88	23	=	=	SYM
ejde-388	88	24	3	3	NUM
ejde-388	88	25	)	)	PUNCT
ejde-388	88	26	,	,	PUNCT
ejde-388	88	27	global	global	ADJ
ejde-388	88	28	existence	existence	NOUN
ejde-388	88	29	is	be	AUX
ejde-388	88	30	still	still	ADV
ejde-388	88	31	an	an	DET
ejde-388	88	32	open	open	ADJ
ejde-388	88	33	problem	problem	NOUN
ejde-388	88	34	.	.	PUNCT
ejde-388	89	1	the	the	DET
ejde-388	89	2	above	above	ADJ
ejde-388	89	3	claims	claim	NOUN
ejde-388	89	4	apply	apply	VERB
ejde-388	89	5	also	also	ADV
ejde-388	89	6	to	to	ADP
ejde-388	89	7	spatially	spatially	ADV
ejde-388	89	8	periodic	periodic	ADJ
ejde-388	89	9	domain	domain	NOUN
ejde-388	89	10	td	td	NOUN
ejde-388	89	11	in	in	ADP
ejde-388	89	12	stead	stead	NOUN
ejde-388	89	13	of	of	ADP
ejde-388	89	14	rd	rd	PROPN
ejde-388	89	15	.	.	PROPN
ejde-388	89	16	4	4	NUM
ejde-388	89	17	z.	z.	PROPN
ejde-388	89	18	feng	feng	PROPN
ejde-388	89	19	,	,	PUNCT
ejde-388	89	20	y.	y.	PROPN
ejde-388	89	21	c.	c.	PROPN
ejde-388	89	22	li	li	PROPN
ejde-388	90	1	ejde-2020/104	ejde-2020/104	PROPN
ejde-388	90	2	one	one	PRON
ejde-388	90	3	can	can	AUX
ejde-388	90	4	define	define	VERB
ejde-388	90	5	a	a	DET
ejde-388	90	6	solution	solution	NOUN
ejde-388	90	7	map	map	NOUN
ejde-388	90	8	in	in	ADP
ejde-388	90	9	the	the	DET
ejde-388	90	10	phase	phase	NOUN
ejde-388	90	11	space	space	NOUN
ejde-388	90	12	by	by	ADP
ejde-388	90	13	mapping	map	VERB
ejde-388	90	14	the	the	DET
ejde-388	90	15	initial	initial	ADJ
ejde-388	90	16	condition	condition	NOUN
ejde-388	90	17	to	to	ADP
ejde-388	90	18	the	the	DET
ejde-388	90	19	solution	solution	NOUN
ejde-388	90	20	’s	’s	PART
ejde-388	90	21	value	value	NOUN
ejde-388	90	22	at	at	ADP
ejde-388	90	23	time	time	NOUN
ejde-388	90	24	t.	t.	NOUN
ejde-388	90	25	the	the	DET
ejde-388	90	26	solution	solution	NOUN
ejde-388	90	27	map	map	NOUN
ejde-388	90	28	for	for	ADP
ejde-388	90	29	euler	euler	NOUN
ejde-388	90	30	equations	equation	NOUN
ejde-388	90	31	(	(	PUNCT
ejde-388	90	32	d	d	NOUN
ejde-388	90	33	=	=	SYM
ejde-388	90	34	2	2	NUM
ejde-388	90	35	,	,	PUNCT
ejde-388	90	36	3	3	NUM
ejde-388	90	37	)	)	PUNCT
ejde-388	90	38	is	be	AUX
ejde-388	90	39	continuous	continuous	ADJ
ejde-388	90	40	,	,	PUNCT
ejde-388	90	41	but	but	CCONJ
ejde-388	90	42	nowhere	nowhere	ADV
ejde-388	90	43	uniformly	uniformly	ADV
ejde-388	90	44	continuous	continuous	ADJ
ejde-388	90	45	,	,	PUNCT
ejde-388	90	46	and	and	CCONJ
ejde-388	90	47	more	more	ADV
ejde-388	90	48	importantly	importantly	ADV
ejde-388	90	49	nowhere	nowhere	ADV
ejde-388	90	50	differentiable	differentiable	ADJ
ejde-388	91	1	[	[	X
ejde-388	91	2	3	3	NUM
ejde-388	91	3	]	]	PUNCT
ejde-388	91	4	.	.	PUNCT
ejde-388	92	1	then	then	ADV
ejde-388	92	2	it	it	PRON
ejde-388	92	3	is	be	AUX
ejde-388	92	4	natural	natural	ADJ
ejde-388	92	5	to	to	PART
ejde-388	92	6	expect	expect	VERB
ejde-388	92	7	that	that	SCONJ
ejde-388	92	8	the	the	DET
ejde-388	92	9	norm	norm	NOUN
ejde-388	92	10	of	of	ADP
ejde-388	92	11	the	the	DET
ejde-388	92	12	derivative	derivative	NOUN
ejde-388	92	13	of	of	ADP
ejde-388	92	14	the	the	DET
ejde-388	92	15	solution	solution	NOUN
ejde-388	92	16	map	map	NOUN
ejde-388	92	17	for	for	ADP
ejde-388	92	18	navier	navier	NOUN
ejde-388	92	19	-	-	PUNCT
ejde-388	92	20	stokes	stoke	NOUN
ejde-388	92	21	equations	equation	NOUN
ejde-388	92	22	approaches	approach	VERB
ejde-388	92	23	infinity	infinity	NOUN
ejde-388	92	24	as	as	SCONJ
ejde-388	92	25	the	the	DET
ejde-388	92	26	reynolds	reynolds	PROPN
ejde-388	92	27	number	number	NOUN
ejde-388	92	28	approaches	approach	VERB
ejde-388	92	29	infinity	infinity	NOUN
ejde-388	92	30	.	.	PUNCT
ejde-388	93	1	under	under	ADP
ejde-388	93	2	euler	euler	NOUN
ejde-388	93	3	dynamics	dynamic	NOUN
ejde-388	93	4	,	,	PUNCT
ejde-388	93	5	any	any	DET
ejde-388	93	6	small	small	ADJ
ejde-388	93	7	perturbation	perturbation	NOUN
ejde-388	93	8	of	of	ADP
ejde-388	93	9	the	the	DET
ejde-388	93	10	initial	initial	ADJ
ejde-388	93	11	condition	condition	NOUN
ejde-388	93	12	can	can	AUX
ejde-388	93	13	potentially	potentially	ADV
ejde-388	93	14	reach	reach	VERB
ejde-388	93	15	substantial	substantial	ADJ
ejde-388	93	16	amount	amount	NOUN
ejde-388	93	17	instantly	instantly	ADV
ejde-388	93	18	.	.	PUNCT
ejde-388	94	1	it	it	PRON
ejde-388	94	2	is	be	AUX
ejde-388	94	3	natural	natural	ADJ
ejde-388	94	4	to	to	PART
ejde-388	94	5	expect	expect	VERB
ejde-388	94	6	that	that	SCONJ
ejde-388	94	7	under	under	ADP
ejde-388	94	8	high	high	ADJ
ejde-388	94	9	reynolds	reynold	NOUN
ejde-388	94	10	number	number	NOUN
ejde-388	94	11	navier	navier	NOUN
ejde-388	94	12	-	-	PUNCT
ejde-388	94	13	stokes	stoke	NOUN
ejde-388	94	14	dynamics	dynamic	NOUN
ejde-388	94	15	,	,	PUNCT
ejde-388	94	16	small	small	ADJ
ejde-388	94	17	perturbation	perturbation	NOUN
ejde-388	94	18	of	of	ADP
ejde-388	94	19	the	the	DET
ejde-388	94	20	initial	initial	ADJ
ejde-388	94	21	condition	condition	NOUN
ejde-388	94	22	can	can	AUX
ejde-388	94	23	potentially	potentially	ADV
ejde-388	94	24	reach	reach	VERB
ejde-388	94	25	substantial	substantial	ADJ
ejde-388	94	26	amount	amount	NOUN
ejde-388	94	27	in	in	ADP
ejde-388	94	28	a	a	DET
ejde-388	94	29	very	very	ADV
ejde-388	94	30	short	short	ADJ
ejde-388	94	31	time	time	NOUN
ejde-388	94	32	(	(	PUNCT
ejde-388	94	33	the	the	DET
ejde-388	94	34	larger	large	ADJ
ejde-388	94	35	reynolds	reynold	NOUN
ejde-388	94	36	number	number	NOUN
ejde-388	94	37	,	,	PUNCT
ejde-388	94	38	the	the	DET
ejde-388	94	39	shorter	short	ADJ
ejde-388	94	40	)	)	PUNCT
ejde-388	94	41	.	.	PUNCT
ejde-388	95	1	we	we	PRON
ejde-388	95	2	call	call	VERB
ejde-388	95	3	this	this	DET
ejde-388	95	4	phenomenon	phenomenon	NOUN
ejde-388	95	5	“	"	PUNCT
ejde-388	95	6	rough	rough	ADJ
ejde-388	95	7	dependence	dependence	NOUN
ejde-388	95	8	on	on	ADP
ejde-388	95	9	initial	initial	ADJ
ejde-388	95	10	data	datum	NOUN
ejde-388	95	11	”	"	PUNCT
ejde-388	95	12	.	.	PUNCT
ejde-388	96	1	such	such	ADJ
ejde-388	96	2	rough	rough	ADJ
ejde-388	96	3	dependence	dependence	NOUN
ejde-388	96	4	on	on	ADP
ejde-388	96	5	initial	initial	ADJ
ejde-388	96	6	data	datum	NOUN
ejde-388	96	7	naturally	naturally	ADV
ejde-388	96	8	leads	lead	VERB
ejde-388	96	9	to	to	ADP
ejde-388	96	10	the	the	DET
ejde-388	96	11	violent	violent	ADJ
ejde-388	96	12	fully	fully	ADV
ejde-388	96	13	developed	develop	VERB
ejde-388	96	14	turbulence	turbulence	NOUN
ejde-388	96	15	as	as	SCONJ
ejde-388	96	16	observed	observe	VERB
ejde-388	96	17	in	in	ADP
ejde-388	96	18	experiments	experiment	NOUN
ejde-388	96	19	.	.	PUNCT
ejde-388	97	1	one	one	PRON
ejde-388	97	2	can	can	AUX
ejde-388	97	3	try	try	VERB
ejde-388	97	4	to	to	PART
ejde-388	97	5	estimate	estimate	VERB
ejde-388	97	6	the	the	DET
ejde-388	97	7	size	size	NOUN
ejde-388	97	8	of	of	ADP
ejde-388	97	9	the	the	DET
ejde-388	97	10	derivative	derivative	NOUN
ejde-388	97	11	of	of	ADP
ejde-388	97	12	the	the	DET
ejde-388	97	13	solution	solution	NOUN
ejde-388	97	14	map	map	NOUN
ejde-388	97	15	for	for	ADP
ejde-388	97	16	navier	navier	NOUN
ejde-388	97	17	-	-	PUNCT
ejde-388	97	18	stokes	stoke	NOUN
ejde-388	97	19	equations	equation	NOUN
ejde-388	97	20	.	.	PUNCT
ejde-388	98	1	the	the	DET
ejde-388	98	2	navier	navier	NOUN
ejde-388	98	3	-	-	PUNCT
ejde-388	98	4	stokes	stoke	NOUN
ejde-388	98	5	equations	equation	NOUN
ejde-388	98	6	are	be	AUX
ejde-388	98	7	ut	ut	PROPN
ejde-388	98	8	−	−	PROPN
ejde-388	98	9	1	1	NUM
ejde-388	98	10	re	re	VERB
ejde-388	98	11	∆u	∆u	PROPN
ejde-388	98	12	=	=	SYM
ejde-388	98	13	−∇p−	−∇p−	SYM
ejde-388	98	14	u	u	NOUN
ejde-388	98	15	·	·	PUNCT
ejde-388	98	16	∇u	∇u	PROPN
ejde-388	98	17	,	,	PUNCT
ejde-388	98	18	∇	∇	X
ejde-388	98	19	·	·	PUNCT
ejde-388	98	20	u	u	NOUN
ejde-388	98	21	=	=	NOUN
ejde-388	98	22	0	0	NUM
ejde-388	98	23	,	,	PUNCT
ejde-388	98	24	(	(	PUNCT
ejde-388	98	25	3.1	3.1	NUM
ejde-388	98	26	)	)	PUNCT
ejde-388	98	27	where	where	SCONJ
ejde-388	98	28	u	u	NOUN
ejde-388	98	29	is	be	AUX
ejde-388	98	30	the	the	DET
ejde-388	98	31	d	d	ADJ
ejde-388	98	32	-	-	ADJ
ejde-388	98	33	dimensional	dimensional	ADJ
ejde-388	98	34	fluid	fluid	ADJ
ejde-388	98	35	velocity	velocity	NOUN
ejde-388	98	36	(	(	PUNCT
ejde-388	98	37	d	d	NOUN
ejde-388	98	38	=	=	SYM
ejde-388	98	39	2	2	NUM
ejde-388	98	40	,	,	PUNCT
ejde-388	98	41	3	3	NUM
ejde-388	98	42	)	)	PUNCT
ejde-388	98	43	,	,	PUNCT
ejde-388	98	44	p	p	NOUN
ejde-388	98	45	is	be	AUX
ejde-388	98	46	the	the	DET
ejde-388	98	47	fluid	fluid	ADJ
ejde-388	98	48	pressure	pressure	NOUN
ejde-388	98	49	,	,	PUNCT
ejde-388	98	50	and	and	CCONJ
ejde-388	98	51	re	re	ADJ
ejde-388	98	52	is	be	AUX
ejde-388	98	53	the	the	DET
ejde-388	98	54	reynolds	reynolds	PROPN
ejde-388	98	55	number	number	NOUN
ejde-388	98	56	.	.	PUNCT
ejde-388	99	1	setting	set	VERB
ejde-388	99	2	the	the	DET
ejde-388	99	3	reynolds	reynold	NOUN
ejde-388	99	4	number	number	NOUN
ejde-388	99	5	to	to	PART
ejde-388	99	6	infinity	infinity	NOUN
ejde-388	99	7	re	re	ADP
ejde-388	99	8	=	=	NOUN
ejde-388	99	9	∞	∞	PROPN
ejde-388	99	10	,	,	PUNCT
ejde-388	99	11	the	the	DET
ejde-388	99	12	navier	navier	NOUN
ejde-388	99	13	-	-	PUNCT
ejde-388	99	14	stokes	stokes	PROPN
ejde-388	99	15	equations	equation	NOUN
ejde-388	99	16	(	(	PUNCT
ejde-388	99	17	3.1	3.1	NUM
ejde-388	99	18	)	)	PUNCT
ejde-388	99	19	reduces	reduce	VERB
ejde-388	99	20	to	to	ADP
ejde-388	99	21	the	the	DET
ejde-388	99	22	euler	euler	PROPN
ejde-388	99	23	equations	equation	NOUN
ejde-388	99	24	ut	ut	PROPN
ejde-388	100	1	=	=	SYM
ejde-388	100	2	−∇p−	−∇p−	PROPN
ejde-388	100	3	u	u	NOUN
ejde-388	100	4	·	·	PUNCT
ejde-388	100	5	∇u	∇u	PROPN
ejde-388	100	6	,	,	PUNCT
ejde-388	100	7	∇	∇	X
ejde-388	100	8	·	·	PUNCT
ejde-388	100	9	u	u	NOUN
ejde-388	100	10	=	=	NOUN
ejde-388	100	11	0	0	PROPN
ejde-388	100	12	.	.	PUNCT
ejde-388	101	1	for	for	ADP
ejde-388	101	2	any	any	DET
ejde-388	101	3	u	u	PROPN
ejde-388	101	4	∈	∈	PROPN
ejde-388	101	5	hn(rd	hn(rd	NOUN
ejde-388	101	6	)	)	PUNCT
ejde-388	101	7	,	,	PUNCT
ejde-388	101	8	there	there	PRON
ejde-388	101	9	is	be	VERB
ejde-388	101	10	a	a	DET
ejde-388	101	11	neighborhood	neighborhood	NOUN
ejde-388	101	12	b	b	NOUN
ejde-388	101	13	and	and	CCONJ
ejde-388	101	14	a	a	DET
ejde-388	101	15	short	short	ADJ
ejde-388	101	16	time	time	NOUN
ejde-388	101	17	t	t	X
ejde-388	101	18	>	>	X
ejde-388	101	19	0	0	PROPN
ejde-388	101	20	,	,	PUNCT
ejde-388	101	21	such	such	ADJ
ejde-388	101	22	that	that	PRON
ejde-388	101	23	for	for	ADP
ejde-388	101	24	any	any	DET
ejde-388	101	25	v	v	NOUN
ejde-388	101	26	∈	∈	PROPN
ejde-388	101	27	b	b	NOUN
ejde-388	101	28	there	there	PRON
ejde-388	101	29	exists	exist	VERB
ejde-388	101	30	a	a	DET
ejde-388	101	31	unique	unique	ADJ
ejde-388	101	32	solution	solution	NOUN
ejde-388	101	33	to	to	ADP
ejde-388	101	34	the	the	DET
ejde-388	101	35	navier	navier	NOUN
ejde-388	101	36	-	-	PUNCT
ejde-388	101	37	stokes	stoke	NOUN
ejde-388	101	38	equations	equation	NOUN
ejde-388	101	39	(	(	PUNCT
ejde-388	101	40	3.1	3.1	NUM
ejde-388	101	41	)	)	PUNCT
ejde-388	101	42	in	in	ADP
ejde-388	101	43	c0([0	c0([0	PROPN
ejde-388	101	44	,	,	PUNCT
ejde-388	101	45	t	t	X
ejde-388	101	46	]	]	PUNCT
ejde-388	101	47	;	;	PUNCT
ejde-388	101	48	hn(rd	hn(rd	PROPN
ejde-388	101	49	)	)	PUNCT
ejde-388	101	50	)	)	PUNCT
ejde-388	101	51	.	.	PUNCT
ejde-388	102	1	as	as	ADP
ejde-388	102	2	re	re	X
ejde-388	102	3	→	→	SYM
ejde-388	102	4	∞	∞	PROPN
ejde-388	102	5	,	,	PUNCT
ejde-388	102	6	this	this	DET
ejde-388	102	7	solution	solution	NOUN
ejde-388	102	8	converges	converge	VERB
ejde-388	102	9	to	to	ADP
ejde-388	102	10	that	that	PRON
ejde-388	102	11	of	of	ADP
ejde-388	102	12	the	the	DET
ejde-388	102	13	euler	euler	PROPN
ejde-388	102	14	equations	equation	NOUN
ejde-388	102	15	(	(	PUNCT
ejde-388	102	16	3	3	NUM
ejde-388	102	17	)	)	PUNCT
ejde-388	102	18	in	in	ADP
ejde-388	102	19	the	the	DET
ejde-388	102	20	same	same	ADJ
ejde-388	102	21	space	space	NOUN
ejde-388	102	22	.	.	PUNCT
ejde-388	103	1	for	for	ADP
ejde-388	103	2	any	any	DET
ejde-388	103	3	t	t	NOUN
ejde-388	103	4	∈	∈	PROPN
ejde-388	104	1	[	[	X
ejde-388	104	2	0	0	NUM
ejde-388	104	3	,	,	PUNCT
ejde-388	104	4	t	t	X
ejde-388	104	5	]	]	PUNCT
ejde-388	104	6	,	,	PUNCT
ejde-388	104	7	let	let	VERB
ejde-388	104	8	st	st	PROPN
ejde-388	104	9	be	be	AUX
ejde-388	104	10	the	the	DET
ejde-388	104	11	solution	solution	NOUN
ejde-388	104	12	map	map	NOUN
ejde-388	104	13	st	st	PROPN
ejde-388	104	14	:	:	PUNCT
ejde-388	104	15	b	b	PROPN
ejde-388	104	16	7→	7→	NUM
ejde-388	104	17	hn(rd	hn(rd	NOUN
ejde-388	104	18	)	)	PUNCT
ejde-388	104	19	,	,	PUNCT
ejde-388	104	20	st(u(0	st(u(0	NUM
ejde-388	104	21	)	)	PUNCT
ejde-388	104	22	)	)	PUNCT
ejde-388	105	1	=	=	SYM
ejde-388	105	2	u(t	u(t	NOUN
ejde-388	105	3	)	)	PUNCT
ejde-388	105	4	,	,	PUNCT
ejde-388	105	5	(	(	PUNCT
ejde-388	105	6	3.2	3.2	NUM
ejde-388	105	7	)	)	PUNCT
ejde-388	105	8	i.e.	i.e.	X
ejde-388	105	9	the	the	DET
ejde-388	105	10	solution	solution	NOUN
ejde-388	105	11	map	map	NOUN
ejde-388	105	12	maps	map	VERB
ejde-388	105	13	the	the	DET
ejde-388	105	14	initial	initial	ADJ
ejde-388	105	15	condition	condition	NOUN
ejde-388	105	16	to	to	ADP
ejde-388	105	17	the	the	DET
ejde-388	105	18	solution	solution	NOUN
ejde-388	105	19	’s	’s	PART
ejde-388	105	20	value	value	NOUN
ejde-388	105	21	at	at	ADP
ejde-388	105	22	time	time	NOUN
ejde-388	105	23	t.	t.	NOUN
ejde-388	105	24	the	the	DET
ejde-388	105	25	solution	solution	NOUN
ejde-388	105	26	map	map	NOUN
ejde-388	105	27	is	be	AUX
ejde-388	105	28	continuous	continuous	ADJ
ejde-388	105	29	for	for	ADP
ejde-388	105	30	both	both	PRON
ejde-388	105	31	navier	navier	NOUN
ejde-388	105	32	-	-	PUNCT
ejde-388	105	33	stokes	stoke	NOUN
ejde-388	105	34	equations	equation	NOUN
ejde-388	105	35	(	(	PUNCT
ejde-388	105	36	3.1	3.1	NUM
ejde-388	105	37	)	)	PUNCT
ejde-388	105	38	and	and	CCONJ
ejde-388	105	39	euler	euler	PROPN
ejde-388	105	40	equations	equation	NOUN
ejde-388	105	41	(	(	PUNCT
ejde-388	105	42	3	3	X
ejde-388	105	43	)	)	PUNCT
ejde-388	106	1	[	[	X
ejde-388	106	2	4	4	NUM
ejde-388	106	3	,	,	PUNCT
ejde-388	106	4	5	5	NUM
ejde-388	106	5	]	]	PUNCT
ejde-388	106	6	.	.	PUNCT
ejde-388	107	1	a	a	DET
ejde-388	107	2	recent	recent	ADJ
ejde-388	107	3	result	result	NOUN
ejde-388	107	4	of	of	ADP
ejde-388	107	5	inci	inci	PROPN
ejde-388	107	6	[	[	X
ejde-388	107	7	3	3	X
ejde-388	107	8	]	]	PUNCT
ejde-388	107	9	shows	show	VERB
ejde-388	107	10	that	that	SCONJ
ejde-388	107	11	for	for	ADP
ejde-388	107	12	euler	euler	PROPN
ejde-388	107	13	equations	equation	NOUN
ejde-388	107	14	(	(	PUNCT
ejde-388	107	15	3	3	X
ejde-388	107	16	)	)	PUNCT
ejde-388	107	17	the	the	DET
ejde-388	107	18	solution	solution	NOUN
ejde-388	107	19	map	map	NOUN
ejde-388	107	20	is	be	AUX
ejde-388	107	21	nowhere	nowhere	ADV
ejde-388	107	22	differentiable	differentiable	ADJ
ejde-388	107	23	.	.	PUNCT
ejde-388	108	1	even	even	ADV
ejde-388	108	2	though	though	SCONJ
ejde-388	108	3	the	the	DET
ejde-388	108	4	derivative	derivative	NOUN
ejde-388	108	5	of	of	ADP
ejde-388	108	6	the	the	DET
ejde-388	108	7	solution	solution	NOUN
ejde-388	108	8	map	map	NOUN
ejde-388	108	9	for	for	ADP
ejde-388	108	10	navier	navier	NOUN
ejde-388	108	11	-	-	PUNCT
ejde-388	108	12	stokes	stoke	NOUN
ejde-388	108	13	equations	equation	NOUN
ejde-388	108	14	(	(	PUNCT
ejde-388	108	15	3.1	3.1	NUM
ejde-388	108	16	)	)	PUNCT
ejde-388	108	17	exists	exist	VERB
ejde-388	108	18	,	,	PUNCT
ejde-388	108	19	it	it	PRON
ejde-388	108	20	is	be	AUX
ejde-388	108	21	natural	natural	ADJ
ejde-388	108	22	to	to	PART
ejde-388	108	23	conjecture	conjecture	VERB
ejde-388	108	24	that	that	SCONJ
ejde-388	108	25	the	the	DET
ejde-388	108	26	norm	norm	NOUN
ejde-388	108	27	of	of	ADP
ejde-388	108	28	the	the	DET
ejde-388	108	29	derivative	derivative	NOUN
ejde-388	108	30	of	of	ADP
ejde-388	108	31	the	the	DET
ejde-388	108	32	solution	solution	NOUN
ejde-388	108	33	map	map	NOUN
ejde-388	108	34	approaches	approach	VERB
ejde-388	108	35	infinity	infinity	NOUN
ejde-388	108	36	as	as	SCONJ
ejde-388	108	37	the	the	DET
ejde-388	108	38	reynolds	reynolds	PROPN
ejde-388	108	39	number	number	NOUN
ejde-388	108	40	approaches	approach	VERB
ejde-388	108	41	infinity	infinity	NOUN
ejde-388	108	42	.	.	PUNCT
ejde-388	109	1	the	the	DET
ejde-388	109	2	following	follow	VERB
ejde-388	109	3	upper	upper	ADJ
ejde-388	109	4	bound	bind	VERB
ejde-388	109	5	was	be	AUX
ejde-388	109	6	obtained	obtain	VERB
ejde-388	109	7	in	in	ADP
ejde-388	109	8	[	[	X
ejde-388	109	9	12	12	NUM
ejde-388	109	10	]	]	PUNCT
ejde-388	109	11	.	.	PUNCT
ejde-388	109	12	‖dst(u(0))‖	‖dst(u(0))‖	X
ejde-388	110	1	=	=	SYM
ejde-388	110	2	sup	sup	PROPN
ejde-388	110	3	du(0	du(0	PROPN
ejde-388	110	4	)	)	PUNCT
ejde-388	110	5	‖du(t)‖	‖du(t)‖	NUM
ejde-388	111	1	‖du(0)‖	‖du(0)‖	NOUN
ejde-388	111	2	≤	≤	NUM
ejde-388	111	3	eσ	eσ	ADP
ejde-388	111	4	√	√	PROPN
ejde-388	111	5	re	re	ADP
ejde-388	111	6	√	√	PROPN
ejde-388	111	7	t	t	PROPN
ejde-388	112	1	+	+	CCONJ
ejde-388	112	2	σ1	σ1	PROPN
ejde-388	112	3	t	t	PROPN
ejde-388	112	4	,	,	PUNCT
ejde-388	112	5	(	(	PUNCT
ejde-388	112	6	3.3	3.3	NUM
ejde-388	112	7	)	)	PUNCT
ejde-388	112	8	where	where	SCONJ
ejde-388	112	9	du(0	du(0	NOUN
ejde-388	112	10	)	)	PUNCT
ejde-388	112	11	is	be	AUX
ejde-388	112	12	any	any	DET
ejde-388	112	13	initial	initial	ADJ
ejde-388	112	14	perturbation	perturbation	NOUN
ejde-388	112	15	of	of	ADP
ejde-388	112	16	u(0	u(0	PROPN
ejde-388	112	17	)	)	PUNCT
ejde-388	112	18	,	,	PUNCT
ejde-388	112	19	and	and	CCONJ
ejde-388	112	20	σ	σ	X
ejde-388	112	21	=	=	SYM
ejde-388	113	1	8c√	8c√	NUM
ejde-388	113	2	2e	2e	NOUN
ejde-388	113	3	max	max	PROPN
ejde-388	113	4	τ∈[0,t	τ∈[0,t	PROPN
ejde-388	113	5	]	]	PUNCT
ejde-388	113	6	‖u(τ)‖n	‖u(τ)‖n	PROPN
ejde-388	113	7	,	,	PUNCT
ejde-388	113	8	σ1	σ1	NOUN
ejde-388	113	9	=	=	PUNCT
ejde-388	113	10	√	√	PROPN
ejde-388	113	11	2e	2e	NOUN
ejde-388	113	12	2	2	NUM
ejde-388	113	13	σ	σ	NOUN
ejde-388	113	14	,	,	PUNCT
ejde-388	113	15	where	where	SCONJ
ejde-388	113	16	c	c	NOUN
ejde-388	113	17	is	be	AUX
ejde-388	113	18	a	a	DET
ejde-388	113	19	constant	constant	ADJ
ejde-388	113	20	that	that	SCONJ
ejde-388	113	21	only	only	ADV
ejde-388	113	22	depends	depend	VERB
ejde-388	113	23	on	on	ADP
ejde-388	113	24	the	the	DET
ejde-388	113	25	spatial	spatial	ADJ
ejde-388	113	26	domain	domain	NOUN
ejde-388	113	27	and	and	CCONJ
ejde-388	113	28	n.	n.	NOUN
ejde-388	113	29	the	the	PRON
ejde-388	113	30	above	above	ADJ
ejde-388	113	31	bound	bind	VERB
ejde-388	113	32	also	also	ADV
ejde-388	113	33	applies	apply	VERB
ejde-388	113	34	to	to	ADP
ejde-388	113	35	spatially	spatially	ADV
ejde-388	113	36	periodic	periodic	ADJ
ejde-388	113	37	domain	domain	NOUN
ejde-388	113	38	td	td	NOUN
ejde-388	113	39	in	in	ADP
ejde-388	113	40	stead	stead	NOUN
ejde-388	113	41	of	of	ADP
ejde-388	113	42	rd	rd	PROPN
ejde-388	113	43	.	.	PUNCT
ejde-388	114	1	the	the	DET
ejde-388	114	2	main	main	ADJ
ejde-388	114	3	aim	aim	NOUN
ejde-388	114	4	of	of	ADP
ejde-388	114	5	this	this	DET
ejde-388	114	6	article	article	NOUN
ejde-388	114	7	is	be	AUX
ejde-388	114	8	to	to	PART
ejde-388	114	9	numerically	numerically	ADV
ejde-388	114	10	demonstrate	demonstrate	VERB
ejde-388	114	11	that	that	SCONJ
ejde-388	114	12	in	in	ADP
ejde-388	114	13	fully	fully	ADV
ejde-388	114	14	developed	develop	VERB
ejde-388	114	15	turbulence	turbulence	NOUN
ejde-388	114	16	,	,	PUNCT
ejde-388	114	17	perturbations	perturbation	NOUN
ejde-388	114	18	amplify	amplify	VERB
ejde-388	114	19	according	accord	VERB
ejde-388	114	20	to	to	ADP
ejde-388	114	21	the	the	DET
ejde-388	114	22	growth	growth	NOUN
ejde-388	114	23	rate	rate	NOUN
ejde-388	114	24	given	give	VERB
ejde-388	114	25	by	by	ADP
ejde-388	114	26	the	the	DET
ejde-388	114	27	right	right	ADJ
ejde-388	114	28	hand	hand	NOUN
ejde-388	114	29	side	side	NOUN
ejde-388	114	30	of	of	ADP
ejde-388	114	31	(	(	PUNCT
ejde-388	114	32	3.3	3.3	NUM
ejde-388	114	33	)	)	PUNCT
ejde-388	114	34	.	.	PUNCT
ejde-388	115	1	ejde-2020/104	ejde-2020/104	PROPN
ejde-388	115	2	short	short	ADJ
ejde-388	115	3	term	term	NOUN
ejde-388	115	4	unpredictability	unpredictability	NOUN
ejde-388	115	5	5	5	NUM
ejde-388	115	6	4	4	NUM
ejde-388	115	7	.	.	PUNCT
ejde-388	116	1	classical	classical	ADJ
ejde-388	116	2	hydrodynamic	hydrodynamic	ADJ
ejde-388	116	3	instability	instability	NOUN
ejde-388	116	4	–	–	PUNCT
ejde-388	116	5	directional	directional	ADJ
ejde-388	116	6	derivative	derivative	ADJ
ejde-388	116	7	classical	classical	ADJ
ejde-388	116	8	hydrodynamic	hydrodynamic	ADJ
ejde-388	116	9	instability	instability	NOUN
ejde-388	116	10	theory	theory	NOUN
ejde-388	116	11	mainly	mainly	ADV
ejde-388	116	12	focuses	focus	VERB
ejde-388	116	13	on	on	ADP
ejde-388	116	14	the	the	DET
ejde-388	116	15	so	so	ADV
ejde-388	116	16	-	-	PUNCT
ejde-388	116	17	called	call	VERB
ejde-388	116	18	linear	linear	ADJ
ejde-388	116	19	instability	instability	NOUN
ejde-388	116	20	of	of	ADP
ejde-388	116	21	steady	steady	ADJ
ejde-388	116	22	fluid	fluid	ADJ
ejde-388	116	23	flows	flow	NOUN
ejde-388	116	24	.	.	PUNCT
ejde-388	117	1	we	we	PRON
ejde-388	117	2	can	can	AUX
ejde-388	117	3	think	think	VERB
ejde-388	117	4	that	that	SCONJ
ejde-388	117	5	the	the	DET
ejde-388	117	6	linear	linear	ADJ
ejde-388	117	7	instability	instability	NOUN
ejde-388	117	8	theory	theory	NOUN
ejde-388	117	9	is	be	AUX
ejde-388	117	10	based	base	VERB
ejde-388	117	11	on	on	ADP
ejde-388	117	12	taylor	taylor	PROPN
ejde-388	117	13	expansion	expansion	NOUN
ejde-388	117	14	of	of	ADP
ejde-388	117	15	the	the	DET
ejde-388	117	16	solution	solution	NOUN
ejde-388	117	17	map	map	NOUN
ejde-388	117	18	for	for	ADP
ejde-388	117	19	navier	navier	NOUN
ejde-388	117	20	-	-	PUNCT
ejde-388	117	21	stokes	stoke	NOUN
ejde-388	117	22	equations	equation	NOUN
ejde-388	117	23	(	(	PUNCT
ejde-388	117	24	3.1	3.1	NUM
ejde-388	117	25	)	)	PUNCT
ejde-388	117	26	.	.	PUNCT
ejde-388	118	1	let	let	AUX
ejde-388	118	2	u∗	u∗	ADV
ejde-388	118	3	be	be	AUX
ejde-388	118	4	the	the	DET
ejde-388	118	5	steady	steady	ADJ
ejde-388	118	6	flow	flow	NOUN
ejde-388	118	7	(	(	PUNCT
ejde-388	118	8	a	a	DET
ejde-388	118	9	fixed	fix	VERB
ejde-388	118	10	point	point	NOUN
ejde-388	118	11	in	in	ADP
ejde-388	118	12	the	the	DET
ejde-388	118	13	phase	phase	NOUN
ejde-388	118	14	space	space	NOUN
ejde-388	118	15	)	)	PUNCT
ejde-388	118	16	,	,	PUNCT
ejde-388	118	17	v0	v0	NOUN
ejde-388	118	18	be	be	AUX
ejde-388	118	19	its	its	PRON
ejde-388	118	20	initial	initial	ADJ
ejde-388	118	21	perturbation	perturbation	NOUN
ejde-388	118	22	,	,	PUNCT
ejde-388	118	23	and	and	CCONJ
ejde-388	118	24	u∗	u∗	VERB
ejde-388	118	25	+	+	CCONJ
ejde-388	118	26	v(t	v(t	VERB
ejde-388	118	27	)	)	PUNCT
ejde-388	118	28	be	be	VERB
ejde-388	118	29	the	the	DET
ejde-388	118	30	solution	solution	NOUN
ejde-388	118	31	to	to	ADP
ejde-388	118	32	the	the	DET
ejde-388	118	33	navier	navier	NOUN
ejde-388	118	34	-	-	PUNCT
ejde-388	118	35	stokes	stoke	NOUN
ejde-388	118	36	equations	equation	NOUN
ejde-388	118	37	(	(	PUNCT
ejde-388	118	38	3.1	3.1	NUM
ejde-388	118	39	)	)	PUNCT
ejde-388	118	40	with	with	ADP
ejde-388	118	41	the	the	DET
ejde-388	118	42	initial	initial	ADJ
ejde-388	118	43	condition	condition	NOUN
ejde-388	118	44	u∗	u∗	ADJ
ejde-388	118	45	+	+	CCONJ
ejde-388	118	46	v0	v0	NOUN
ejde-388	118	47	.	.	PUNCT
ejde-388	119	1	according	accord	VERB
ejde-388	119	2	to	to	ADP
ejde-388	119	3	taylor	taylor	PROPN
ejde-388	119	4	expansion	expansion	NOUN
ejde-388	119	5	,	,	PUNCT
ejde-388	119	6	v(t	v(t	NOUN
ejde-388	119	7	)	)	PUNCT
ejde-388	119	8	=	=	PUNCT
ejde-388	119	9	dv(t	dv(t	PUNCT
ejde-388	119	10	)	)	PUNCT
ejde-388	119	11	+	+	CCONJ
ejde-388	119	12	d2v(t	d2v(t	NOUN
ejde-388	119	13	)	)	PUNCT
ejde-388	119	14	+	+	NUM
ejde-388	119	15	·	·	PUNCT
ejde-388	119	16	·	·	PUNCT
ejde-388	119	17	·	·	PUNCT
ejde-388	119	18	,	,	PUNCT
ejde-388	119	19	where	where	SCONJ
ejde-388	119	20	dv(t	dv(t	VERB
ejde-388	119	21	)	)	PUNCT
ejde-388	119	22	is	be	AUX
ejde-388	119	23	the	the	DET
ejde-388	119	24	first	first	ADJ
ejde-388	119	25	differential	differential	NOUN
ejde-388	119	26	in	in	ADP
ejde-388	119	27	u∗	u∗	NOUN
ejde-388	119	28	+	+	CCONJ
ejde-388	119	29	v0	v0	NOUN
ejde-388	119	30	of	of	ADP
ejde-388	119	31	the	the	DET
ejde-388	119	32	solution	solution	NOUN
ejde-388	119	33	map	map	NOUN
ejde-388	119	34	at	at	ADP
ejde-388	119	35	the	the	DET
ejde-388	119	36	steady	steady	ADJ
ejde-388	119	37	flow	flow	NOUN
ejde-388	119	38	u∗	u∗	NOUN
ejde-388	119	39	,	,	PUNCT
ejde-388	119	40	similarly	similarly	ADV
ejde-388	119	41	for	for	ADP
ejde-388	119	42	d2v(t	d2v(t	NOUN
ejde-388	119	43	)	)	PUNCT
ejde-388	119	44	etc	etc	X
ejde-388	119	45	..	..	X
ejde-388	119	46	under	under	ADP
ejde-388	119	47	the	the	DET
ejde-388	119	48	euler	euler	NOUN
ejde-388	119	49	dynamics	dynamic	NOUN
ejde-388	119	50	,	,	PUNCT
ejde-388	119	51	this	this	DET
ejde-388	119	52	expansion	expansion	NOUN
ejde-388	119	53	fails	fail	VERB
ejde-388	119	54	since	since	SCONJ
ejde-388	119	55	the	the	DET
ejde-388	119	56	first	first	ADJ
ejde-388	119	57	differential	differential	NOUN
ejde-388	119	58	does	do	AUX
ejde-388	119	59	not	not	PART
ejde-388	119	60	exist	exist	VERB
ejde-388	119	61	[	[	X
ejde-388	119	62	3	3	NUM
ejde-388	119	63	]	]	PUNCT
ejde-388	119	64	.	.	PUNCT
ejde-388	120	1	under	under	ADP
ejde-388	120	2	the	the	DET
ejde-388	120	3	navier	navier	NOUN
ejde-388	120	4	-	-	PUNCT
ejde-388	120	5	stokes	stoke	NOUN
ejde-388	120	6	dynamics	dynamic	NOUN
ejde-388	120	7	,	,	PUNCT
ejde-388	120	8	this	this	DET
ejde-388	120	9	expansion	expansion	NOUN
ejde-388	120	10	is	be	AUX
ejde-388	120	11	valid	valid	ADJ
ejde-388	120	12	,	,	PUNCT
ejde-388	120	13	and	and	CCONJ
ejde-388	120	14	the	the	DET
ejde-388	120	15	first	first	ADJ
ejde-388	120	16	differential	differential	ADJ
ejde-388	120	17	satisfies	satisfie	NOUN
ejde-388	120	18	the	the	DET
ejde-388	120	19	differential	differential	ADJ
ejde-388	120	20	form	form	NOUN
ejde-388	120	21	dvt	dvt	PROPN
ejde-388	120	22	−	−	PROPN
ejde-388	120	23	1	1	NUM
ejde-388	120	24	re	re	NOUN
ejde-388	120	25	∆dv	∆dv	NOUN
ejde-388	121	1	=	=	SYM
ejde-388	121	2	−∇dp−	−∇dp−	PROPN
ejde-388	121	3	dv	dv	PROPN
ejde-388	121	4	·	·	PUNCT
ejde-388	121	5	∇u∗	∇u∗	PROPN
ejde-388	122	1	−	−	PROPN
ejde-388	122	2	u∗	u∗	INTJ
ejde-388	122	3	·	·	PUNCT
ejde-388	122	4	∇dv	∇dv	ADJ
ejde-388	122	5	,	,	PUNCT
ejde-388	122	6	∇	∇	X
ejde-388	122	7	·	·	PUNCT
ejde-388	122	8	dv	dv	PROPN
ejde-388	122	9	=	=	PROPN
ejde-388	122	10	0	0	PROPN
ejde-388	122	11	,	,	PUNCT
ejde-388	122	12	(	(	PUNCT
ejde-388	122	13	4.1	4.1	NUM
ejde-388	122	14	)	)	PUNCT
ejde-388	122	15	where	where	SCONJ
ejde-388	122	16	dp	dp	NOUN
ejde-388	122	17	is	be	AUX
ejde-388	122	18	the	the	DET
ejde-388	122	19	pressure	pressure	NOUN
ejde-388	122	20	differential	differential	NOUN
ejde-388	122	21	.	.	PUNCT
ejde-388	123	1	the	the	DET
ejde-388	123	2	linear	linear	PROPN
ejde-388	123	3	instability	instability	NOUN
ejde-388	123	4	refers	refer	VERB
ejde-388	123	5	to	to	ADP
ejde-388	123	6	the	the	DET
ejde-388	123	7	instability	instability	NOUN
ejde-388	123	8	of	of	ADP
ejde-388	123	9	the	the	DET
ejde-388	123	10	differential	differential	ADJ
ejde-388	123	11	form	form	NOUN
ejde-388	123	12	(	(	PUNCT
ejde-388	123	13	4.1	4.1	NUM
ejde-388	123	14	)	)	PUNCT
ejde-388	123	15	.	.	PUNCT
ejde-388	124	1	in	in	ADP
ejde-388	124	2	most	most	ADJ
ejde-388	124	3	cases	case	NOUN
ejde-388	124	4	studied	study	VERB
ejde-388	124	5	,	,	PUNCT
ejde-388	124	6	the	the	DET
ejde-388	124	7	steady	steady	ADJ
ejde-388	124	8	flow	flow	NOUN
ejde-388	124	9	u∗	u∗	NOUN
ejde-388	124	10	depends	depend	VERB
ejde-388	124	11	on	on	ADP
ejde-388	124	12	only	only	ADV
ejde-388	124	13	one	one	NUM
ejde-388	124	14	spatial	spatial	ADJ
ejde-388	124	15	variable	variable	ADJ
ejde-388	124	16	y	y	PROPN
ejde-388	124	17	(	(	PUNCT
ejde-388	124	18	the	the	DET
ejde-388	124	19	so	so	ADV
ejde-388	124	20	-	-	PUNCT
ejde-388	124	21	called	call	VERB
ejde-388	124	22	channel	channel	NOUN
ejde-388	124	23	flow	flow	NOUN
ejde-388	124	24	)	)	PUNCT
ejde-388	124	25	.	.	PUNCT
ejde-388	125	1	this	this	PRON
ejde-388	125	2	permits	permit	VERB
ejde-388	125	3	the	the	DET
ejde-388	125	4	following	follow	VERB
ejde-388	125	5	type	type	NOUN
ejde-388	125	6	solutions	solution	NOUN
ejde-388	125	7	to	to	ADP
ejde-388	125	8	the	the	DET
ejde-388	125	9	differential	differential	ADJ
ejde-388	125	10	form	form	NOUN
ejde-388	125	11	,	,	PUNCT
ejde-388	125	12	dv(t	dv(t	NOUN
ejde-388	125	13	)	)	PUNCT
ejde-388	125	14	=	=	SYM
ejde-388	125	15	exp{i(σt+	exp{i(σt+	NUM
ejde-388	125	16	k1x+	k1x+	NOUN
ejde-388	125	17	k3z)}v	k3z)}v	NOUN
ejde-388	125	18	(	(	PUNCT
ejde-388	125	19	y	y	NOUN
ejde-388	125	20	)	)	PUNCT
ejde-388	125	21	,	,	PUNCT
ejde-388	125	22	(	(	PUNCT
ejde-388	125	23	4.2	4.2	NUM
ejde-388	125	24	)	)	PUNCT
ejde-388	125	25	where	where	SCONJ
ejde-388	125	26	(	(	PUNCT
ejde-388	125	27	x	x	X
ejde-388	125	28	,	,	PUNCT
ejde-388	125	29	y	y	PROPN
ejde-388	125	30	,	,	PUNCT
ejde-388	125	31	z	z	NOUN
ejde-388	125	32	)	)	PUNCT
ejde-388	125	33	are	be	AUX
ejde-388	125	34	the	the	DET
ejde-388	125	35	spatial	spatial	ADJ
ejde-388	125	36	coordinates	coordinate	NOUN
ejde-388	125	37	,	,	PUNCT
ejde-388	125	38	σ	σ	PROPN
ejde-388	125	39	is	be	AUX
ejde-388	125	40	a	a	DET
ejde-388	125	41	complex	complex	ADJ
ejde-388	125	42	parameter	parameter	NOUN
ejde-388	125	43	,	,	PUNCT
ejde-388	125	44	and	and	CCONJ
ejde-388	125	45	(	(	PUNCT
ejde-388	125	46	k1	k1	PROPN
ejde-388	125	47	,	,	PUNCT
ejde-388	125	48	k3	k3	VERB
ejde-388	125	49	)	)	PUNCT
ejde-388	125	50	are	be	AUX
ejde-388	125	51	real	real	ADJ
ejde-388	125	52	parameters	parameter	NOUN
ejde-388	125	53	.	.	PUNCT
ejde-388	126	1	one	one	PRON
ejde-388	126	2	can	can	AUX
ejde-388	126	3	view	view	VERB
ejde-388	126	4	(	(	PUNCT
ejde-388	126	5	4.2	4.2	NUM
ejde-388	126	6	)	)	PUNCT
ejde-388	126	7	as	as	ADP
ejde-388	126	8	a	a	DET
ejde-388	126	9	single	single	ADJ
ejde-388	126	10	fourier	fourier	NOUN
ejde-388	126	11	mode	mode	NOUN
ejde-388	126	12	out	out	ADP
ejde-388	126	13	of	of	ADP
ejde-388	126	14	the	the	DET
ejde-388	126	15	fourier	fourier	NOUN
ejde-388	126	16	transform	transform	NOUN
ejde-388	126	17	of	of	ADP
ejde-388	126	18	dv(t	dv(t	NOUN
ejde-388	126	19	)	)	PUNCT
ejde-388	126	20	.	.	PUNCT
ejde-388	127	1	in	in	ADP
ejde-388	127	2	the	the	DET
ejde-388	127	3	phase	phase	NOUN
ejde-388	127	4	space	space	NOUN
ejde-388	127	5	of	of	ADP
ejde-388	127	6	the	the	DET
ejde-388	127	7	dynamics	dynamic	NOUN
ejde-388	127	8	,	,	PUNCT
ejde-388	127	9	(	(	PUNCT
ejde-388	127	10	4.2	4.2	NUM
ejde-388	127	11	)	)	PUNCT
ejde-388	127	12	is	be	AUX
ejde-388	127	13	a	a	DET
ejde-388	127	14	directional	directional	ADJ
ejde-388	127	15	differential	differential	NOUN
ejde-388	127	16	with	with	ADP
ejde-388	127	17	the	the	DET
ejde-388	127	18	specific	specific	ADJ
ejde-388	127	19	direction	direction	NOUN
ejde-388	127	20	specified	specify	VERB
ejde-388	127	21	by	by	ADP
ejde-388	127	22	the	the	DET
ejde-388	127	23	(	(	PUNCT
ejde-388	127	24	k1	k1	PROPN
ejde-388	127	25	,	,	PUNCT
ejde-388	127	26	k3	k3	ADJ
ejde-388	127	27	)	)	PUNCT
ejde-388	127	28	fourier	fourier	ADJ
ejde-388	127	29	mode	mode	NOUN
ejde-388	127	30	.	.	PUNCT
ejde-388	128	1	v	v	X
ejde-388	128	2	(	(	PUNCT
ejde-388	128	3	y	y	NOUN
ejde-388	128	4	)	)	PUNCT
ejde-388	128	5	satisfies	satisfy	VERB
ejde-388	128	6	the	the	DET
ejde-388	128	7	well	well	ADV
ejde-388	128	8	-	-	PUNCT
ejde-388	128	9	known	know	VERB
ejde-388	128	10	orr	orr	NOUN
ejde-388	128	11	-	-	PUNCT
ejde-388	128	12	sommerfeld	sommerfeld	ADJ
ejde-388	128	13	equation	equation	NOUN
ejde-388	128	14	(	(	PUNCT
ejde-388	128	15	rayleigh	rayleigh	NOUN
ejde-388	128	16	equation	equation	NOUN
ejde-388	128	17	in	in	ADP
ejde-388	128	18	the	the	DET
ejde-388	128	19	inviscid	inviscid	ADJ
ejde-388	128	20	case	case	NOUN
ejde-388	128	21	re	re	ADP
ejde-388	128	22	=	=	NOUN
ejde-388	128	23	∞	∞	NUM
ejde-388	128	24	)	)	PUNCT
ejde-388	128	25	.	.	PUNCT
ejde-388	129	1	even	even	ADV
ejde-388	129	2	though	though	SCONJ
ejde-388	129	3	the	the	DET
ejde-388	129	4	first	first	ADJ
ejde-388	129	5	differential	differential	NOUN
ejde-388	129	6	dv(t	dv(t	PUNCT
ejde-388	129	7	)	)	PUNCT
ejde-388	129	8	does	do	AUX
ejde-388	129	9	not	not	PART
ejde-388	129	10	exist	exist	VERB
ejde-388	129	11	in	in	ADP
ejde-388	129	12	the	the	DET
ejde-388	129	13	inviscid	inviscid	ADJ
ejde-388	129	14	case	case	NOUN
ejde-388	129	15	(	(	PUNCT
ejde-388	129	16	(	(	PUNCT
ejde-388	129	17	4.1	4.1	NUM
ejde-388	129	18	)	)	PUNCT
ejde-388	129	19	with	with	ADP
ejde-388	129	20	re	re	NOUN
ejde-388	129	21	=	=	NOUN
ejde-388	129	22	∞	∞	PROPN
ejde-388	129	23	)	)	PUNCT
ejde-388	129	24	,	,	PUNCT
ejde-388	129	25	the	the	DET
ejde-388	129	26	directional	directional	ADJ
ejde-388	129	27	differential	differential	NOUN
ejde-388	129	28	(	(	PUNCT
ejde-388	129	29	4.2	4.2	NUM
ejde-388	129	30	)	)	PUNCT
ejde-388	129	31	can	can	AUX
ejde-388	129	32	exist	exist	VERB
ejde-388	129	33	with	with	ADP
ejde-388	129	34	v	v	PROPN
ejde-388	129	35	(	(	PUNCT
ejde-388	129	36	y	y	NOUN
ejde-388	129	37	)	)	PUNCT
ejde-388	129	38	solving	solve	VERB
ejde-388	129	39	the	the	DET
ejde-388	129	40	rayleigh	rayleigh	PROPN
ejde-388	129	41	equation	equation	NOUN
ejde-388	129	42	.	.	PUNCT
ejde-388	130	1	thus	thus	ADV
ejde-388	130	2	,	,	PUNCT
ejde-388	130	3	the	the	DET
ejde-388	130	4	linear	linear	ADJ
ejde-388	130	5	stability	stability	NOUN
ejde-388	130	6	/	/	SYM
ejde-388	130	7	instability	instability	NOUN
ejde-388	130	8	predicted	predict	VERB
ejde-388	130	9	by	by	ADP
ejde-388	130	10	the	the	DET
ejde-388	130	11	rayleigh	rayleigh	PROPN
ejde-388	130	12	equation	equation	NOUN
ejde-388	130	13	only	only	ADV
ejde-388	130	14	represents	represent	VERB
ejde-388	130	15	a	a	DET
ejde-388	130	16	directional	directional	ADJ
ejde-388	130	17	linear	linear	NOUN
ejde-388	130	18	stability	stability	NOUN
ejde-388	130	19	/	/	SYM
ejde-388	130	20	instability	instability	NOUN
ejde-388	130	21	of	of	ADP
ejde-388	130	22	the	the	DET
ejde-388	130	23	euler	euler	NOUN
ejde-388	130	24	dynamics	dynamic	NOUN
ejde-388	130	25	while	while	SCONJ
ejde-388	130	26	the	the	DET
ejde-388	130	27	full	full	ADJ
ejde-388	130	28	first	first	ADJ
ejde-388	130	29	differential	differential	NOUN
ejde-388	130	30	of	of	ADP
ejde-388	130	31	the	the	DET
ejde-388	130	32	euler	euler	NOUN
ejde-388	130	33	dynamics	dynamic	NOUN
ejde-388	130	34	does	do	AUX
ejde-388	130	35	not	not	PART
ejde-388	130	36	exist	exist	VERB
ejde-388	130	37	.	.	PUNCT
ejde-388	131	1	the	the	DET
ejde-388	131	2	classical	classical	ADJ
ejde-388	131	3	hydrodynamic	hydrodynamic	ADJ
ejde-388	131	4	instability	instability	NOUN
ejde-388	131	5	theory	theory	NOUN
ejde-388	131	6	heavily	heavily	ADV
ejde-388	131	7	focuses	focus	VERB
ejde-388	131	8	on	on	ADP
ejde-388	131	9	the	the	DET
ejde-388	131	10	studies	study	NOUN
ejde-388	131	11	of	of	ADP
ejde-388	131	12	the	the	DET
ejde-388	131	13	rayleigh	rayleigh	PROPN
ejde-388	131	14	equation	equation	NOUN
ejde-388	131	15	.	.	PUNCT
ejde-388	132	1	the	the	DET
ejde-388	132	2	directional	directional	ADJ
ejde-388	132	3	linear	linear	NOUN
ejde-388	132	4	instability	instability	NOUN
ejde-388	132	5	derived	derive	VERB
ejde-388	132	6	from	from	ADP
ejde-388	132	7	rayleigh	rayleigh	PROPN
ejde-388	132	8	equation	equation	NOUN
ejde-388	132	9	often	often	ADV
ejde-388	132	10	imply	imply	VERB
ejde-388	132	11	linear	linear	ADJ
ejde-388	132	12	instability	instability	NOUN
ejde-388	132	13	in	in	ADP
ejde-388	132	14	orr	orr	PROPN
ejde-388	132	15	-	-	PUNCT
ejde-388	132	16	sommerfeld	sommerfeld	ADJ
ejde-388	132	17	equation	equation	NOUN
ejde-388	132	18	[	[	X
ejde-388	132	19	15	15	NUM
ejde-388	132	20	]	]	PUNCT
ejde-388	132	21	.	.	PUNCT
ejde-388	133	1	nevertheless	nevertheless	ADV
ejde-388	133	2	,	,	PUNCT
ejde-388	133	3	linear	linear	ADJ
ejde-388	133	4	instability	instability	NOUN
ejde-388	133	5	due	due	ADP
ejde-388	133	6	to	to	ADP
ejde-388	133	7	unstable	unstable	ADJ
ejde-388	133	8	eigenvalues	eigenvalue	NOUN
ejde-388	133	9	can	can	AUX
ejde-388	133	10	not	not	PART
ejde-388	133	11	capture	capture	VERB
ejde-388	133	12	the	the	DET
ejde-388	133	13	dominant	dominant	ADJ
ejde-388	133	14	linear	linear	ADJ
ejde-388	133	15	instability	instability	NOUN
ejde-388	133	16	of	of	ADP
ejde-388	133	17	super	super	ADJ
ejde-388	133	18	fast	fast	ADJ
ejde-388	133	19	growth	growth	NOUN
ejde-388	133	20	.	.	PUNCT
ejde-388	134	1	for	for	ADP
ejde-388	134	2	a	a	DET
ejde-388	134	3	detailed	detailed	ADJ
ejde-388	134	4	evaluation	evaluation	NOUN
ejde-388	134	5	on	on	ADP
ejde-388	134	6	the	the	DET
ejde-388	134	7	rigorous	rigorous	ADJ
ejde-388	134	8	mathematical	mathematical	ADJ
ejde-388	134	9	foundation	foundation	NOUN
ejde-388	134	10	of	of	ADP
ejde-388	134	11	linear	linear	PROPN
ejde-388	134	12	hydrodynamic	hydrodynamic	ADJ
ejde-388	134	13	stability	stability	NOUN
ejde-388	134	14	theory	theory	NOUN
ejde-388	134	15	,	,	PUNCT
ejde-388	134	16	see	see	VERB
ejde-388	134	17	[	[	X
ejde-388	134	18	14	14	NUM
ejde-388	134	19	]	]	SYM
ejde-388	134	20	.	.	PUNCT
ejde-388	135	1	5	5	X
ejde-388	135	2	.	.	X
ejde-388	135	3	2d	2d	PROPN
ejde-388	135	4	numerical	numerical	ADJ
ejde-388	135	5	simulations	simulation	NOUN
ejde-388	135	6	on	on	ADP
ejde-388	135	7	rough	rough	ADJ
ejde-388	135	8	dependence	dependence	NOUN
ejde-388	135	9	on	on	ADP
ejde-388	135	10	initial	initial	ADJ
ejde-388	135	11	data	datum	NOUN
ejde-388	135	12	in	in	ADP
ejde-388	135	13	this	this	DET
ejde-388	135	14	section	section	NOUN
ejde-388	135	15	,	,	PUNCT
ejde-388	135	16	we	we	PRON
ejde-388	135	17	will	will	AUX
ejde-388	135	18	demonstrate	demonstrate	VERB
ejde-388	135	19	numerically	numerically	ADV
ejde-388	135	20	the	the	DET
ejde-388	135	21	super	super	ADV
ejde-388	135	22	fast	fast	ADJ
ejde-388	135	23	amplification	amplification	NOUN
ejde-388	135	24	of	of	ADP
ejde-388	135	25	perturbations	perturbation	NOUN
ejde-388	135	26	to	to	ADP
ejde-388	135	27	the	the	DET
ejde-388	135	28	solutions	solution	NOUN
ejde-388	135	29	of	of	ADP
ejde-388	135	30	2d	2d	NUM
ejde-388	135	31	navier	navier	NOUN
ejde-388	135	32	-	-	PUNCT
ejde-388	135	33	stokes	stoke	NOUN
ejde-388	135	34	equations	equation	NOUN
ejde-388	135	35	.	.	PUNCT
ejde-388	136	1	in	in	ADP
ejde-388	136	2	particular	particular	ADJ
ejde-388	136	3	,	,	PUNCT
ejde-388	136	4	we	we	PRON
ejde-388	136	5	shall	shall	AUX
ejde-388	136	6	demonstrate	demonstrate	VERB
ejde-388	136	7	that	that	SCONJ
ejde-388	136	8	such	such	ADJ
ejde-388	136	9	super	super	ADJ
ejde-388	136	10	fast	fast	ADJ
ejde-388	136	11	amplification	amplification	NOUN
ejde-388	136	12	of	of	ADP
ejde-388	136	13	perturbations	perturbation	NOUN
ejde-388	136	14	is	be	AUX
ejde-388	136	15	ubiquitous	ubiquitous	ADJ
ejde-388	136	16	.	.	PUNCT
ejde-388	137	1	microscopically	microscopically	ADV
ejde-388	137	2	,	,	PUNCT
ejde-388	137	3	navier	navier	NOUN
ejde-388	137	4	-	-	PUNCT
ejde-388	137	5	stokes	stokes	PROPN
ejde-388	137	6	equations	equation	NOUN
ejde-388	137	7	model	model	NOUN
ejde-388	137	8	fluid	fluid	NOUN
ejde-388	137	9	flows	flow	VERB
ejde-388	137	10	well	well	ADV
ejde-388	137	11	.	.	PUNCT
ejde-388	138	1	thus	thus	ADV
ejde-388	138	2	,	,	PUNCT
ejde-388	138	3	the	the	DET
ejde-388	138	4	super	super	ADV
ejde-388	138	5	fast	fast	ADJ
ejde-388	138	6	amplification	amplification	NOUN
ejde-388	138	7	phenomenon	phenomenon	NOUN
ejde-388	138	8	in	in	ADP
ejde-388	138	9	navier	navier	NOUN
ejde-388	138	10	-	-	PUNCT
ejde-388	138	11	stokes	stoke	NOUN
ejde-388	138	12	equations	equation	NOUN
ejde-388	138	13	also	also	ADV
ejde-388	138	14	reflects	reflect	VERB
ejde-388	138	15	the	the	DET
ejde-388	138	16	same	same	ADJ
ejde-388	138	17	phenomenon	phenomenon	NOUN
ejde-388	138	18	in	in	ADP
ejde-388	138	19	physical	physical	ADJ
ejde-388	138	20	fluid	fluid	NOUN
ejde-388	138	21	flows	flow	NOUN
ejde-388	138	22	.	.	PUNCT
ejde-388	139	1	6	6	NUM
ejde-388	139	2	z.	z.	PROPN
ejde-388	139	3	feng	feng	PROPN
ejde-388	139	4	,	,	PUNCT
ejde-388	139	5	y.	y.	PROPN
ejde-388	139	6	c.	c.	PROPN
ejde-388	139	7	li	li	PROPN
ejde-388	140	1	ejde-2020/104	ejde-2020/104	PROPN
ejde-388	141	1	5.1	5.1	NUM
ejde-388	141	2	.	.	PUNCT
ejde-388	142	1	a	a	DET
ejde-388	142	2	fundamental	fundamental	ADJ
ejde-388	142	3	problem	problem	NOUN
ejde-388	142	4	in	in	ADP
ejde-388	142	5	the	the	DET
ejde-388	142	6	numerical	numerical	ADJ
ejde-388	142	7	simulations	simulation	NOUN
ejde-388	142	8	.	.	PUNCT
ejde-388	143	1	first	first	ADV
ejde-388	143	2	we	we	PRON
ejde-388	143	3	numerically	numerically	ADV
ejde-388	143	4	simulate	simulate	VERB
ejde-388	143	5	an	an	DET
ejde-388	143	6	explicit	explicit	ADJ
ejde-388	143	7	example	example	NOUN
ejde-388	144	1	[	[	X
ejde-388	144	2	13	13	NUM
ejde-388	144	3	]	]	PUNCT
ejde-388	144	4	to	to	PART
ejde-388	144	5	test	test	VERB
ejde-388	144	6	the	the	DET
ejde-388	144	7	numerical	numerical	ADJ
ejde-388	144	8	performance	performance	NOUN
ejde-388	144	9	.	.	PUNCT
ejde-388	145	1	consider	consider	VERB
ejde-388	145	2	the	the	DET
ejde-388	145	3	2d	2d	NUM
ejde-388	145	4	navier	navier	NOUN
ejde-388	145	5	-	-	PUNCT
ejde-388	145	6	stokes	stoke	NOUN
ejde-388	145	7	equation	equation	NOUN
ejde-388	145	8	∂tu+	∂tu+	VERB
ejde-388	145	9	u	u	NOUN
ejde-388	145	10	·	·	PUNCT
ejde-388	145	11	∇u	∇u	PROPN
ejde-388	145	12	=	=	SYM
ejde-388	146	1	−∇p+	−∇p+	NUM
ejde-388	146	2	1	1	NUM
ejde-388	146	3	re	re	NOUN
ejde-388	146	4	∆u	∆u	PROPN
ejde-388	146	5	,	,	PUNCT
ejde-388	146	6	∇	∇	X
ejde-388	146	7	·	·	PUNCT
ejde-388	146	8	u	u	NOUN
ejde-388	146	9	=	=	NOUN
ejde-388	146	10	0	0	NUM
ejde-388	146	11	,	,	PUNCT
ejde-388	146	12	(	(	PUNCT
ejde-388	146	13	5.1	5.1	NUM
ejde-388	146	14	)	)	PUNCT
ejde-388	146	15	under	under	ADP
ejde-388	146	16	periodic	periodic	ADJ
ejde-388	146	17	boundary	boundary	ADJ
ejde-388	146	18	condition	condition	NOUN
ejde-388	146	19	with	with	ADP
ejde-388	146	20	period	period	NOUN
ejde-388	146	21	domain	domain	NOUN
ejde-388	146	22	[	[	X
ejde-388	146	23	0	0	NUM
ejde-388	146	24	,	,	PUNCT
ejde-388	146	25	2π]×	2π]×	NUM
ejde-388	147	1	[	[	X
ejde-388	147	2	0	0	NUM
ejde-388	147	3	,	,	PUNCT
ejde-388	147	4	2π	2π	NOUN
ejde-388	147	5	]	]	PUNCT
ejde-388	147	6	,	,	PUNCT
ejde-388	147	7	where	where	SCONJ
ejde-388	147	8	u	u	NOUN
ejde-388	147	9	=	=	SYM
ejde-388	147	10	(	(	PUNCT
ejde-388	147	11	u1	u1	PROPN
ejde-388	147	12	,	,	PUNCT
ejde-388	147	13	u2	u2	PROPN
ejde-388	147	14	)	)	PUNCT
ejde-388	147	15	is	be	AUX
ejde-388	147	16	the	the	DET
ejde-388	147	17	velocity	velocity	NOUN
ejde-388	147	18	,	,	PUNCT
ejde-388	147	19	p	p	NOUN
ejde-388	147	20	is	be	AUX
ejde-388	147	21	pressure	pressure	NOUN
ejde-388	147	22	,	,	PUNCT
ejde-388	147	23	and	and	CCONJ
ejde-388	147	24	the	the	DET
ejde-388	147	25	spatial	spatial	ADJ
ejde-388	147	26	coordinate	coordinate	NOUN
ejde-388	147	27	is	be	AUX
ejde-388	147	28	denoted	denote	VERB
ejde-388	147	29	by	by	ADP
ejde-388	147	30	x	x	X
ejde-388	147	31	=	=	SYM
ejde-388	147	32	(	(	PUNCT
ejde-388	147	33	x1	x1	PROPN
ejde-388	147	34	,	,	PUNCT
ejde-388	147	35	x2	x2	PROPN
ejde-388	147	36	)	)	PUNCT
ejde-388	147	37	.	.	PUNCT
ejde-388	148	1	a	a	DET
ejde-388	148	2	simple	simple	ADJ
ejde-388	148	3	solution	solution	NOUN
ejde-388	148	4	to	to	ADP
ejde-388	148	5	the	the	DET
ejde-388	148	6	2d	2d	PROPN
ejde-388	148	7	navier	navier	NOUN
ejde-388	148	8	-	-	PUNCT
ejde-388	148	9	stokes	stoke	NOUN
ejde-388	148	10	equations	equation	NOUN
ejde-388	148	11	(	(	PUNCT
ejde-388	148	12	5.1	5.1	NUM
ejde-388	148	13	)	)	PUNCT
ejde-388	148	14	is	be	AUX
ejde-388	148	15	u1	u1	NOUN
ejde-388	148	16	=	=	NOUN
ejde-388	148	17	∞∑	∞∑	NUM
ejde-388	148	18	n=1	n=1	ADP
ejde-388	148	19	1	1	NUM
ejde-388	148	20	n3+γ	n3+γ	PROPN
ejde-388	148	21	e−	e−	PROPN
ejde-388	148	22	n2	n2	PROPN
ejde-388	148	23	re	re	ADP
ejde-388	148	24	t	t	PROPN
ejde-388	148	25	sin[n(x2	sin[n(x2	NOUN
ejde-388	148	26	−	−	PROPN
ejde-388	148	27	σt	σt	ADP
ejde-388	148	28	)	)	PUNCT
ejde-388	148	29	]	]	PUNCT
ejde-388	148	30	,	,	PUNCT
ejde-388	148	31	u2	u2	PROPN
ejde-388	148	32	=	=	SYM
ejde-388	148	33	σ	σ	PROPN
ejde-388	148	34	,	,	PUNCT
ejde-388	148	35	(	(	PUNCT
ejde-388	148	36	5.2	5.2	NUM
ejde-388	148	37	)	)	PUNCT
ejde-388	148	38	where	where	SCONJ
ejde-388	148	39	1/2	1/2	NUM
ejde-388	148	40	<	<	X
ejde-388	148	41	γ	γ	X
ejde-388	148	42	≤	≤	NOUN
ejde-388	148	43	1	1	NUM
ejde-388	148	44	,	,	PUNCT
ejde-388	148	45	and	and	CCONJ
ejde-388	148	46	σ	σ	PROPN
ejde-388	148	47	is	be	AUX
ejde-388	148	48	a	a	DET
ejde-388	148	49	real	real	ADJ
ejde-388	148	50	parameter	parameter	NOUN
ejde-388	148	51	.	.	PUNCT
ejde-388	149	1	by	by	ADP
ejde-388	149	2	varying	vary	VERB
ejde-388	149	3	σ	σ	NOUN
ejde-388	149	4	,	,	PUNCT
ejde-388	149	5	we	we	PRON
ejde-388	149	6	get	get	VERB
ejde-388	149	7	a	a	DET
ejde-388	149	8	variation	variation	NOUN
ejde-388	149	9	direction	direction	NOUN
ejde-388	149	10	of	of	ADP
ejde-388	149	11	the	the	DET
ejde-388	149	12	initial	initial	ADJ
ejde-388	149	13	condition	condition	NOUN
ejde-388	149	14	,	,	PUNCT
ejde-388	149	15	du1(0	du1(0	NOUN
ejde-388	149	16	)	)	PUNCT
ejde-388	149	17	=	=	SYM
ejde-388	149	18	0	0	NUM
ejde-388	149	19	,	,	PUNCT
ejde-388	149	20	du2(0	du2(0	NOUN
ejde-388	149	21	)	)	PUNCT
ejde-388	149	22	=	=	SYM
ejde-388	150	1	dσ	dσ	PROPN
ejde-388	150	2	,	,	PUNCT
ejde-388	150	3	which	which	PRON
ejde-388	150	4	leads	lead	VERB
ejde-388	150	5	to	to	ADP
ejde-388	150	6	the	the	DET
ejde-388	150	7	variation	variation	NOUN
ejde-388	150	8	of	of	ADP
ejde-388	150	9	the	the	DET
ejde-388	150	10	solution	solution	NOUN
ejde-388	150	11	(	(	PUNCT
ejde-388	150	12	du1(t	du1(t	PROPN
ejde-388	150	13	)	)	PUNCT
ejde-388	150	14	,	,	PUNCT
ejde-388	150	15	du2(t	du2(t	PROPN
ejde-388	150	16	)	)	PUNCT
ejde-388	150	17	)	)	PUNCT
ejde-388	150	18	.	.	PUNCT
ejde-388	151	1	let	let	VERB
ejde-388	151	2	λ	λ	X
ejde-388	151	3	=	=	PRON
ejde-388	151	4	‖(du1(t	‖(du1(t	NUM
ejde-388	151	5	)	)	PUNCT
ejde-388	151	6	,	,	PUNCT
ejde-388	151	7	du2(t))‖h3	du2(t))‖h3	PROPN
ejde-388	151	8	,	,	PUNCT
ejde-388	151	9	λ0	λ0	NOUN
ejde-388	151	10	=	=	SYM
ejde-388	151	11	‖(du1(0	‖(du1(0	NOUN
ejde-388	151	12	)	)	PUNCT
ejde-388	151	13	,	,	PUNCT
ejde-388	151	14	du2(0))‖h3	du2(0))‖h3	PROPN
ejde-388	151	15	,	,	PUNCT
ejde-388	151	16	then	then	ADV
ejde-388	151	17	one	one	PRON
ejde-388	151	18	has	have	VERB
ejde-388	151	19	the	the	DET
ejde-388	151	20	analytical	analytical	ADJ
ejde-388	151	21	result	result	NOUN
ejde-388	152	1	[	[	X
ejde-388	152	2	13	13	NUM
ejde-388	152	3	]	]	SYM
ejde-388	152	4	:	:	PUNCT
ejde-388	152	5	λ	λ	X
ejde-388	152	6	λ0	λ0	NOUN
ejde-388	152	7	≥	≥	NOUN
ejde-388	152	8	(	(	PUNCT
ejde-388	152	9	1	1	NUM
ejde-388	152	10	+	+	CCONJ
ejde-388	152	11	[	[	PUNCT
ejde-388	152	12	1√	1√	ADJ
ejde-388	152	13	2e	2e	PROPN
ejde-388	152	14	tγ	tγ	NOUN
ejde-388	152	15	(	(	PUNCT
ejde-388	152	16	√t√re	√t√re	SYM
ejde-388	152	17	2	2	NUM
ejde-388	152	18	√	√	NUM
ejde-388	152	19	2	2	NUM
ejde-388	152	20	)	)	PUNCT
ejde-388	152	21	1−γ]2)1/2	1−γ]2)1/2	NUM
ejde-388	152	22	.	.	PUNCT
ejde-388	153	1	(	(	PUNCT
ejde-388	153	2	5.3	5.3	NUM
ejde-388	153	3	)	)	PUNCT
ejde-388	153	4	this	this	DET
ejde-388	153	5	lower	lower	ADV
ejde-388	153	6	bound	bind	VERB
ejde-388	153	7	is	be	AUX
ejde-388	153	8	obtained	obtain	VERB
ejde-388	153	9	by	by	ADP
ejde-388	153	10	keeping	keep	VERB
ejde-388	153	11	only	only	ADV
ejde-388	153	12	the	the	DET
ejde-388	153	13	fastest	fast	ADJ
ejde-388	153	14	growing	grow	VERB
ejde-388	153	15	mode	mode	NOUN
ejde-388	153	16	given	give	VERB
ejde-388	153	17	by	by	ADP
ejde-388	153	18	n	n	NOUN
ejde-388	153	19	=	=	PUNCT
ejde-388	154	1	[	[	X
ejde-388	154	2	√re	√re	X
ejde-388	154	3	2	2	NUM
ejde-388	154	4	t	t	NOUN
ejde-388	154	5	]	]	PUNCT
ejde-388	154	6	,	,	PUNCT
ejde-388	154	7	(	(	PUNCT
ejde-388	154	8	the	the	DET
ejde-388	154	9	integer	integer	ADJ
ejde-388	154	10	part	part	NOUN
ejde-388	154	11	of	of	ADP
ejde-388	154	12	√	√	NUM
ejde-388	154	13	re	re	PROPN
ejde-388	154	14	2	2	NUM
ejde-388	154	15	t	t	NOUN
ejde-388	154	16	)	)	PUNCT
ejde-388	154	17	.	.	PUNCT
ejde-388	155	1	(	(	PUNCT
ejde-388	155	2	5.4	5.4	NUM
ejde-388	155	3	)	)	PUNCT
ejde-388	155	4	note	note	VERB
ejde-388	155	5	that	that	SCONJ
ejde-388	155	6	as	as	ADP
ejde-388	155	7	t	t	PROPN
ejde-388	155	8	→	→	SYM
ejde-388	155	9	0	0	NUM
ejde-388	155	10	+	+	PROPN
ejde-388	155	11	,	,	PUNCT
ejde-388	155	12	the	the	DET
ejde-388	155	13	time	time	NOUN
ejde-388	155	14	derivative	derivative	NOUN
ejde-388	155	15	of	of	ADP
ejde-388	155	16	the	the	DET
ejde-388	155	17	lower	lower	ADV
ejde-388	155	18	bound	bound	ADJ
ejde-388	155	19	approaches	approach	NOUN
ejde-388	155	20	positive	positive	ADJ
ejde-388	155	21	infinity	infinity	NOUN
ejde-388	155	22	due	due	ADP
ejde-388	155	23	to	to	ADP
ejde-388	155	24	the	the	DET
ejde-388	155	25	fractional	fractional	ADJ
ejde-388	155	26	power	power	NOUN
ejde-388	155	27	of	of	ADP
ejde-388	155	28	t.	t.	PROPN
ejde-388	155	29	that	that	PRON
ejde-388	155	30	is	be	AUX
ejde-388	155	31	,	,	PUNCT
ejde-388	155	32	the	the	DET
ejde-388	155	33	lower	lower	ADV
ejde-388	155	34	bound	bind	VERB
ejde-388	155	35	curve	curve	NOUN
ejde-388	155	36	is	be	AUX
ejde-388	155	37	tangent	tangent	NOUN
ejde-388	155	38	to	to	ADP
ejde-388	155	39	the	the	DET
ejde-388	155	40	vertical	vertical	ADJ
ejde-388	155	41	axis	axis	NOUN
ejde-388	155	42	at	at	ADP
ejde-388	155	43	t	t	PROPN
ejde-388	155	44	=	=	SYM
ejde-388	155	45	0	0	X
ejde-388	155	46	.	.	PUNCT
ejde-388	156	1	as	as	ADP
ejde-388	156	2	t	t	PROPN
ejde-388	156	3	→	→	SYM
ejde-388	156	4	0	0	NUM
ejde-388	156	5	+	+	PROPN
ejde-388	156	6	,	,	PUNCT
ejde-388	156	7	the	the	DET
ejde-388	156	8	fastest	fast	ADJ
ejde-388	156	9	growing	grow	VERB
ejde-388	156	10	mode	mode	NOUN
ejde-388	156	11	(	(	PUNCT
ejde-388	156	12	5.4	5.4	NUM
ejde-388	156	13	)	)	PUNCT
ejde-388	156	14	n	n	NOUN
ejde-388	156	15	→	→	PUNCT
ejde-388	156	16	+	+	NOUN
ejde-388	156	17	∞.	∞.	PROPN
ejde-388	156	18	thus	thus	ADV
ejde-388	156	19	a	a	DET
ejde-388	156	20	numerical	numerical	ADJ
ejde-388	156	21	simulation	simulation	NOUN
ejde-388	156	22	will	will	AUX
ejde-388	156	23	never	never	ADV
ejde-388	156	24	capture	capture	VERB
ejde-388	156	25	the	the	DET
ejde-388	156	26	fastest	fast	ADJ
ejde-388	156	27	growing	grow	VERB
ejde-388	156	28	mode	mode	NOUN
ejde-388	156	29	as	as	ADP
ejde-388	156	30	t	t	PROPN
ejde-388	156	31	→	→	SYM
ejde-388	156	32	0	0	NUM
ejde-388	156	33	+	+	NOUN
ejde-388	156	34	no	no	ADV
ejde-388	156	35	matter	matter	ADV
ejde-388	156	36	how	how	SCONJ
ejde-388	156	37	many	many	ADJ
ejde-388	156	38	fourier	fouri	ADJ
ejde-388	156	39	modes	mode	NOUN
ejde-388	156	40	are	be	AUX
ejde-388	156	41	kept	keep	VERB
ejde-388	156	42	in	in	ADP
ejde-388	156	43	the	the	DET
ejde-388	156	44	numerical	numerical	PROPN
ejde-388	156	45	simulation	simulation	PROPN
ejde-388	156	46	.	.	PUNCT
ejde-388	157	1	this	this	PRON
ejde-388	157	2	demonstrates	demonstrate	VERB
ejde-388	157	3	a	a	DET
ejde-388	157	4	fundamental	fundamental	ADJ
ejde-388	157	5	problem	problem	NOUN
ejde-388	157	6	in	in	ADP
ejde-388	157	7	numerical	numerical	ADJ
ejde-388	157	8	simulations	simulation	NOUN
ejde-388	157	9	.	.	PUNCT
ejde-388	158	1	when	when	SCONJ
ejde-388	158	2	we	we	PRON
ejde-388	158	3	numerically	numerically	ADV
ejde-388	158	4	simulate	simulate	VERB
ejde-388	158	5	the	the	DET
ejde-388	158	6	quantity	quantity	NOUN
ejde-388	158	7	λ	λ	NOUN
ejde-388	158	8	λ0	λ0	NOUN
ejde-388	158	9	(	(	PUNCT
ejde-388	158	10	5.3	5.3	NUM
ejde-388	158	11	)	)	PUNCT
ejde-388	158	12	,	,	PUNCT
ejde-388	158	13	we	we	PRON
ejde-388	158	14	obtained	obtain	VERB
ejde-388	158	15	the	the	DET
ejde-388	158	16	solid	solid	ADJ
ejde-388	158	17	curve	curve	NOUN
ejde-388	158	18	in	in	ADP
ejde-388	158	19	figure	figure	NOUN
ejde-388	158	20	1	1	NUM
ejde-388	158	21	.	.	PUNCT
ejde-388	158	22	notice	notice	VERB
ejde-388	158	23	that	that	SCONJ
ejde-388	158	24	as	as	ADP
ejde-388	158	25	t	t	PROPN
ejde-388	158	26	→	→	SYM
ejde-388	158	27	0	0	NUM
ejde-388	158	28	+	+	PROPN
ejde-388	158	29	,	,	PUNCT
ejde-388	158	30	the	the	DET
ejde-388	158	31	numerical	numerical	ADJ
ejde-388	158	32	solid	solid	ADJ
ejde-388	158	33	curve	curve	NOUN
ejde-388	158	34	gets	get	VERB
ejde-388	158	35	below	below	ADP
ejde-388	158	36	the	the	DET
ejde-388	158	37	dash	dash	NOUN
ejde-388	158	38	lower	lower	ADV
ejde-388	158	39	bound	bind	VERB
ejde-388	158	40	curve	curve	NOUN
ejde-388	158	41	(	(	PUNCT
ejde-388	158	42	violating	violate	VERB
ejde-388	158	43	the	the	DET
ejde-388	158	44	lower	low	ADJ
ejde-388	158	45	bound	bound	ADJ
ejde-388	158	46	nature	nature	NOUN
ejde-388	158	47	)	)	PUNCT
ejde-388	158	48	.	.	PUNCT
ejde-388	159	1	the	the	DET
ejde-388	159	2	numerical	numerical	PROPN
ejde-388	159	3	solid	solid	ADJ
ejde-388	159	4	curve	curve	NOUN
ejde-388	159	5	has	have	VERB
ejde-388	159	6	a	a	DET
ejde-388	159	7	finite	finite	ADJ
ejde-388	159	8	time	time	NOUN
ejde-388	159	9	derivation	derivation	NOUN
ejde-388	159	10	at	at	ADP
ejde-388	159	11	t	t	PROPN
ejde-388	159	12	=	=	SYM
ejde-388	159	13	0	0	NUM
ejde-388	159	14	,	,	PUNCT
ejde-388	159	15	and	and	CCONJ
ejde-388	159	16	does	do	AUX
ejde-388	159	17	not	not	PART
ejde-388	159	18	capture	capture	VERB
ejde-388	159	19	the	the	DET
ejde-388	159	20	infinite	infinite	ADJ
ejde-388	159	21	derivative	derivative	ADJ
ejde-388	159	22	nature	nature	NOUN
ejde-388	159	23	at	at	ADP
ejde-388	159	24	t	t	PROPN
ejde-388	159	25	=	=	SYM
ejde-388	159	26	0	0	NUM
ejde-388	159	27	.	.	X
ejde-388	160	1	5.2	5.2	NUM
ejde-388	160	2	.	.	PUNCT
ejde-388	161	1	fixed	fix	VERB
ejde-388	161	2	base	base	NOUN
ejde-388	161	3	solution	solution	NOUN
ejde-388	161	4	and	and	CCONJ
ejde-388	161	5	different	different	ADJ
ejde-388	161	6	perturbations	perturbation	NOUN
ejde-388	161	7	.	.	PUNCT
ejde-388	162	1	we	we	PRON
ejde-388	162	2	will	will	AUX
ejde-388	162	3	numerically	numerically	ADV
ejde-388	162	4	simulate	simulate	VERB
ejde-388	162	5	the	the	DET
ejde-388	162	6	2d	2d	NUM
ejde-388	162	7	navier	navier	NOUN
ejde-388	162	8	-	-	PUNCT
ejde-388	162	9	stokes	stoke	NOUN
ejde-388	162	10	equations	equation	NOUN
ejde-388	162	11	under	under	ADP
ejde-388	162	12	periodic	periodic	ADJ
ejde-388	162	13	boundary	boundary	ADJ
ejde-388	162	14	condition	condition	NOUN
ejde-388	162	15	(	(	PUNCT
ejde-388	162	16	5.1	5.1	NUM
ejde-388	162	17	)	)	PUNCT
ejde-388	162	18	.	.	PUNCT
ejde-388	163	1	we	we	PRON
ejde-388	163	2	have	have	VERB
ejde-388	163	3	two	two	NUM
ejde-388	163	4	goals	goal	NOUN
ejde-388	163	5	here	here	ADV
ejde-388	163	6	:	:	PUNCT
ejde-388	163	7	first	first	ADV
ejde-388	163	8	,	,	PUNCT
ejde-388	163	9	we	we	PRON
ejde-388	163	10	want	want	VERB
ejde-388	163	11	to	to	PART
ejde-388	163	12	realize	realize	VERB
ejde-388	163	13	the	the	DET
ejde-388	163	14	super	super	ADV
ejde-388	163	15	fast	fast	ADJ
ejde-388	163	16	amplification	amplification	NOUN
ejde-388	163	17	of	of	ADP
ejde-388	163	18	perturbations	perturbation	NOUN
ejde-388	163	19	.	.	PUNCT
ejde-388	164	1	second	second	ADV
ejde-388	164	2	,	,	PUNCT
ejde-388	164	3	we	we	PRON
ejde-388	164	4	want	want	VERB
ejde-388	164	5	to	to	PART
ejde-388	164	6	show	show	VERB
ejde-388	164	7	that	that	SCONJ
ejde-388	164	8	such	such	ADJ
ejde-388	164	9	super	super	ADJ
ejde-388	164	10	fast	fast	ADJ
ejde-388	164	11	amplification	amplification	NOUN
ejde-388	164	12	of	of	ADP
ejde-388	164	13	perturbations	perturbation	NOUN
ejde-388	164	14	is	be	AUX
ejde-388	164	15	abundant	abundant	ADJ
ejde-388	164	16	among	among	ADP
ejde-388	164	17	perturbations	perturbation	NOUN
ejde-388	164	18	.	.	PUNCT
ejde-388	165	1	for	for	ADP
ejde-388	165	2	the	the	DET
ejde-388	165	3	two	two	NUM
ejde-388	165	4	goals	goal	NOUN
ejde-388	165	5	,	,	PUNCT
ejde-388	165	6	we	we	PRON
ejde-388	165	7	shall	shall	AUX
ejde-388	165	8	choose	choose	VERB
ejde-388	165	9	the	the	DET
ejde-388	165	10	initial	initial	ADJ
ejde-388	165	11	conditions	condition	NOUN
ejde-388	165	12	of	of	ADP
ejde-388	165	13	the	the	DET
ejde-388	165	14	base	base	NOUN
ejde-388	165	15	solution	solution	NOUN
ejde-388	165	16	and	and	CCONJ
ejde-388	165	17	the	the	DET
ejde-388	165	18	perturbations	perturbation	NOUN
ejde-388	165	19	,	,	PUNCT
ejde-388	165	20	to	to	PART
ejde-388	165	21	be	be	AUX
ejde-388	165	22	of	of	ADP
ejde-388	165	23	the	the	DET
ejde-388	165	24	form	form	NOUN
ejde-388	165	25	of	of	ADP
ejde-388	165	26	single	single	ADJ
ejde-388	165	27	fourier	fourier	NOUN
ejde-388	165	28	modes	mode	NOUN
ejde-388	165	29	.	.	PUNCT
ejde-388	166	1	since	since	SCONJ
ejde-388	166	2	the	the	DET
ejde-388	166	3	perturbation	perturbation	NOUN
ejde-388	166	4	equations	equation	NOUN
ejde-388	166	5	are	be	AUX
ejde-388	166	6	linear	linear	ADJ
ejde-388	166	7	,	,	PUNCT
ejde-388	166	8	perturbation	perturbation	NOUN
ejde-388	166	9	solutions	solution	NOUN
ejde-388	166	10	generated	generate	VERB
ejde-388	166	11	from	from	ADP
ejde-388	166	12	such	such	ADJ
ejde-388	166	13	single	single	ADJ
ejde-388	166	14	fourier	fourier	NOUN
ejde-388	166	15	modes	mode	NOUN
ejde-388	166	16	form	form	VERB
ejde-388	166	17	a	a	DET
ejde-388	166	18	base	base	NOUN
ejde-388	166	19	of	of	ADP
ejde-388	166	20	superposition	superposition	NOUN
ejde-388	166	21	.	.	PUNCT
ejde-388	167	1	for	for	ADP
ejde-388	167	2	the	the	DET
ejde-388	167	3	base	base	NOUN
ejde-388	167	4	solution	solution	NOUN
ejde-388	167	5	,	,	PUNCT
ejde-388	167	6	we	we	PRON
ejde-388	167	7	choose	choose	VERB
ejde-388	167	8	the	the	DET
ejde-388	167	9	initial	initial	ADJ
ejde-388	167	10	condition	condition	NOUN
ejde-388	167	11	u1(0	u1(0	NOUN
ejde-388	167	12	)	)	PUNCT
ejde-388	167	13	=	=	PROPN
ejde-388	167	14	−8	−8	PRON
ejde-388	167	15	sin(9x1	sin(9x1	PROPN
ejde-388	167	16	)	)	PUNCT
ejde-388	167	17	sin(8x2	sin(8x2	PROPN
ejde-388	167	18	)	)	PUNCT
ejde-388	167	19	,	,	PUNCT
ejde-388	167	20	u2(0	u2(0	NOUN
ejde-388	167	21	)	)	PUNCT
ejde-388	167	22	=	=	PUNCT
ejde-388	167	23	−9	−9	NOUN
ejde-388	167	24	cos(9x1	cos(9x1	NOUN
ejde-388	167	25	)	)	PUNCT
ejde-388	167	26	cos(8x2	cos(8x2	NOUN
ejde-388	167	27	)	)	PUNCT
ejde-388	167	28	,	,	PUNCT
ejde-388	167	29	(	(	PUNCT
ejde-388	167	30	5.5	5.5	NUM
ejde-388	167	31	)	)	PUNCT
ejde-388	167	32	ejde-2020/104	ejde-2020/104	PRON
ejde-388	167	33	short	short	ADJ
ejde-388	167	34	term	term	NOUN
ejde-388	167	35	unpredictability	unpredictability	NOUN
ejde-388	167	36	7	7	NUM
ejde-388	167	37	0	0	NUM
ejde-388	167	38	5	5	NUM
ejde-388	167	39	10	10	NUM
ejde-388	167	40	15	15	NUM
ejde-388	167	41	20	20	NUM
ejde-388	167	42	t	t	NOUN
ejde-388	167	43	0	0	NUM
ejde-388	167	44	50	50	NUM
ejde-388	167	45	100	100	NUM
ejde-388	167	46	150	150	NUM
ejde-388	167	47	λ	λ	NOUN
ejde-388	167	48	/λ	/λ	SYM
ejde-388	167	49	0	0	NUM
ejde-388	167	50	figure	figure	NOUN
ejde-388	167	51	1	1	NUM
ejde-388	167	52	.	.	PUNCT
ejde-388	167	53	fundamental	fundamental	ADJ
ejde-388	167	54	obstacle	obstacle	NOUN
ejde-388	167	55	in	in	ADP
ejde-388	167	56	numerical	numerical	ADJ
ejde-388	167	57	simulation	simulation	NOUN
ejde-388	167	58	on	on	ADP
ejde-388	167	59	the	the	DET
ejde-388	167	60	norm	norm	NOUN
ejde-388	167	61	of	of	ADP
ejde-388	167	62	the	the	DET
ejde-388	167	63	solution	solution	NOUN
ejde-388	167	64	map	map	NOUN
ejde-388	167	65	’s	’s	PART
ejde-388	167	66	derivative	derivative	NOUN
ejde-388	167	67	as	as	ADP
ejde-388	167	68	t	t	PROPN
ejde-388	167	69	→	→	SYM
ejde-388	167	70	0	0	NUM
ejde-388	167	71	+	+	NOUN
ejde-388	167	72	.	.	PUNCT
ejde-388	168	1	the	the	DET
ejde-388	168	2	dash	dash	NOUN
ejde-388	168	3	curve	curve	NOUN
ejde-388	168	4	represents	represent	VERB
ejde-388	168	5	the	the	DET
ejde-388	168	6	analytically	analytically	ADV
ejde-388	168	7	obtained	obtain	VERB
ejde-388	168	8	lower	lower	ADV
ejde-388	168	9	bound	bind	VERB
ejde-388	168	10	(	(	PUNCT
ejde-388	168	11	5.3	5.3	NUM
ejde-388	168	12	)	)	PUNCT
ejde-388	168	13	on	on	ADP
ejde-388	168	14	the	the	DET
ejde-388	168	15	norm	norm	NOUN
ejde-388	168	16	of	of	ADP
ejde-388	168	17	the	the	DET
ejde-388	168	18	directional	directional	ADJ
ejde-388	168	19	derivative	derivative	NOUN
ejde-388	168	20	of	of	ADP
ejde-388	168	21	a	a	DET
ejde-388	168	22	family	family	NOUN
ejde-388	168	23	of	of	ADP
ejde-388	168	24	explicit	explicit	ADJ
ejde-388	168	25	solutions	solution	NOUN
ejde-388	168	26	,	,	PUNCT
ejde-388	168	27	where	where	SCONJ
ejde-388	168	28	γ	γ	X
ejde-388	168	29	=	=	SYM
ejde-388	168	30	0.6	0.6	NUM
ejde-388	168	31	and	and	CCONJ
ejde-388	168	32	σ	σ	NUM
ejde-388	168	33	=	=	SYM
ejde-388	168	34	27.5	27.5	NUM
ejde-388	168	35	are	be	AUX
ejde-388	168	36	chosen	choose	VERB
ejde-388	168	37	.	.	PUNCT
ejde-388	169	1	the	the	DET
ejde-388	169	2	solid	solid	ADJ
ejde-388	169	3	curve	curve	NOUN
ejde-388	169	4	represents	represent	VERB
ejde-388	169	5	the	the	DET
ejde-388	169	6	numerical	numerical	ADJ
ejde-388	169	7	simulation	simulation	NOUN
ejde-388	169	8	on	on	ADP
ejde-388	169	9	the	the	DET
ejde-388	169	10	norm	norm	NOUN
ejde-388	169	11	of	of	ADP
ejde-388	169	12	the	the	DET
ejde-388	169	13	directional	directional	ADJ
ejde-388	169	14	derivative	derivative	NOUN
ejde-388	169	15	of	of	ADP
ejde-388	169	16	the	the	DET
ejde-388	169	17	same	same	ADJ
ejde-388	169	18	family	family	NOUN
ejde-388	169	19	of	of	ADP
ejde-388	169	20	explicit	explicit	ADJ
ejde-388	169	21	solutions	solution	NOUN
ejde-388	169	22	.	.	PUNCT
ejde-388	170	1	one	one	PRON
ejde-388	170	2	can	can	AUX
ejde-388	170	3	see	see	VERB
ejde-388	170	4	clearly	clearly	ADV
ejde-388	170	5	that	that	SCONJ
ejde-388	170	6	near	near	ADP
ejde-388	170	7	t	t	PROPN
ejde-388	170	8	=	=	SYM
ejde-388	170	9	0	0	PROPN
ejde-388	170	10	,	,	PUNCT
ejde-388	170	11	the	the	DET
ejde-388	170	12	rigorous	rigorous	ADJ
ejde-388	170	13	lower	low	ADJ
ejde-388	170	14	bound	bind	VERB
ejde-388	170	15	is	be	AUX
ejde-388	170	16	violated	violate	VERB
ejde-388	170	17	.	.	PUNCT
ejde-388	171	1	in	in	ADP
ejde-388	171	2	particular	particular	ADJ
ejde-388	171	3	,	,	PUNCT
ejde-388	171	4	the	the	DET
ejde-388	171	5	dash	dash	NOUN
ejde-388	171	6	curve	curve	NOUN
ejde-388	171	7	has	have	AUX
ejde-388	171	8	infinite	infinite	ADJ
ejde-388	171	9	derivative	derivative	NOUN
ejde-388	171	10	at	at	ADP
ejde-388	171	11	t	t	PROPN
ejde-388	171	12	=	=	SYM
ejde-388	171	13	0	0	NUM
ejde-388	171	14	,	,	PUNCT
ejde-388	171	15	while	while	SCONJ
ejde-388	171	16	the	the	DET
ejde-388	171	17	solid	solid	ADJ
ejde-388	171	18	curve	curve	NOUN
ejde-388	171	19	has	have	AUX
ejde-388	171	20	finite	finite	VERB
ejde-388	171	21	derivative	derivative	NOUN
ejde-388	171	22	.	.	PUNCT
ejde-388	172	1	starting	start	VERB
ejde-388	172	2	from	from	ADP
ejde-388	172	3	this	this	DET
ejde-388	172	4	initial	initial	ADJ
ejde-388	172	5	condition	condition	NOUN
ejde-388	172	6	,	,	PUNCT
ejde-388	172	7	we	we	PRON
ejde-388	172	8	solve	solve	VERB
ejde-388	172	9	(	(	PUNCT
ejde-388	172	10	5.1	5.1	NUM
ejde-388	172	11	)	)	PUNCT
ejde-388	172	12	numerically	numerically	ADV
ejde-388	172	13	to	to	PART
ejde-388	172	14	generate	generate	VERB
ejde-388	172	15	the	the	DET
ejde-388	172	16	base	base	NOUN
ejde-388	172	17	solution	solution	NOUN
ejde-388	172	18	.	.	PUNCT
ejde-388	173	1	the	the	DET
ejde-388	173	2	perturbation	perturbation	NOUN
ejde-388	173	3	du	du	NOUN
ejde-388	173	4	based	base	VERB
ejde-388	173	5	upon	upon	SCONJ
ejde-388	173	6	a	a	DET
ejde-388	173	7	base	base	NOUN
ejde-388	173	8	solution	solution	NOUN
ejde-388	173	9	u	u	NOUN
ejde-388	173	10	solves	solve	VERB
ejde-388	173	11	the	the	DET
ejde-388	173	12	linearized	linearize	VERB
ejde-388	173	13	2d	2d	NUM
ejde-388	173	14	navier	navier	NOUN
ejde-388	173	15	-	-	PUNCT
ejde-388	173	16	stokes	stoke	NOUN
ejde-388	173	17	equations	equation	NOUN
ejde-388	173	18	,	,	PUNCT
ejde-388	173	19	∂tdu+	∂tdu+	PROPN
ejde-388	173	20	u	u	X
ejde-388	173	21	·	·	PUNCT
ejde-388	173	22	∇du+	∇du+	X
ejde-388	173	23	du	du	X
ejde-388	173	24	·	·	PUNCT
ejde-388	173	25	∇u	∇u	NOUN
ejde-388	173	26	=	=	PUNCT
ejde-388	173	27	−∇dp+	−∇dp+	PROPN
ejde-388	173	28	1	1	NUM
ejde-388	173	29	re	re	ADP
ejde-388	173	30	∆du	∆du	PROPN
ejde-388	173	31	,	,	PUNCT
ejde-388	173	32	∇	∇	X
ejde-388	173	33	·	·	PUNCT
ejde-388	173	34	du	du	X
ejde-388	173	35	=	=	SYM
ejde-388	173	36	0	0	PROPN
ejde-388	173	37	,	,	PUNCT
ejde-388	173	38	(	(	PUNCT
ejde-388	173	39	5.6	5.6	NUM
ejde-388	173	40	)	)	PUNCT
ejde-388	173	41	under	under	ADP
ejde-388	173	42	the	the	DET
ejde-388	173	43	same	same	ADJ
ejde-388	173	44	periodic	periodic	ADJ
ejde-388	173	45	boundary	boundary	ADJ
ejde-388	173	46	condition	condition	NOUN
ejde-388	173	47	as	as	ADP
ejde-388	173	48	in	in	ADP
ejde-388	173	49	(	(	PUNCT
ejde-388	173	50	5.1	5.1	NUM
ejde-388	173	51	)	)	PUNCT
ejde-388	173	52	.	.	PUNCT
ejde-388	174	1	since	since	SCONJ
ejde-388	174	2	(	(	PUNCT
ejde-388	174	3	5.6	5.6	NUM
ejde-388	174	4	)	)	PUNCT
ejde-388	174	5	is	be	AUX
ejde-388	174	6	linear	linear	ADJ
ejde-388	174	7	,	,	PUNCT
ejde-388	174	8	we	we	PRON
ejde-388	174	9	can	can	AUX
ejde-388	174	10	choose	choose	VERB
ejde-388	174	11	single	single	ADJ
ejde-388	174	12	fourier	fourier	NOUN
ejde-388	174	13	modes	mode	NOUN
ejde-388	174	14	as	as	ADP
ejde-388	174	15	the	the	DET
ejde-388	174	16	initial	initial	ADJ
ejde-388	174	17	conditions	condition	NOUN
ejde-388	174	18	of	of	ADP
ejde-388	174	19	the	the	DET
ejde-388	174	20	perturbations	perturbation	NOUN
ejde-388	174	21	,	,	PUNCT
ejde-388	174	22	du1(0	du1(0	NOUN
ejde-388	174	23	)	)	PUNCT
ejde-388	174	24	=	=	PUNCT
ejde-388	174	25	−0.1k2	−0.1k2	NOUN
ejde-388	174	26	sin(k1x1	sin(k1x1	NOUN
ejde-388	174	27	)	)	PUNCT
ejde-388	174	28	sin(k2x2	sin(k2x2	NOUN
ejde-388	174	29	)	)	PUNCT
ejde-388	174	30	,	,	PUNCT
ejde-388	174	31	du2(0	du2(0	NOUN
ejde-388	174	32	)	)	PUNCT
ejde-388	174	33	=	=	NUM
ejde-388	174	34	−0.1k1	−0.1k1	NOUN
ejde-388	174	35	cos(k1x1	cos(k1x1	NOUN
ejde-388	174	36	)	)	PUNCT
ejde-388	174	37	cos(k2x2	cos(k2x2	NOUN
ejde-388	174	38	)	)	PUNCT
ejde-388	174	39	.	.	PUNCT
ejde-388	175	1	(	(	PUNCT
ejde-388	175	2	5.7	5.7	NUM
ejde-388	175	3	)	)	PUNCT
ejde-388	175	4	figure	figure	NOUN
ejde-388	175	5	2	2	NUM
ejde-388	175	6	shows	show	VERB
ejde-388	175	7	the	the	DET
ejde-388	175	8	super	super	ADV
ejde-388	175	9	fast	fast	ADJ
ejde-388	175	10	growth	growth	NOUN
ejde-388	175	11	of	of	ADP
ejde-388	175	12	the	the	DET
ejde-388	175	13	perturbation	perturbation	NOUN
ejde-388	175	14	when	when	SCONJ
ejde-388	175	15	k1	k1	X
ejde-388	175	16	=	=	SYM
ejde-388	175	17	1	1	NUM
ejde-388	175	18	,	,	PUNCT
ejde-388	175	19	k2	k2	NOUN
ejde-388	175	20	=	=	SYM
ejde-388	175	21	1	1	NUM
ejde-388	175	22	,	,	PUNCT
ejde-388	175	23	re	re	ADP
ejde-388	175	24	=	=	NOUN
ejde-388	175	25	1000	1000	NUM
ejde-388	175	26	and	and	CCONJ
ejde-388	175	27	re	re	ADP
ejde-388	175	28	=	=	NOUN
ejde-388	175	29	100000	100000	NUM
ejde-388	175	30	,	,	PUNCT
ejde-388	175	31	(	(	PUNCT
ejde-388	175	32	5.8	5.8	NUM
ejde-388	175	33	)	)	PUNCT
ejde-388	175	34	where	where	SCONJ
ejde-388	175	35	the	the	DET
ejde-388	175	36	time	time	NOUN
ejde-388	175	37	step	step	NOUN
ejde-388	175	38	for	for	ADP
ejde-388	175	39	the	the	DET
ejde-388	175	40	numerical	numerical	PROPN
ejde-388	175	41	simulation	simulation	NOUN
ejde-388	175	42	is	be	AUX
ejde-388	175	43	∆t	∆t	PROPN
ejde-388	175	44	=	=	SYM
ejde-388	175	45	0.0005	0.0005	NUM
ejde-388	175	46	.	.	PUNCT
ejde-388	176	1	we	we	PRON
ejde-388	176	2	use	use	VERB
ejde-388	176	3	the	the	DET
ejde-388	176	4	notation	notation	NOUN
ejde-388	176	5	λ(t	λ(t	PROPN
ejde-388	176	6	)	)	PUNCT
ejde-388	176	7	=	=	SYM
ejde-388	176	8	‖du(t)‖h3	‖du(t)‖h3	PROPN
ejde-388	176	9	.	.	PUNCT
ejde-388	177	1	(	(	PUNCT
ejde-388	177	2	5.9	5.9	NUM
ejde-388	177	3	)	)	PUNCT
ejde-388	177	4	then	then	ADV
ejde-388	177	5	the	the	DET
ejde-388	177	6	norm	norm	NOUN
ejde-388	177	7	of	of	ADP
ejde-388	177	8	the	the	DET
ejde-388	177	9	derivative	derivative	NOUN
ejde-388	177	10	of	of	ADP
ejde-388	177	11	the	the	DET
ejde-388	177	12	solution	solution	NOUN
ejde-388	177	13	map	map	NOUN
ejde-388	177	14	at	at	ADP
ejde-388	177	15	the	the	DET
ejde-388	177	16	base	base	NOUN
ejde-388	177	17	solution	solution	NOUN
ejde-388	177	18	u(t	u(t	NOUN
ejde-388	177	19	)	)	PUNCT
ejde-388	177	20	is	be	AUX
ejde-388	177	21	given	give	VERB
ejde-388	177	22	by	by	ADP
ejde-388	177	23	‖dst(u(0))‖	‖dst(u(0))‖	X
ejde-388	177	24	=	=	SYM
ejde-388	177	25	sup	sup	PROPN
ejde-388	177	26	du(0	du(0	NOUN
ejde-388	177	27	)	)	PUNCT
ejde-388	177	28	λ(t	λ(t	NOUN
ejde-388	177	29	)	)	PUNCT
ejde-388	177	30	λ(0	λ(0	PROPN
ejde-388	177	31	)	)	PUNCT
ejde-388	177	32	.	.	PUNCT
ejde-388	178	1	(	(	PUNCT
ejde-388	178	2	5.10	5.10	NUM
ejde-388	178	3	)	)	PUNCT
ejde-388	178	4	note	note	VERB
ejde-388	178	5	that	that	SCONJ
ejde-388	178	6	for	for	ADP
ejde-388	178	7	any	any	DET
ejde-388	178	8	fixed	fixed	ADJ
ejde-388	178	9	t	t	PROPN
ejde-388	178	10	,	,	PUNCT
ejde-388	178	11	the	the	DET
ejde-388	178	12	supremum	supremum	NOUN
ejde-388	178	13	is	be	AUX
ejde-388	178	14	taken	take	VERB
ejde-388	178	15	with	with	ADP
ejde-388	178	16	respect	respect	NOUN
ejde-388	178	17	to	to	ADP
ejde-388	178	18	all	all	DET
ejde-388	178	19	initial	initial	ADJ
ejde-388	178	20	perturbation	perturbation	NOUN
ejde-388	178	21	du(0	du(0	NOUN
ejde-388	178	22	)	)	PUNCT
ejde-388	178	23	.	.	PUNCT
ejde-388	179	1	if	if	SCONJ
ejde-388	179	2	one	one	NUM
ejde-388	179	3	initial	initial	ADJ
ejde-388	179	4	perturbation	perturbation	NOUN
ejde-388	179	5	leads	lead	VERB
ejde-388	179	6	to	to	ADP
ejde-388	179	7	a	a	DET
ejde-388	179	8	perturbation	perturbation	NOUN
ejde-388	179	9	that	that	PRON
ejde-388	179	10	is	be	AUX
ejde-388	179	11	near	near	ADP
ejde-388	179	12	the	the	DET
ejde-388	179	13	supremum	supremum	NOUN
ejde-388	179	14	for	for	ADP
ejde-388	179	15	some	some	DET
ejde-388	179	16	t	t	PROPN
ejde-388	179	17	,	,	PUNCT
ejde-388	179	18	it	it	PRON
ejde-388	179	19	may	may	AUX
ejde-388	179	20	not	not	PART
ejde-388	179	21	be	be	AUX
ejde-388	179	22	near	near	ADP
ejde-388	179	23	the	the	DET
ejde-388	179	24	supremum	supremum	NOUN
ejde-388	179	25	for	for	ADP
ejde-388	179	26	other	other	ADJ
ejde-388	179	27	t.	t.	NOUN
ejde-388	179	28	the	the	DET
ejde-388	179	29	norm	norm	NOUN
ejde-388	179	30	of	of	ADP
ejde-388	179	31	the	the	DET
ejde-388	179	32	derivative	derivative	NOUN
ejde-388	179	33	‖dst(u(0))‖	‖dst(u(0))‖	X
ejde-388	179	34	has	have	VERB
ejde-388	179	35	an	an	DET
ejde-388	179	36	upper	upper	ADJ
ejde-388	179	37	bound	bind	VERB
ejde-388	179	38	given	give	VERB
ejde-388	179	39	by	by	ADP
ejde-388	179	40	(	(	PUNCT
ejde-388	179	41	3.3	3.3	NUM
ejde-388	179	42	)	)	PUNCT
ejde-388	179	43	.	.	PUNCT
ejde-388	180	1	we	we	PRON
ejde-388	180	2	anticipate	anticipate	VERB
ejde-388	180	3	that	that	SCONJ
ejde-388	180	4	the	the	DET
ejde-388	180	5	nature	nature	NOUN
ejde-388	180	6	of	of	ADP
ejde-388	180	7	the	the	DET
ejde-388	180	8	square	square	ADJ
ejde-388	180	9	root	root	NOUN
ejde-388	180	10	of	of	ADP
ejde-388	180	11	time	time	NOUN
ejde-388	180	12	in	in	ADP
ejde-388	180	13	the	the	DET
ejde-388	180	14	exponent	exponent	NOUN
ejde-388	180	15	of	of	ADP
ejde-388	180	16	the	the	DET
ejde-388	180	17	upper	upper	ADJ
ejde-388	180	18	bound	bound	ADJ
ejde-388	180	19	(	(	PUNCT
ejde-388	180	20	3.3	3.3	NUM
ejde-388	180	21	)	)	PUNCT
ejde-388	180	22	can	can	AUX
ejde-388	180	23	8	8	NUM
ejde-388	180	24	z.	z.	NOUN
ejde-388	180	25	feng	feng	PROPN
ejde-388	180	26	,	,	PUNCT
ejde-388	180	27	y.	y.	PROPN
ejde-388	180	28	c.	c.	PROPN
ejde-388	180	29	li	li	PROPN
ejde-388	181	1	ejde-2020/104	ejde-2020/104	PROPN
ejde-388	181	2	0	0	NUM
ejde-388	181	3	0.1	0.1	NUM
ejde-388	181	4	0.2	0.2	NUM
ejde-388	181	5	0.3	0.3	NUM
ejde-388	181	6	t	t	NOUN
ejde-388	181	7	0	0	NUM
ejde-388	181	8	0.5	0.5	NUM
ejde-388	181	9	1	1	NUM
ejde-388	181	10	1.5	1.5	NUM
ejde-388	181	11	2	2	NUM
ejde-388	181	12	λ	λ	NOUN
ejde-388	181	13	/λ	/λ	X
ejde-388	181	14	0	0	NUM
ejde-388	181	15	×10	×10	NOUN
ejde-388	181	16	5	5	NUM
ejde-388	181	17	0	0	NUM
ejde-388	181	18	0.1	0.1	NUM
ejde-388	181	19	0.2	0.2	NUM
ejde-388	181	20	0.3	0.3	NUM
ejde-388	181	21	t	t	NOUN
ejde-388	181	22	0	0	NUM
ejde-388	181	23	5	5	NUM
ejde-388	181	24	10	10	NUM
ejde-388	181	25	15	15	NUM
ejde-388	181	26	ln	ln	NOUN
ejde-388	181	27	(	(	PUNCT
ejde-388	181	28	λ	λ	NOUN
ejde-388	181	29	/λ	/λ	NOUN
ejde-388	181	30	0	0	NUM
ejde-388	181	31	)	)	PUNCT
ejde-388	181	32	(	(	PUNCT
ejde-388	181	33	a	a	X
ejde-388	181	34	)	)	PUNCT
ejde-388	181	35	re	re	NOUN
ejde-388	181	36	=	=	NOUN
ejde-388	181	37	1000	1000	NUM
ejde-388	181	38	(	(	PUNCT
ejde-388	181	39	b	b	NOUN
ejde-388	181	40	)	)	PUNCT
ejde-388	181	41	re	re	NOUN
ejde-388	181	42	=	=	NOUN
ejde-388	181	43	1000	1000	NUM
ejde-388	181	44	0	0	NUM
ejde-388	181	45	0.1	0.1	NUM
ejde-388	181	46	0.2	0.2	NUM
ejde-388	181	47	0.3	0.3	NUM
ejde-388	181	48	t	t	NOUN
ejde-388	181	49	0	0	NUM
ejde-388	181	50	0.5	0.5	NUM
ejde-388	181	51	1	1	NUM
ejde-388	181	52	1.5	1.5	NUM
ejde-388	181	53	2	2	NUM
ejde-388	181	54	λ	λ	NOUN
ejde-388	181	55	/λ	/λ	X
ejde-388	181	56	0	0	NUM
ejde-388	181	57	×10	×10	NOUN
ejde-388	181	58	5	5	NUM
ejde-388	181	59	0	0	NUM
ejde-388	181	60	0.1	0.1	NUM
ejde-388	181	61	0.2	0.2	NUM
ejde-388	181	62	0.3	0.3	NUM
ejde-388	181	63	t	t	NOUN
ejde-388	181	64	0	0	NUM
ejde-388	181	65	5	5	NUM
ejde-388	181	66	10	10	NUM
ejde-388	181	67	15	15	NUM
ejde-388	181	68	ln	ln	NOUN
ejde-388	181	69	(	(	PUNCT
ejde-388	181	70	λ	λ	NOUN
ejde-388	181	71	/λ	/λ	NOUN
ejde-388	181	72	0	0	NUM
ejde-388	181	73	)	)	PUNCT
ejde-388	181	74	(	(	PUNCT
ejde-388	181	75	c	c	X
ejde-388	181	76	)	)	PUNCT
ejde-388	181	77	re	re	NOUN
ejde-388	181	78	=	=	NOUN
ejde-388	181	79	100000	100000	NUM
ejde-388	181	80	(	(	PUNCT
ejde-388	181	81	d	d	NOUN
ejde-388	181	82	)	)	PUNCT
ejde-388	181	83	re	re	NOUN
ejde-388	181	84	=	=	NOUN
ejde-388	181	85	100000	100000	NUM
ejde-388	181	86	figure	figure	NOUN
ejde-388	181	87	2	2	NUM
ejde-388	181	88	.	.	PUNCT
ejde-388	182	1	the	the	DET
ejde-388	182	2	solid	solid	ADJ
ejde-388	182	3	curve	curve	NOUN
ejde-388	182	4	is	be	AUX
ejde-388	182	5	the	the	DET
ejde-388	182	6	numerical	numerical	ADJ
ejde-388	182	7	result	result	NOUN
ejde-388	182	8	of	of	ADP
ejde-388	182	9	the	the	DET
ejde-388	182	10	super	super	ADV
ejde-388	182	11	fast	fast	ADJ
ejde-388	182	12	growth	growth	NOUN
ejde-388	182	13	of	of	ADP
ejde-388	182	14	perturbations	perturbation	NOUN
ejde-388	182	15	with	with	ADP
ejde-388	182	16	initial	initial	ADJ
ejde-388	182	17	condition	condition	NOUN
ejde-388	182	18	(	(	PUNCT
ejde-388	182	19	5.7)-(5.8	5.7)-(5.8	NOUN
ejde-388	182	20	)	)	PUNCT
ejde-388	182	21	where	where	SCONJ
ejde-388	182	22	λ(t	λ(t	NOUN
ejde-388	182	23	)	)	PUNCT
ejde-388	182	24	=	=	SYM
ejde-388	182	25	‖du(t)‖h3	‖du(t)‖h3	PROPN
ejde-388	182	26	.	.	PUNCT
ejde-388	183	1	the	the	DET
ejde-388	183	2	lower	lower	ADV
ejde-388	183	3	fitting	fitting	ADJ
ejde-388	183	4	dashed	dash	VERB
ejde-388	183	5	curve	curve	NOUN
ejde-388	183	6	is	be	AUX
ejde-388	183	7	e21.2	e21.2	NOUN
ejde-388	183	8	√	√	NUM
ejde-388	183	9	t	t	NOUN
ejde-388	183	10	when	when	SCONJ
ejde-388	183	11	re	re	ADP
ejde-388	183	12	=	=	NOUN
ejde-388	183	13	1000	1000	NUM
ejde-388	183	14	and	and	CCONJ
ejde-388	183	15	e21.7	e21.7	PROPN
ejde-388	183	16	√	√	NUM
ejde-388	183	17	t	t	NOUN
ejde-388	183	18	when	when	SCONJ
ejde-388	183	19	re	re	ADP
ejde-388	183	20	=	=	NOUN
ejde-388	183	21	100000	100000	NUM
ejde-388	183	22	.	.	PUNCT
ejde-388	184	1	the	the	DET
ejde-388	184	2	closest	close	ADV
ejde-388	184	3	fitting	fitting	ADJ
ejde-388	184	4	dashed	dash	VERB
ejde-388	184	5	curve	curve	NOUN
ejde-388	184	6	is	be	AUX
ejde-388	184	7	e30	e30	ADJ
ejde-388	184	8	√	√	ADP
ejde-388	184	9	t	t	PROPN
ejde-388	184	10	when	when	SCONJ
ejde-388	184	11	re	re	ADP
ejde-388	184	12	=	=	NOUN
ejde-388	184	13	1000	1000	NUM
ejde-388	184	14	and	and	CCONJ
ejde-388	184	15	re	re	NOUN
ejde-388	184	16	=	=	NOUN
ejde-388	184	17	100000	100000	NUM
ejde-388	184	18	.	.	PUNCT
ejde-388	185	1	be	be	AUX
ejde-388	185	2	realized	realize	VERB
ejde-388	185	3	by	by	ADP
ejde-388	185	4	an	an	DET
ejde-388	185	5	individual	individual	ADJ
ejde-388	185	6	perturbation	perturbation	NOUN
ejde-388	185	7	,	,	PUNCT
ejde-388	185	8	while	while	SCONJ
ejde-388	185	9	the	the	DET
ejde-388	185	10	nature	nature	NOUN
ejde-388	185	11	of	of	ADP
ejde-388	185	12	the	the	DET
ejde-388	185	13	square	square	ADJ
ejde-388	185	14	root	root	NOUN
ejde-388	185	15	of	of	ADP
ejde-388	185	16	the	the	DET
ejde-388	185	17	reynolds	reynolds	PROPN
ejde-388	185	18	number	number	NOUN
ejde-388	185	19	can	can	AUX
ejde-388	185	20	only	only	ADV
ejde-388	185	21	be	be	AUX
ejde-388	185	22	realized	realize	VERB
ejde-388	185	23	by	by	ADP
ejde-388	185	24	the	the	DET
ejde-388	185	25	supremum	supremum	NOUN
ejde-388	185	26	over	over	ADP
ejde-388	185	27	a	a	DET
ejde-388	185	28	lot	lot	NOUN
ejde-388	185	29	of	of	ADP
ejde-388	185	30	perturbations	perturbation	NOUN
ejde-388	185	31	.	.	PUNCT
ejde-388	186	1	for	for	ADP
ejde-388	186	2	any	any	DET
ejde-388	186	3	particular	particular	ADJ
ejde-388	186	4	perturbation	perturbation	NOUN
ejde-388	186	5	,	,	PUNCT
ejde-388	186	6	the	the	DET
ejde-388	186	7	viscous	viscous	ADJ
ejde-388	186	8	effect	effect	NOUN
ejde-388	186	9	is	be	AUX
ejde-388	186	10	negligible	negligible	ADJ
ejde-388	186	11	when	when	SCONJ
ejde-388	186	12	the	the	DET
ejde-388	186	13	reynolds	reynolds	PROPN
ejde-388	186	14	number	number	NOUN
ejde-388	186	15	is	be	AUX
ejde-388	186	16	relatively	relatively	ADV
ejde-388	186	17	large	large	ADJ
ejde-388	186	18	.	.	PUNCT
ejde-388	187	1	on	on	ADP
ejde-388	187	2	the	the	DET
ejde-388	187	3	other	other	ADJ
ejde-388	187	4	hand	hand	NOUN
ejde-388	187	5	,	,	PUNCT
ejde-388	187	6	a	a	DET
ejde-388	187	7	generic	generic	ADJ
ejde-388	187	8	perturbation	perturbation	NOUN
ejde-388	187	9	in	in	ADP
ejde-388	187	10	physics	physics	NOUN
ejde-388	187	11	contains	contain	VERB
ejde-388	187	12	all	all	DET
ejde-388	187	13	“	"	PUNCT
ejde-388	187	14	basic	basic	ADJ
ejde-388	187	15	perturbation	perturbation	NOUN
ejde-388	187	16	directions	direction	NOUN
ejde-388	187	17	”	"	PUNCT
ejde-388	187	18	,	,	PUNCT
ejde-388	187	19	and	and	CCONJ
ejde-388	187	20	the	the	DET
ejde-388	187	21	fastest	fast	ADJ
ejde-388	187	22	growing	grow	VERB
ejde-388	187	23	direction	direction	NOUN
ejde-388	187	24	will	will	AUX
ejde-388	187	25	quickly	quickly	ADV
ejde-388	187	26	dominate	dominate	VERB
ejde-388	187	27	the	the	DET
ejde-388	187	28	amplification	amplification	NOUN
ejde-388	187	29	.	.	PUNCT
ejde-388	188	1	in	in	ADP
ejde-388	188	2	fact	fact	NOUN
ejde-388	188	3	,	,	PUNCT
ejde-388	188	4	the	the	DET
ejde-388	188	5	fastest	fast	ADJ
ejde-388	188	6	growing	grow	VERB
ejde-388	188	7	direction	direction	NOUN
ejde-388	188	8	may	may	AUX
ejde-388	188	9	change	change	VERB
ejde-388	188	10	in	in	ADP
ejde-388	188	11	time	time	NOUN
ejde-388	188	12	.	.	PUNCT
ejde-388	189	1	due	due	ADP
ejde-388	189	2	to	to	ADP
ejde-388	189	3	numerical	numerical	ADJ
ejde-388	189	4	obstacles	obstacle	NOUN
ejde-388	189	5	such	such	ADJ
ejde-388	189	6	as	as	ADP
ejde-388	189	7	that	that	PRON
ejde-388	189	8	demonstrated	demonstrate	VERB
ejde-388	189	9	in	in	ADP
ejde-388	189	10	figure	figure	NOUN
ejde-388	189	11	1	1	NUM
ejde-388	189	12	,	,	PUNCT
ejde-388	189	13	numerical	numerical	ADJ
ejde-388	189	14	simulations	simulation	NOUN
ejde-388	189	15	as	as	ADP
ejde-388	189	16	t→	t→	X
ejde-388	189	17	0	0	NUM
ejde-388	189	18	+	+	NUM
ejde-388	189	19	are	be	AUX
ejde-388	189	20	not	not	PART
ejde-388	189	21	quite	quite	ADV
ejde-388	189	22	reliable	reliable	ADJ
ejde-388	189	23	.	.	PUNCT
ejde-388	190	1	that	that	PRON
ejde-388	190	2	is	be	AUX
ejde-388	190	3	the	the	DET
ejde-388	190	4	reason	reason	NOUN
ejde-388	190	5	that	that	PRON
ejde-388	190	6	our	our	PRON
ejde-388	190	7	1	1	NUM
ejde-388	190	8	ln	ln	NOUN
ejde-388	190	9	t	t	PROPN
ejde-388	190	10	ln	ln	NOUN
ejde-388	190	11	ln	ln	PROPN
ejde-388	190	12	λ	λ	PROPN
ejde-388	190	13	λ0	λ0	NOUN
ejde-388	190	14	numerical	numerical	ADJ
ejde-388	190	15	simulations	simulation	NOUN
ejde-388	190	16	do	do	AUX
ejde-388	190	17	not	not	PART
ejde-388	190	18	converge	converge	VERB
ejde-388	190	19	to	to	ADP
ejde-388	190	20	a	a	DET
ejde-388	190	21	constant	constant	ADJ
ejde-388	190	22	.	.	PUNCT
ejde-388	191	1	nevertheless	nevertheless	ADV
ejde-388	191	2	,	,	PUNCT
ejde-388	191	3	in	in	ADP
ejde-388	191	4	appropriate	appropriate	ADJ
ejde-388	191	5	time	time	NOUN
ejde-388	191	6	interval	interval	NOUN
ejde-388	191	7	,	,	PUNCT
ejde-388	191	8	we	we	PRON
ejde-388	191	9	are	be	AUX
ejde-388	191	10	confident	confident	ADJ
ejde-388	191	11	that	that	SCONJ
ejde-388	191	12	our	our	PRON
ejde-388	191	13	numerical	numerical	ADJ
ejde-388	191	14	simulations	simulation	NOUN
ejde-388	191	15	clearly	clearly	ADV
ejde-388	191	16	show	show	VERB
ejde-388	191	17	super	super	ADJ
ejde-388	191	18	fast	fast	ADJ
ejde-388	191	19	growth	growth	NOUN
ejde-388	191	20	(	(	PUNCT
ejde-388	191	21	faster	fast	ADJ
ejde-388	191	22	than	than	ADP
ejde-388	191	23	exponential	exponential	ADJ
ejde-388	191	24	growth	growth	NOUN
ejde-388	191	25	)	)	PUNCT
ejde-388	191	26	as	as	SCONJ
ejde-388	191	27	demonstrated	demonstrate	VERB
ejde-388	191	28	in	in	ADP
ejde-388	191	29	figure	figure	NOUN
ejde-388	191	30	2	2	NUM
ejde-388	191	31	.	.	PUNCT
ejde-388	191	32	increasing	increase	VERB
ejde-388	191	33	the	the	DET
ejde-388	191	34	wave	wave	NOUN
ejde-388	191	35	number	number	NOUN
ejde-388	191	36	(	(	PUNCT
ejde-388	191	37	k1	k1	NOUN
ejde-388	191	38	,	,	PUNCT
ejde-388	191	39	k2	k2	NOUN
ejde-388	191	40	)	)	PUNCT
ejde-388	191	41	,	,	PUNCT
ejde-388	191	42	the	the	DET
ejde-388	191	43	perturbation	perturbation	NOUN
ejde-388	191	44	’s	’s	PART
ejde-388	191	45	growth	growth	NOUN
ejde-388	191	46	rate	rate	NOUN
ejde-388	191	47	decreases	decrease	NOUN
ejde-388	191	48	as	as	SCONJ
ejde-388	191	49	shown	show	VERB
ejde-388	191	50	in	in	ADP
ejde-388	191	51	figures	figure	NOUN
ejde-388	191	52	3	3	NUM
ejde-388	191	53	4	4	NUM
ejde-388	191	54	.	.	PUNCT
ejde-388	192	1	when	when	SCONJ
ejde-388	192	2	the	the	DET
ejde-388	192	3	wave	wave	NOUN
ejde-388	192	4	number	number	NOUN
ejde-388	192	5	of	of	ADP
ejde-388	192	6	the	the	DET
ejde-388	192	7	initial	initial	ADJ
ejde-388	192	8	perturbation	perturbation	NOUN
ejde-388	192	9	is	be	AUX
ejde-388	192	10	larger	large	ADJ
ejde-388	192	11	,	,	PUNCT
ejde-388	192	12	the	the	DET
ejde-388	192	13	viscous	viscous	ADJ
ejde-388	192	14	effect	effect	NOUN
ejde-388	192	15	is	be	AUX
ejde-388	192	16	more	more	ADV
ejde-388	192	17	significant	significant	ADJ
ejde-388	192	18	.	.	PUNCT
ejde-388	193	1	our	our	PRON
ejde-388	193	2	conclusion	conclusion	NOUN
ejde-388	193	3	is	be	AUX
ejde-388	193	4	that	that	SCONJ
ejde-388	193	5	the	the	DET
ejde-388	193	6	super	super	ADV
ejde-388	193	7	fast	fast	ADJ
ejde-388	193	8	growth	growth	NOUN
ejde-388	193	9	(	(	PUNCT
ejde-388	193	10	rough	rough	ADJ
ejde-388	193	11	dependence	dependence	NOUN
ejde-388	193	12	)	)	PUNCT
ejde-388	193	13	is	be	AUX
ejde-388	193	14	abundant	abundant	ADJ
ejde-388	193	15	among	among	ADP
ejde-388	193	16	perturbations	perturbation	NOUN
ejde-388	193	17	in	in	ADP
ejde-388	193	18	the	the	DET
ejde-388	193	19	sense	sense	NOUN
ejde-388	193	20	that	that	SCONJ
ejde-388	193	21	generic	generic	ADJ
ejde-388	193	22	perturbations	perturbation	NOUN
ejde-388	193	23	contain	contain	VERB
ejde-388	193	24	all	all	DET
ejde-388	193	25	fourier	fourier	NOUN
ejde-388	193	26	modes	mode	NOUN
ejde-388	193	27	,	,	PUNCT
ejde-388	193	28	and	and	CCONJ
ejde-388	193	29	low	low	ADJ
ejde-388	193	30	fourier	fourier	NOUN
ejde-388	193	31	modes	mode	NOUN
ejde-388	193	32	display	display	VERB
ejde-388	193	33	the	the	DET
ejde-388	193	34	super	super	ADV
ejde-388	193	35	fast	fast	ADJ
ejde-388	193	36	growth	growth	NOUN
ejde-388	193	37	.	.	PUNCT
ejde-388	194	1	next	next	ADV
ejde-388	194	2	we	we	PRON
ejde-388	194	3	shall	shall	AUX
ejde-388	194	4	study	study	VERB
ejde-388	194	5	the	the	DET
ejde-388	194	6	abundance	abundance	NOUN
ejde-388	194	7	of	of	ADP
ejde-388	194	8	the	the	DET
ejde-388	194	9	super	super	ADV
ejde-388	194	10	fast	fast	ADJ
ejde-388	194	11	growth	growth	NOUN
ejde-388	194	12	among	among	ADP
ejde-388	194	13	base	base	NOUN
ejde-388	194	14	solutions	solution	NOUN
ejde-388	194	15	,	,	PUNCT
ejde-388	194	16	that	that	ADV
ejde-388	194	17	is	is	ADV
ejde-388	194	18	,	,	PUNCT
ejde-388	194	19	whether	whether	SCONJ
ejde-388	194	20	or	or	CCONJ
ejde-388	194	21	not	not	PART
ejde-388	194	22	there	there	PRON
ejde-388	194	23	are	be	VERB
ejde-388	194	24	abundant	abundant	ADJ
ejde-388	194	25	base	base	NOUN
ejde-388	194	26	solutions	solution	NOUN
ejde-388	194	27	of	of	ADP
ejde-388	194	28	which	which	PRON
ejde-388	194	29	the	the	DET
ejde-388	194	30	perturbations	perturbation	NOUN
ejde-388	194	31	have	have	VERB
ejde-388	194	32	super	super	ADJ
ejde-388	194	33	fast	fast	ADJ
ejde-388	194	34	growth	growth	NOUN
ejde-388	194	35	.	.	PUNCT
ejde-388	195	1	ejde-2020/104	ejde-2020/104	X
ejde-388	195	2	short	short	ADJ
ejde-388	195	3	term	term	NOUN
ejde-388	195	4	unpredictability	unpredictability	NOUN
ejde-388	195	5	9	9	NUM
ejde-388	195	6	0	0	NUM
ejde-388	195	7	0.1	0.1	NUM
ejde-388	195	8	0.2	0.2	NUM
ejde-388	195	9	0.3	0.3	NUM
ejde-388	195	10	t	t	NOUN
ejde-388	195	11	0	0	NUM
ejde-388	195	12	5	5	NUM
ejde-388	195	13	10	10	NUM
ejde-388	195	14	15	15	NUM
ejde-388	195	15	ln	ln	NOUN
ejde-388	195	16	(	(	PUNCT
ejde-388	195	17	λ	λ	NOUN
ejde-388	195	18	/λ	/λ	NOUN
ejde-388	195	19	0	0	NUM
ejde-388	195	20	)	)	PUNCT
ejde-388	195	21	0	0	NUM
ejde-388	195	22	0.1	0.1	NUM
ejde-388	195	23	0.2	0.2	NUM
ejde-388	195	24	0.3	0.3	NUM
ejde-388	195	25	t	t	NOUN
ejde-388	195	26	0	0	NUM
ejde-388	195	27	5	5	NUM
ejde-388	195	28	10	10	NUM
ejde-388	195	29	15	15	NUM
ejde-388	195	30	ln	ln	NOUN
ejde-388	195	31	(	(	PUNCT
ejde-388	195	32	λ	λ	NOUN
ejde-388	195	33	/λ	/λ	NOUN
ejde-388	195	34	0	0	NUM
ejde-388	195	35	)	)	PUNCT
ejde-388	195	36	(	(	PUNCT
ejde-388	195	37	a	a	X
ejde-388	195	38	)	)	PUNCT
ejde-388	195	39	re	re	NOUN
ejde-388	195	40	=	=	NOUN
ejde-388	195	41	1000	1000	NUM
ejde-388	195	42	,	,	PUNCT
ejde-388	195	43	k1	k1	NOUN
ejde-388	195	44	=	=	SYM
ejde-388	195	45	k2	k2	NOUN
ejde-388	195	46	=	=	SYM
ejde-388	195	47	1	1	NUM
ejde-388	195	48	(	(	PUNCT
ejde-388	195	49	b	b	NOUN
ejde-388	195	50	)	)	PUNCT
ejde-388	195	51	re	re	NOUN
ejde-388	195	52	=	=	NOUN
ejde-388	195	53	1000	1000	NUM
ejde-388	195	54	,	,	PUNCT
ejde-388	195	55	k1	k1	NOUN
ejde-388	195	56	=	=	SYM
ejde-388	195	57	k2	k2	NOUN
ejde-388	195	58	=	=	NOUN
ejde-388	195	59	2	2	NUM
ejde-388	195	60	0	0	NUM
ejde-388	195	61	0.1	0.1	NUM
ejde-388	195	62	0.2	0.2	NUM
ejde-388	195	63	0.3	0.3	NUM
ejde-388	195	64	t	t	NOUN
ejde-388	195	65	0	0	NUM
ejde-388	195	66	5	5	NUM
ejde-388	195	67	10	10	NUM
ejde-388	195	68	15	15	NUM
ejde-388	195	69	ln	ln	NOUN
ejde-388	195	70	(	(	PUNCT
ejde-388	195	71	λ	λ	NOUN
ejde-388	195	72	/λ	/λ	NOUN
ejde-388	195	73	0	0	NUM
ejde-388	195	74	)	)	PUNCT
ejde-388	195	75	0	0	NUM
ejde-388	195	76	0.1	0.1	NUM
ejde-388	195	77	0.2	0.2	NUM
ejde-388	195	78	0.3	0.3	NUM
ejde-388	195	79	t	t	NOUN
ejde-388	195	80	0	0	NUM
ejde-388	195	81	5	5	NUM
ejde-388	195	82	10	10	NUM
ejde-388	195	83	15	15	NUM
ejde-388	195	84	ln	ln	NOUN
ejde-388	195	85	(	(	PUNCT
ejde-388	195	86	λ	λ	NOUN
ejde-388	195	87	/λ	/λ	NOUN
ejde-388	195	88	0	0	NUM
ejde-388	195	89	)	)	PUNCT
ejde-388	195	90	(	(	PUNCT
ejde-388	195	91	c	c	X
ejde-388	195	92	)	)	PUNCT
ejde-388	195	93	re	re	NOUN
ejde-388	195	94	=	=	NOUN
ejde-388	195	95	1000	1000	NUM
ejde-388	195	96	,	,	PUNCT
ejde-388	195	97	k1	k1	NOUN
ejde-388	195	98	=	=	SYM
ejde-388	195	99	k2	k2	NOUN
ejde-388	195	100	=	=	SYM
ejde-388	195	101	3	3	NUM
ejde-388	195	102	(	(	PUNCT
ejde-388	195	103	d	d	NOUN
ejde-388	195	104	)	)	PUNCT
ejde-388	195	105	re	re	NOUN
ejde-388	195	106	=	=	NOUN
ejde-388	195	107	1000	1000	NUM
ejde-388	195	108	,	,	PUNCT
ejde-388	195	109	k1	k1	NOUN
ejde-388	195	110	=	=	SYM
ejde-388	195	111	k2	k2	NOUN
ejde-388	195	112	=	=	SYM
ejde-388	195	113	4	4	NUM
ejde-388	195	114	figure	figure	NOUN
ejde-388	195	115	3	3	NUM
ejde-388	195	116	.	.	PUNCT
ejde-388	196	1	the	the	DET
ejde-388	196	2	solid	solid	ADJ
ejde-388	196	3	curve	curve	NOUN
ejde-388	196	4	is	be	AUX
ejde-388	196	5	the	the	DET
ejde-388	196	6	numerical	numerical	ADJ
ejde-388	196	7	result	result	NOUN
ejde-388	196	8	of	of	ADP
ejde-388	196	9	the	the	DET
ejde-388	196	10	super	super	ADV
ejde-388	196	11	fast	fast	ADJ
ejde-388	196	12	growth	growth	NOUN
ejde-388	196	13	of	of	ADP
ejde-388	196	14	perturbations	perturbation	NOUN
ejde-388	196	15	with	with	ADP
ejde-388	196	16	initial	initial	ADJ
ejde-388	196	17	condition	condition	NOUN
ejde-388	196	18	(	(	PUNCT
ejde-388	196	19	5.7	5.7	NUM
ejde-388	196	20	)	)	PUNCT
ejde-388	196	21	with	with	ADP
ejde-388	196	22	different	different	ADJ
ejde-388	196	23	(	(	PUNCT
ejde-388	196	24	k1	k1	NOUN
ejde-388	196	25	,	,	PUNCT
ejde-388	196	26	k2	k2	NOUN
ejde-388	196	27	)	)	PUNCT
ejde-388	196	28	where	where	SCONJ
ejde-388	196	29	λ(t	λ(t	NOUN
ejde-388	196	30	)	)	PUNCT
ejde-388	196	31	=	=	SYM
ejde-388	196	32	‖du(t)‖h3	‖du(t)‖h3	PROPN
ejde-388	196	33	.	.	PUNCT
ejde-388	197	1	the	the	DET
ejde-388	197	2	fitting	fitting	ADJ
ejde-388	197	3	dashed	dash	VERB
ejde-388	197	4	curve	curve	NOUN
ejde-388	197	5	is	be	AUX
ejde-388	197	6	e21.2	e21.2	NOUN
ejde-388	197	7	√	√	ADJ
ejde-388	197	8	t.	t.	NOUN
ejde-388	197	9	5.3	5.3	NUM
ejde-388	197	10	.	.	PUNCT
ejde-388	198	1	fixed	fix	VERB
ejde-388	198	2	perturbation	perturbation	NOUN
ejde-388	198	3	and	and	CCONJ
ejde-388	198	4	different	different	ADJ
ejde-388	198	5	base	base	NOUN
ejde-388	198	6	solutions	solution	NOUN
ejde-388	198	7	.	.	PUNCT
ejde-388	199	1	our	our	PRON
ejde-388	199	2	goal	goal	NOUN
ejde-388	199	3	here	here	ADV
ejde-388	199	4	is	be	AUX
ejde-388	199	5	to	to	PART
ejde-388	199	6	show	show	VERB
ejde-388	199	7	that	that	SCONJ
ejde-388	199	8	the	the	DET
ejde-388	199	9	super	super	ADV
ejde-388	199	10	fast	fast	ADJ
ejde-388	199	11	amplification	amplification	NOUN
ejde-388	199	12	of	of	ADP
ejde-388	199	13	perturbations	perturbation	NOUN
ejde-388	199	14	is	be	AUX
ejde-388	199	15	abundant	abundant	ADJ
ejde-388	199	16	among	among	ADP
ejde-388	199	17	base	base	NOUN
ejde-388	199	18	solutions	solution	NOUN
ejde-388	199	19	.	.	PUNCT
ejde-388	200	1	for	for	ADP
ejde-388	200	2	this	this	DET
ejde-388	200	3	goal	goal	NOUN
ejde-388	200	4	,	,	PUNCT
ejde-388	200	5	we	we	PRON
ejde-388	200	6	will	will	AUX
ejde-388	200	7	again	again	ADV
ejde-388	200	8	choose	choose	VERB
ejde-388	200	9	the	the	DET
ejde-388	200	10	initial	initial	ADJ
ejde-388	200	11	conditions	condition	NOUN
ejde-388	200	12	of	of	ADP
ejde-388	200	13	the	the	DET
ejde-388	200	14	base	base	NOUN
ejde-388	200	15	solutions	solution	NOUN
ejde-388	200	16	and	and	CCONJ
ejde-388	200	17	the	the	DET
ejde-388	200	18	perturbation	perturbation	NOUN
ejde-388	200	19	,	,	PUNCT
ejde-388	200	20	to	to	PART
ejde-388	200	21	be	be	AUX
ejde-388	200	22	of	of	ADP
ejde-388	200	23	the	the	DET
ejde-388	200	24	form	form	NOUN
ejde-388	200	25	of	of	ADP
ejde-388	200	26	single	single	ADJ
ejde-388	200	27	fourier	fourier	NOUN
ejde-388	200	28	modes	mode	NOUN
ejde-388	200	29	.	.	PUNCT
ejde-388	201	1	first	first	ADV
ejde-388	201	2	we	we	PRON
ejde-388	201	3	fix	fix	VERB
ejde-388	201	4	the	the	DET
ejde-388	201	5	initial	initial	ADJ
ejde-388	201	6	condition	condition	NOUN
ejde-388	201	7	of	of	ADP
ejde-388	201	8	the	the	DET
ejde-388	201	9	perturbation	perturbation	NOUN
ejde-388	201	10	to	to	PART
ejde-388	201	11	be	be	AUX
ejde-388	201	12	the	the	DET
ejde-388	201	13	case	case	NOUN
ejde-388	201	14	of	of	ADP
ejde-388	201	15	k1	k1	NOUN
ejde-388	201	16	=	=	SYM
ejde-388	201	17	1	1	NUM
ejde-388	201	18	and	and	CCONJ
ejde-388	201	19	k2	k2	NOUN
ejde-388	201	20	=	=	NOUN
ejde-388	201	21	1	1	NUM
ejde-388	201	22	in	in	ADP
ejde-388	201	23	(	(	PUNCT
ejde-388	201	24	5.7	5.7	NUM
ejde-388	201	25	)	)	PUNCT
ejde-388	201	26	,	,	PUNCT
ejde-388	201	27	and	and	CCONJ
ejde-388	201	28	the	the	DET
ejde-388	201	29	reynolds	reynolds	PROPN
ejde-388	201	30	number	number	NOUN
ejde-388	201	31	re	re	NOUN
ejde-388	201	32	=	=	NOUN
ejde-388	201	33	1000	1000	NUM
ejde-388	201	34	.	.	PUNCT
ejde-388	202	1	then	then	ADV
ejde-388	202	2	we	we	PRON
ejde-388	202	3	simulate	simulate	VERB
ejde-388	202	4	different	different	ADJ
ejde-388	202	5	base	base	NOUN
ejde-388	202	6	solutions	solution	NOUN
ejde-388	202	7	with	with	ADP
ejde-388	202	8	initial	initial	ADJ
ejde-388	202	9	conditions	condition	NOUN
ejde-388	202	10	of	of	ADP
ejde-388	202	11	the	the	DET
ejde-388	202	12	form	form	NOUN
ejde-388	202	13	,	,	PUNCT
ejde-388	202	14	u1(0	u1(0	PROPN
ejde-388	202	15	)	)	PUNCT
ejde-388	202	16	=	=	PUNCT
ejde-388	203	1	−k2	−k2	PROPN
ejde-388	203	2	sin(k1x1	sin(k1x1	NOUN
ejde-388	203	3	)	)	PUNCT
ejde-388	203	4	sin(k2x2	sin(k2x2	NOUN
ejde-388	203	5	)	)	PUNCT
ejde-388	203	6	,	,	PUNCT
ejde-388	203	7	u2(0	u2(0	NOUN
ejde-388	203	8	)	)	PUNCT
ejde-388	203	9	=	=	SYM
ejde-388	203	10	−k1	−k1	NOUN
ejde-388	203	11	cos(k1x1	cos(k1x1	NOUN
ejde-388	203	12	)	)	PUNCT
ejde-388	203	13	cos(k2x2	cos(k2x2	NOUN
ejde-388	203	14	)	)	PUNCT
ejde-388	203	15	.	.	PUNCT
ejde-388	204	1	(	(	PUNCT
ejde-388	204	2	5.11	5.11	NUM
ejde-388	204	3	)	)	PUNCT
ejde-388	204	4	for	for	ADP
ejde-388	204	5	several	several	ADJ
ejde-388	204	6	choices	choice	NOUN
ejde-388	204	7	of	of	ADP
ejde-388	204	8	(	(	PUNCT
ejde-388	204	9	k1	k1	NOUN
ejde-388	204	10	,	,	PUNCT
ejde-388	204	11	k2	k2	NOUN
ejde-388	204	12	)	)	PUNCT
ejde-388	204	13	,	,	PUNCT
ejde-388	204	14	the	the	DET
ejde-388	204	15	super	super	ADJ
ejde-388	204	16	fast	fast	ADJ
ejde-388	204	17	growths	growth	NOUN
ejde-388	204	18	are	be	AUX
ejde-388	204	19	shown	show	VERB
ejde-388	204	20	in	in	ADP
ejde-388	204	21	figures	figure	NOUN
ejde-388	204	22	5	5	NUM
ejde-388	204	23	-	-	SYM
ejde-388	204	24	6	6	NUM
ejde-388	204	25	.	.	PUNCT
ejde-388	205	1	as	as	ADP
ejde-388	205	2	the	the	DET
ejde-388	205	3	wave	wave	NOUN
ejde-388	205	4	numbers	number	NOUN
ejde-388	205	5	(	(	PUNCT
ejde-388	205	6	k1	k1	NOUN
ejde-388	205	7	,	,	PUNCT
ejde-388	205	8	k2	k2	NOUN
ejde-388	205	9	)	)	PUNCT
ejde-388	205	10	of	of	ADP
ejde-388	205	11	the	the	DET
ejde-388	205	12	base	base	NOUN
ejde-388	205	13	solutions	solution	NOUN
ejde-388	205	14	decrease	decrease	NOUN
ejde-388	205	15	,	,	PUNCT
ejde-388	205	16	the	the	DET
ejde-388	205	17	super	super	ADV
ejde-388	205	18	fast	fast	ADJ
ejde-388	205	19	growth	growth	NOUN
ejde-388	205	20	rates	rate	NOUN
ejde-388	205	21	of	of	ADP
ejde-388	205	22	the	the	DET
ejde-388	205	23	perturbation	perturbation	NOUN
ejde-388	205	24	decrease	decrease	NOUN
ejde-388	205	25	.	.	PUNCT
ejde-388	206	1	together	together	ADV
ejde-388	206	2	with	with	ADP
ejde-388	206	3	the	the	DET
ejde-388	206	4	result	result	NOUN
ejde-388	206	5	of	of	ADP
ejde-388	206	6	last	last	ADJ
ejde-388	206	7	subsection	subsection	NOUN
ejde-388	206	8	,	,	PUNCT
ejde-388	206	9	we	we	PRON
ejde-388	206	10	conclude	conclude	VERB
ejde-388	206	11	that	that	SCONJ
ejde-388	206	12	higher	high	ADJ
ejde-388	206	13	wave	wave	NOUN
ejde-388	206	14	number	number	NOUN
ejde-388	206	15	base	base	NOUN
ejde-388	206	16	solutions	solution	NOUN
ejde-388	206	17	and	and	CCONJ
ejde-388	206	18	lower	low	ADJ
ejde-388	206	19	wave	wave	NOUN
ejde-388	206	20	number	number	NOUN
ejde-388	206	21	perturbations	perturbation	NOUN
ejde-388	206	22	correspond	correspond	VERB
ejde-388	206	23	to	to	ADP
ejde-388	206	24	faster	fast	ADV
ejde-388	206	25	super	super	ADV
ejde-388	206	26	fast	fast	ADJ
ejde-388	206	27	growth	growth	NOUN
ejde-388	206	28	of	of	ADP
ejde-388	206	29	the	the	DET
ejde-388	206	30	perturbations	perturbation	NOUN
ejde-388	206	31	.	.	PUNCT
ejde-388	207	1	numerical	numerical	ADJ
ejde-388	207	2	simulations	simulation	NOUN
ejde-388	207	3	on	on	ADP
ejde-388	207	4	other	other	ADJ
ejde-388	207	5	base	base	NOUN
ejde-388	207	6	solutions	solution	NOUN
ejde-388	207	7	also	also	ADV
ejde-388	207	8	show	show	VERB
ejde-388	207	9	super	super	ADJ
ejde-388	207	10	fast	fast	ADJ
ejde-388	207	11	growth	growth	NOUN
ejde-388	207	12	of	of	ADP
ejde-388	207	13	the	the	DET
ejde-388	207	14	perturbations	perturbation	NOUN
ejde-388	207	15	.	.	PUNCT
ejde-388	208	1	thus	thus	ADV
ejde-388	208	2	super	sup	ADJ
ejde-388	208	3	fast	fast	ADJ
ejde-388	208	4	growth	growth	NOUN
ejde-388	208	5	of	of	ADP
ejde-388	208	6	the	the	DET
ejde-388	208	7	perturbations	perturbation	NOUN
ejde-388	208	8	(	(	PUNCT
ejde-388	208	9	rough	rough	ADJ
ejde-388	208	10	dependence	dependence	NOUN
ejde-388	208	11	)	)	PUNCT
ejde-388	208	12	is	be	AUX
ejde-388	208	13	also	also	ADV
ejde-388	208	14	abundant	abundant	ADJ
ejde-388	208	15	among	among	ADP
ejde-388	208	16	base	base	NOUN
ejde-388	208	17	solutions	solution	NOUN
ejde-388	208	18	.	.	PUNCT
ejde-388	209	1	one	one	PRON
ejde-388	209	2	can	can	AUX
ejde-388	209	3	then	then	ADV
ejde-388	209	4	envision	envision	VERB
ejde-388	209	5	that	that	SCONJ
ejde-388	209	6	when	when	SCONJ
ejde-388	209	7	the	the	DET
ejde-388	209	8	reynolds	reynolds	PROPN
ejde-388	209	9	number	number	NOUN
ejde-388	209	10	is	be	AUX
ejde-388	209	11	large	large	ADJ
ejde-388	209	12	,	,	PUNCT
ejde-388	209	13	the	the	DET
ejde-388	209	14	super	super	ADV
ejde-388	209	15	fast	fast	ADJ
ejde-388	209	16	growth	growth	NOUN
ejde-388	209	17	of	of	ADP
ejde-388	209	18	the	the	DET
ejde-388	209	19	ever	ever	ADV
ejde-388	209	20	present	present	ADJ
ejde-388	209	21	perturbations	perturbation	NOUN
ejde-388	209	22	will	will	AUX
ejde-388	209	23	cause	cause	VERB
ejde-388	209	24	the	the	DET
ejde-388	209	25	abrupt	abrupt	ADJ
ejde-388	209	26	development	development	NOUN
ejde-388	209	27	of	of	ADP
ejde-388	209	28	turbulence	turbulence	NOUN
ejde-388	209	29	,	,	PUNCT
ejde-388	209	30	and	and	CCONJ
ejde-388	209	31	is	be	AUX
ejde-388	209	32	the	the	DET
ejde-388	209	33	mechanism	mechanism	NOUN
ejde-388	209	34	that	that	PRON
ejde-388	209	35	maintains	maintain	VERB
ejde-388	209	36	the	the	DET
ejde-388	209	37	persistence	persistence	NOUN
ejde-388	209	38	of	of	ADP
ejde-388	209	39	turbulence	turbulence	NOUN
ejde-388	209	40	(	(	PUNCT
ejde-388	209	41	the	the	DET
ejde-388	209	42	so	so	ADV
ejde-388	209	43	called	call	VERB
ejde-388	209	44	fully	fully	ADV
ejde-388	209	45	developed	develop	VERB
ejde-388	209	46	turbulence	turbulence	NOUN
ejde-388	209	47	)	)	PUNCT
ejde-388	209	48	.	.	PUNCT
ejde-388	210	1	10	10	NUM
ejde-388	210	2	z.	z.	PROPN
ejde-388	210	3	feng	feng	PROPN
ejde-388	210	4	,	,	PUNCT
ejde-388	210	5	y.	y.	PROPN
ejde-388	210	6	c.	c.	PROPN
ejde-388	210	7	li	li	PROPN
ejde-388	211	1	ejde-2020/104	ejde-2020/104	PROPN
ejde-388	211	2	0	0	NUM
ejde-388	211	3	0.1	0.1	NUM
ejde-388	211	4	0.2	0.2	NUM
ejde-388	211	5	0.3	0.3	NUM
ejde-388	211	6	t	t	NOUN
ejde-388	211	7	0	0	NUM
ejde-388	211	8	5	5	NUM
ejde-388	211	9	10	10	NUM
ejde-388	211	10	15	15	NUM
ejde-388	211	11	ln	ln	NOUN
ejde-388	211	12	(	(	PUNCT
ejde-388	211	13	λ	λ	NOUN
ejde-388	211	14	/λ	/λ	NOUN
ejde-388	211	15	0	0	NUM
ejde-388	211	16	)	)	PUNCT
ejde-388	211	17	0	0	NUM
ejde-388	211	18	0.1	0.1	NUM
ejde-388	211	19	0.2	0.2	NUM
ejde-388	211	20	0.3	0.3	NUM
ejde-388	211	21	t	t	NOUN
ejde-388	211	22	0	0	NUM
ejde-388	211	23	5	5	NUM
ejde-388	211	24	10	10	NUM
ejde-388	211	25	15	15	NUM
ejde-388	211	26	ln	ln	NOUN
ejde-388	211	27	(	(	PUNCT
ejde-388	211	28	λ	λ	NOUN
ejde-388	211	29	/λ	/λ	NOUN
ejde-388	211	30	0	0	NUM
ejde-388	211	31	)	)	PUNCT
ejde-388	211	32	(	(	PUNCT
ejde-388	211	33	a	a	X
ejde-388	211	34	)	)	PUNCT
ejde-388	211	35	re	re	NOUN
ejde-388	211	36	=	=	NOUN
ejde-388	211	37	1000	1000	NUM
ejde-388	211	38	,	,	PUNCT
ejde-388	211	39	k1	k1	NOUN
ejde-388	211	40	=	=	SYM
ejde-388	211	41	k2	k2	NOUN
ejde-388	211	42	=	=	SYM
ejde-388	211	43	5	5	NUM
ejde-388	211	44	(	(	PUNCT
ejde-388	211	45	b	b	NOUN
ejde-388	211	46	)	)	PUNCT
ejde-388	211	47	re	re	NOUN
ejde-388	211	48	=	=	NOUN
ejde-388	211	49	1000	1000	NUM
ejde-388	211	50	,	,	PUNCT
ejde-388	211	51	k1	k1	NOUN
ejde-388	211	52	=	=	SYM
ejde-388	211	53	k2	k2	NOUN
ejde-388	211	54	=	=	NOUN
ejde-388	211	55	6	6	NUM
ejde-388	211	56	0	0	NUM
ejde-388	211	57	0.1	0.1	NUM
ejde-388	211	58	0.2	0.2	NUM
ejde-388	211	59	0.3	0.3	NUM
ejde-388	211	60	t	t	NOUN
ejde-388	211	61	0	0	NUM
ejde-388	211	62	5	5	NUM
ejde-388	211	63	10	10	NUM
ejde-388	211	64	15	15	NUM
ejde-388	211	65	ln	ln	NOUN
ejde-388	211	66	(	(	PUNCT
ejde-388	211	67	λ	λ	NOUN
ejde-388	211	68	/λ	/λ	NOUN
ejde-388	211	69	0	0	NUM
ejde-388	211	70	)	)	PUNCT
ejde-388	211	71	0	0	NUM
ejde-388	211	72	0.1	0.1	NUM
ejde-388	211	73	0.2	0.2	NUM
ejde-388	211	74	0.3	0.3	NUM
ejde-388	211	75	t	t	NOUN
ejde-388	211	76	0	0	NUM
ejde-388	211	77	5	5	NUM
ejde-388	211	78	10	10	NUM
ejde-388	211	79	15	15	NUM
ejde-388	211	80	ln	ln	NOUN
ejde-388	211	81	(	(	PUNCT
ejde-388	211	82	λ	λ	NOUN
ejde-388	211	83	/λ	/λ	NOUN
ejde-388	211	84	0	0	NUM
ejde-388	211	85	)	)	PUNCT
ejde-388	211	86	(	(	PUNCT
ejde-388	211	87	c	c	X
ejde-388	211	88	)	)	PUNCT
ejde-388	211	89	re	re	NOUN
ejde-388	211	90	=	=	NOUN
ejde-388	211	91	1000	1000	NUM
ejde-388	211	92	,	,	PUNCT
ejde-388	211	93	k1	k1	NOUN
ejde-388	211	94	=	=	SYM
ejde-388	211	95	k2	k2	NOUN
ejde-388	211	96	=	=	SYM
ejde-388	211	97	7	7	NUM
ejde-388	211	98	(	(	PUNCT
ejde-388	211	99	d	d	NOUN
ejde-388	211	100	)	)	PUNCT
ejde-388	211	101	re	re	NOUN
ejde-388	211	102	=	=	NOUN
ejde-388	211	103	1000	1000	NUM
ejde-388	211	104	,	,	PUNCT
ejde-388	211	105	k1	k1	NOUN
ejde-388	211	106	=	=	SYM
ejde-388	211	107	k2	k2	NOUN
ejde-388	211	108	=	=	SYM
ejde-388	211	109	8	8	NUM
ejde-388	211	110	figure	figure	NOUN
ejde-388	211	111	4	4	NUM
ejde-388	211	112	.	.	PUNCT
ejde-388	212	1	the	the	DET
ejde-388	212	2	solid	solid	ADJ
ejde-388	212	3	curve	curve	NOUN
ejde-388	212	4	is	be	AUX
ejde-388	212	5	the	the	DET
ejde-388	212	6	numerical	numerical	ADJ
ejde-388	212	7	result	result	NOUN
ejde-388	212	8	of	of	ADP
ejde-388	212	9	the	the	DET
ejde-388	212	10	super	super	ADV
ejde-388	212	11	fast	fast	ADJ
ejde-388	212	12	growth	growth	NOUN
ejde-388	212	13	of	of	ADP
ejde-388	212	14	perturbations	perturbation	NOUN
ejde-388	212	15	with	with	ADP
ejde-388	212	16	initial	initial	ADJ
ejde-388	212	17	condition	condition	NOUN
ejde-388	212	18	(	(	PUNCT
ejde-388	212	19	5.7	5.7	NUM
ejde-388	212	20	)	)	PUNCT
ejde-388	212	21	with	with	ADP
ejde-388	212	22	different	different	ADJ
ejde-388	212	23	(	(	PUNCT
ejde-388	212	24	k1	k1	NOUN
ejde-388	212	25	,	,	PUNCT
ejde-388	212	26	k2	k2	NOUN
ejde-388	212	27	)	)	PUNCT
ejde-388	212	28	where	where	SCONJ
ejde-388	212	29	λ(t	λ(t	NOUN
ejde-388	212	30	)	)	PUNCT
ejde-388	212	31	=	=	SYM
ejde-388	212	32	‖du(t)‖h3	‖du(t)‖h3	PROPN
ejde-388	212	33	.	.	PUNCT
ejde-388	213	1	the	the	DET
ejde-388	213	2	fitting	fitting	ADJ
ejde-388	213	3	dashed	dash	VERB
ejde-388	213	4	curve	curve	NOUN
ejde-388	213	5	is	be	AUX
ejde-388	213	6	e21.2	e21.2	NOUN
ejde-388	213	7	√	√	ADJ
ejde-388	213	8	t.	t.	NOUN
ejde-388	213	9	5.4	5.4	NUM
ejde-388	213	10	.	.	PUNCT
ejde-388	214	1	turbulence	turbulence	NOUN
ejde-388	214	2	regime	regime	NOUN
ejde-388	214	3	.	.	PUNCT
ejde-388	215	1	in	in	ADP
ejde-388	215	2	this	this	DET
ejde-388	215	3	subsection	subsection	NOUN
ejde-388	215	4	,	,	PUNCT
ejde-388	215	5	we	we	PRON
ejde-388	215	6	shall	shall	AUX
ejde-388	215	7	simulate	simulate	VERB
ejde-388	215	8	more	more	ADV
ejde-388	215	9	realistic	realistic	ADJ
ejde-388	215	10	situations	situation	NOUN
ejde-388	215	11	of	of	ADP
ejde-388	215	12	base	base	NOUN
ejde-388	215	13	solutions	solution	NOUN
ejde-388	215	14	in	in	ADP
ejde-388	215	15	the	the	DET
ejde-388	215	16	turbulence	turbulence	NOUN
ejde-388	215	17	regime	regime	NOUN
ejde-388	215	18	.	.	PUNCT
ejde-388	216	1	now	now	ADV
ejde-388	216	2	start	start	VERB
ejde-388	216	3	with	with	ADP
ejde-388	216	4	base	base	NOUN
ejde-388	216	5	solution	solution	NOUN
ejde-388	216	6	’s	’s	PART
ejde-388	216	7	initial	initial	ADJ
ejde-388	216	8	condition	condition	NOUN
ejde-388	216	9	in	in	ADP
ejde-388	216	10	the	the	DET
ejde-388	216	11	form	form	NOUN
ejde-388	216	12	u1(0	u1(0	NOUN
ejde-388	216	13	)	)	PUNCT
ejde-388	217	1	=	=	PUNCT
ejde-388	217	2	∑	∑	PUNCT
ejde-388	217	3	0≤m	0≤m	PROPN
ejde-388	217	4	,	,	PUNCT
ejde-388	217	5	n≤16	n≤16	PRON
ejde-388	217	6	amnn	amnn	NOUN
ejde-388	217	7	sin(mx1	sin(mx1	NOUN
ejde-388	217	8	+	+	CCONJ
ejde-388	217	9	θ1	θ1	NOUN
ejde-388	217	10	)	)	PUNCT
ejde-388	217	11	sin(nx2	sin(nx2	PROPN
ejde-388	217	12	+	+	SYM
ejde-388	217	13	θ2	θ2	PROPN
ejde-388	217	14	)	)	PUNCT
ejde-388	217	15	,	,	PUNCT
ejde-388	217	16	(	(	PUNCT
ejde-388	217	17	5.12	5.12	NUM
ejde-388	217	18	)	)	PUNCT
ejde-388	217	19	u2(0	u2(0	NOUN
ejde-388	217	20	)	)	PUNCT
ejde-388	217	21	=	=	PUNCT
ejde-388	218	1	∑	∑	PUNCT
ejde-388	218	2	0≤m	0≤m	PROPN
ejde-388	218	3	,	,	PUNCT
ejde-388	218	4	n≤16	n≤16	PRON
ejde-388	218	5	amnm	amnm	PROPN
ejde-388	218	6	cos(mx1	cos(mx1	PROPN
ejde-388	218	7	+	+	CCONJ
ejde-388	218	8	θ1	θ1	NOUN
ejde-388	218	9	)	)	PUNCT
ejde-388	218	10	cos(nx2	cos(nx2	PROPN
ejde-388	218	11	+	+	PROPN
ejde-388	218	12	θ2	θ2	PROPN
ejde-388	218	13	)	)	PUNCT
ejde-388	218	14	,	,	PUNCT
ejde-388	218	15	(	(	PUNCT
ejde-388	218	16	5.13	5.13	NUM
ejde-388	218	17	)	)	PUNCT
ejde-388	218	18	where	where	SCONJ
ejde-388	218	19	amn	amn	PROPN
ejde-388	218	20	=	=	SYM
ejde-388	218	21	0.01a	0.01a	PROPN
ejde-388	218	22	and	and	CCONJ
ejde-388	218	23	a	a	PRON
ejde-388	218	24	is	be	AUX
ejde-388	218	25	a	a	DET
ejde-388	218	26	random	random	ADJ
ejde-388	218	27	variable	variable	NOUN
ejde-388	218	28	with	with	ADP
ejde-388	218	29	standard	standard	ADJ
ejde-388	218	30	gaussian	gaussian	ADJ
ejde-388	218	31	distribution	distribution	NOUN
ejde-388	218	32	,	,	PUNCT
ejde-388	218	33	and	and	CCONJ
ejde-388	218	34	θ1	θ1	NOUN
ejde-388	218	35	and	and	CCONJ
ejde-388	218	36	θ2	θ2	PROPN
ejde-388	218	37	are	be	AUX
ejde-388	218	38	random	random	ADJ
ejde-388	218	39	variables	variable	NOUN
ejde-388	218	40	with	with	ADP
ejde-388	218	41	uniform	uniform	ADJ
ejde-388	218	42	distribution	distribution	NOUN
ejde-388	218	43	on	on	ADP
ejde-388	218	44	[	[	X
ejde-388	218	45	0	0	NUM
ejde-388	218	46	,	,	PUNCT
ejde-388	218	47	1	1	NUM
ejde-388	218	48	]	]	PUNCT
ejde-388	218	49	.	.	PUNCT
ejde-388	219	1	this	this	DET
ejde-388	219	2	type	type	NOUN
ejde-388	219	3	of	of	ADP
ejde-388	219	4	initial	initial	ADJ
ejde-388	219	5	conditions	condition	NOUN
ejde-388	219	6	put	put	VERB
ejde-388	219	7	the	the	DET
ejde-388	219	8	flow	flow	NOUN
ejde-388	219	9	into	into	ADP
ejde-388	219	10	the	the	DET
ejde-388	219	11	turbulence	turbulence	NOUN
ejde-388	219	12	regime	regime	NOUN
ejde-388	219	13	.	.	PUNCT
ejde-388	220	1	for	for	ADP
ejde-388	220	2	the	the	DET
ejde-388	220	3	perturbation	perturbation	NOUN
ejde-388	220	4	initial	initial	ADJ
ejde-388	220	5	condition	condition	NOUN
ejde-388	220	6	,	,	PUNCT
ejde-388	220	7	we	we	PRON
ejde-388	220	8	choose	choose	VERB
ejde-388	220	9	du1(0	du1(0	NOUN
ejde-388	220	10	)	)	PUNCT
ejde-388	221	1	=	=	NOUN
ejde-388	221	2	a1	a1	NOUN
ejde-388	221	3	sin(x1	sin(x1	NOUN
ejde-388	221	4	)	)	PUNCT
ejde-388	221	5	sin(x2	sin(x2	NOUN
ejde-388	221	6	)	)	PUNCT
ejde-388	221	7	,	,	PUNCT
ejde-388	221	8	du2(0	du2(0	NOUN
ejde-388	221	9	)	)	PUNCT
ejde-388	221	10	=	=	NOUN
ejde-388	221	11	a1	a1	PROPN
ejde-388	221	12	cos(x1	cos(x1	PROPN
ejde-388	221	13	)	)	PUNCT
ejde-388	221	14	cos(x2	cos(x2	NOUN
ejde-388	221	15	)	)	PUNCT
ejde-388	221	16	,	,	PUNCT
ejde-388	221	17	(	(	PUNCT
ejde-388	221	18	5.14	5.14	NUM
ejde-388	221	19	)	)	PUNCT
ejde-388	221	20	where	where	SCONJ
ejde-388	221	21	a1	a1	NOUN
ejde-388	221	22	is	be	AUX
ejde-388	221	23	a	a	DET
ejde-388	221	24	random	random	ADJ
ejde-388	221	25	variable	variable	NOUN
ejde-388	221	26	with	with	ADP
ejde-388	221	27	standard	standard	ADJ
ejde-388	221	28	gaussian	gaussian	ADJ
ejde-388	221	29	distribution	distribution	NOUN
ejde-388	221	30	(	(	PUNCT
ejde-388	221	31	in	in	ADP
ejde-388	221	32	this	this	DET
ejde-388	221	33	single	single	ADJ
ejde-388	221	34	mode	mode	NOUN
ejde-388	221	35	case	case	NOUN
ejde-388	221	36	,	,	PUNCT
ejde-388	221	37	it	it	PRON
ejde-388	221	38	does	do	AUX
ejde-388	221	39	not	not	PART
ejde-388	221	40	matter	matter	VERB
ejde-388	221	41	whether	whether	SCONJ
ejde-388	221	42	or	or	CCONJ
ejde-388	221	43	not	not	PART
ejde-388	221	44	a1	a1	NOUN
ejde-388	221	45	is	be	AUX
ejde-388	221	46	random	random	ADJ
ejde-388	221	47	since	since	SCONJ
ejde-388	221	48	the	the	DET
ejde-388	221	49	perturbation	perturbation	NOUN
ejde-388	221	50	satisfies	satisfy	VERB
ejde-388	221	51	a	a	DET
ejde-388	221	52	linear	linear	ADJ
ejde-388	221	53	equation	equation	NOUN
ejde-388	221	54	)	)	PUNCT
ejde-388	221	55	.	.	PUNCT
ejde-388	222	1	we	we	PRON
ejde-388	222	2	choose	choose	VERB
ejde-388	222	3	the	the	DET
ejde-388	222	4	reynolds	reynolds	PROPN
ejde-388	222	5	number	number	NOUN
ejde-388	222	6	re	re	NOUN
ejde-388	222	7	=	=	NOUN
ejde-388	222	8	1000	1000	NUM
ejde-388	222	9	.	.	PUNCT
ejde-388	223	1	first	first	ADV
ejde-388	223	2	we	we	PRON
ejde-388	223	3	run	run	VERB
ejde-388	223	4	the	the	DET
ejde-388	223	5	simulation	simulation	NOUN
ejde-388	223	6	for	for	ADP
ejde-388	223	7	a	a	DET
ejde-388	223	8	time	time	NOUN
ejde-388	223	9	period	period	NOUN
ejde-388	223	10	0	0	NUM
ejde-388	223	11	≤	≤	NUM
ejde-388	223	12	t	t	NOUN
ejde-388	223	13	≤	≤	NOUN
ejde-388	223	14	0.03	0.03	NUM
ejde-388	223	15	with	with	ADP
ejde-388	223	16	time	time	NOUN
ejde-388	223	17	step	step	NOUN
ejde-388	223	18	0.0005	0.0005	NUM
ejde-388	223	19	,	,	PUNCT
ejde-388	223	20	the	the	DET
ejde-388	223	21	super	super	ADV
ejde-388	223	22	fast	fast	ADJ
ejde-388	223	23	growth	growth	NOUN
ejde-388	223	24	of	of	ADP
ejde-388	223	25	the	the	DET
ejde-388	223	26	perturbation	perturbation	NOUN
ejde-388	223	27	is	be	AUX
ejde-388	223	28	shown	show	VERB
ejde-388	223	29	in	in	ADP
ejde-388	223	30	figure	figure	NOUN
ejde-388	223	31	7(a	7(a	NUM
ejde-388	223	32	)	)	PUNCT
ejde-388	223	33	.	.	PUNCT
ejde-388	224	1	then	then	ADV
ejde-388	224	2	we	we	PRON
ejde-388	224	3	restart	restart	VERB
ejde-388	224	4	the	the	DET
ejde-388	224	5	base	base	NOUN
ejde-388	224	6	solution	solution	NOUN
ejde-388	224	7	from	from	ADP
ejde-388	224	8	t	t	PROPN
ejde-388	224	9	=	=	SYM
ejde-388	224	10	0.03	0.03	NUM
ejde-388	224	11	,	,	PUNCT
ejde-388	224	12	i.e.	i.e.	X
ejde-388	224	13	we	we	PRON
ejde-388	224	14	take	take	VERB
ejde-388	224	15	the	the	DET
ejde-388	224	16	t	t	NOUN
ejde-388	224	17	=	=	SYM
ejde-388	224	18	0.03	0.03	NUM
ejde-388	224	19	flash	flash	NOUN
ejde-388	224	20	of	of	ADP
ejde-388	224	21	the	the	DET
ejde-388	224	22	base	base	NOUN
ejde-388	224	23	solution	solution	NOUN
ejde-388	224	24	as	as	ADP
ejde-388	224	25	the	the	DET
ejde-388	224	26	new	new	ADJ
ejde-388	224	27	initial	initial	ADJ
ejde-388	224	28	condition	condition	NOUN
ejde-388	224	29	,	,	PUNCT
ejde-388	224	30	introduce	introduce	VERB
ejde-388	224	31	the	the	DET
ejde-388	224	32	same	same	ADJ
ejde-388	224	33	initial	initial	ADJ
ejde-388	224	34	perturbation	perturbation	NOUN
ejde-388	224	35	(	(	PUNCT
ejde-388	224	36	5.14	5.14	NUM
ejde-388	224	37	)	)	PUNCT
ejde-388	224	38	,	,	PUNCT
ejde-388	224	39	and	and	CCONJ
ejde-388	224	40	run	run	VERB
ejde-388	224	41	ejde-2020/104	ejde-2020/104	DET
ejde-388	224	42	short	short	ADJ
ejde-388	224	43	term	term	NOUN
ejde-388	224	44	unpredictability	unpredictability	NOUN
ejde-388	224	45	11	11	NUM
ejde-388	224	46	0	0	NUM
ejde-388	224	47	0.1	0.1	NUM
ejde-388	224	48	0.2	0.2	NUM
ejde-388	224	49	0.3	0.3	NUM
ejde-388	224	50	t	t	NOUN
ejde-388	224	51	0	0	NUM
ejde-388	224	52	5	5	NUM
ejde-388	224	53	10	10	NUM
ejde-388	224	54	15	15	NUM
ejde-388	224	55	ln	ln	NOUN
ejde-388	224	56	(	(	PUNCT
ejde-388	224	57	λ	λ	NOUN
ejde-388	224	58	/λ	/λ	NOUN
ejde-388	224	59	0	0	NUM
ejde-388	224	60	)	)	PUNCT
ejde-388	224	61	0	0	NUM
ejde-388	224	62	0.1	0.1	NUM
ejde-388	224	63	0.2	0.2	NUM
ejde-388	224	64	0.3	0.3	NUM
ejde-388	224	65	t	t	NOUN
ejde-388	224	66	0	0	NUM
ejde-388	224	67	5	5	NUM
ejde-388	224	68	10	10	NUM
ejde-388	224	69	15	15	NUM
ejde-388	224	70	ln	ln	NOUN
ejde-388	224	71	(	(	PUNCT
ejde-388	224	72	λ	λ	NOUN
ejde-388	224	73	/λ	/λ	NOUN
ejde-388	224	74	0	0	NUM
ejde-388	224	75	)	)	PUNCT
ejde-388	224	76	(	(	PUNCT
ejde-388	224	77	a	a	X
ejde-388	224	78	)	)	PUNCT
ejde-388	224	79	re	re	NOUN
ejde-388	224	80	=	=	NOUN
ejde-388	224	81	1000	1000	NUM
ejde-388	224	82	,	,	PUNCT
ejde-388	224	83	k1	k1	NOUN
ejde-388	224	84	=	=	SYM
ejde-388	224	85	9	9	NUM
ejde-388	224	86	,	,	PUNCT
ejde-388	224	87	k2	k2	NOUN
ejde-388	224	88	=	=	SYM
ejde-388	224	89	8	8	NUM
ejde-388	224	90	(	(	PUNCT
ejde-388	224	91	b	b	NOUN
ejde-388	224	92	)	)	PUNCT
ejde-388	224	93	re	re	NOUN
ejde-388	224	94	=	=	NOUN
ejde-388	224	95	1000	1000	NUM
ejde-388	224	96	,	,	PUNCT
ejde-388	224	97	k1	k1	NOUN
ejde-388	224	98	=	=	SYM
ejde-388	224	99	8	8	NUM
ejde-388	224	100	,	,	PUNCT
ejde-388	224	101	k2	k2	NOUN
ejde-388	224	102	=	=	NOUN
ejde-388	224	103	7	7	NUM
ejde-388	224	104	0	0	NUM
ejde-388	224	105	0.1	0.1	NUM
ejde-388	224	106	0.2	0.2	NUM
ejde-388	224	107	0.3	0.3	NUM
ejde-388	224	108	t	t	NOUN
ejde-388	224	109	0	0	NUM
ejde-388	224	110	5	5	NUM
ejde-388	224	111	10	10	NUM
ejde-388	224	112	15	15	NUM
ejde-388	224	113	ln	ln	NOUN
ejde-388	224	114	(	(	PUNCT
ejde-388	224	115	λ	λ	NOUN
ejde-388	224	116	/λ	/λ	NOUN
ejde-388	224	117	0	0	NUM
ejde-388	224	118	)	)	PUNCT
ejde-388	224	119	0	0	NUM
ejde-388	224	120	0.1	0.1	NUM
ejde-388	224	121	0.2	0.2	NUM
ejde-388	224	122	0.3	0.3	NUM
ejde-388	224	123	t	t	NOUN
ejde-388	224	124	0	0	NUM
ejde-388	224	125	5	5	NUM
ejde-388	224	126	10	10	NUM
ejde-388	224	127	15	15	NUM
ejde-388	224	128	ln	ln	NOUN
ejde-388	224	129	(	(	PUNCT
ejde-388	224	130	λ	λ	NOUN
ejde-388	224	131	/λ	/λ	NOUN
ejde-388	224	132	0	0	NUM
ejde-388	224	133	)	)	PUNCT
ejde-388	224	134	(	(	PUNCT
ejde-388	224	135	c	c	X
ejde-388	224	136	)	)	PUNCT
ejde-388	224	137	re	re	NOUN
ejde-388	224	138	=	=	NOUN
ejde-388	224	139	1000	1000	NUM
ejde-388	224	140	,	,	PUNCT
ejde-388	224	141	k1	k1	NOUN
ejde-388	224	142	=	=	SYM
ejde-388	224	143	7	7	NUM
ejde-388	224	144	,	,	PUNCT
ejde-388	224	145	k2	k2	NOUN
ejde-388	224	146	=	=	SYM
ejde-388	224	147	6	6	NUM
ejde-388	224	148	(	(	PUNCT
ejde-388	224	149	d	d	NOUN
ejde-388	224	150	)	)	PUNCT
ejde-388	224	151	re	re	NOUN
ejde-388	224	152	=	=	NOUN
ejde-388	224	153	1000	1000	NUM
ejde-388	224	154	,	,	PUNCT
ejde-388	224	155	k1	k1	NOUN
ejde-388	224	156	=	=	SYM
ejde-388	224	157	6	6	NUM
ejde-388	224	158	,	,	PUNCT
ejde-388	224	159	k2	k2	NOUN
ejde-388	224	160	=	=	SYM
ejde-388	224	161	5	5	NUM
ejde-388	224	162	figure	figure	NOUN
ejde-388	224	163	5	5	NUM
ejde-388	224	164	.	.	PUNCT
ejde-388	225	1	the	the	DET
ejde-388	225	2	solid	solid	ADJ
ejde-388	225	3	curve	curve	NOUN
ejde-388	225	4	is	be	AUX
ejde-388	225	5	the	the	DET
ejde-388	225	6	numerical	numerical	ADJ
ejde-388	225	7	result	result	NOUN
ejde-388	225	8	of	of	ADP
ejde-388	225	9	the	the	DET
ejde-388	225	10	super	super	ADV
ejde-388	225	11	fast	fast	ADJ
ejde-388	225	12	growth	growth	NOUN
ejde-388	225	13	of	of	ADP
ejde-388	225	14	perturbations	perturbation	NOUN
ejde-388	225	15	with	with	ADP
ejde-388	225	16	initial	initial	ADJ
ejde-388	225	17	condition	condition	NOUN
ejde-388	225	18	(	(	PUNCT
ejde-388	225	19	5.7	5.7	NUM
ejde-388	225	20	)	)	PUNCT
ejde-388	225	21	with	with	ADP
ejde-388	225	22	k1	k1	NOUN
ejde-388	225	23	=	=	SYM
ejde-388	225	24	1	1	NUM
ejde-388	225	25	and	and	CCONJ
ejde-388	225	26	k2	k2	NOUN
ejde-388	225	27	=	=	NOUN
ejde-388	225	28	1	1	NUM
ejde-388	225	29	under	under	ADP
ejde-388	225	30	different	different	ADJ
ejde-388	225	31	base	base	NOUN
ejde-388	225	32	solutions	solution	NOUN
ejde-388	225	33	with	with	ADP
ejde-388	225	34	initial	initial	ADJ
ejde-388	225	35	conditions	condition	NOUN
ejde-388	225	36	given	give	VERB
ejde-388	225	37	by	by	ADP
ejde-388	225	38	(	(	PUNCT
ejde-388	225	39	5.11	5.11	NUM
ejde-388	225	40	)	)	PUNCT
ejde-388	225	41	,	,	PUNCT
ejde-388	225	42	where	where	SCONJ
ejde-388	225	43	λ(t	λ(t	NOUN
ejde-388	225	44	)	)	PUNCT
ejde-388	225	45	=	=	SYM
ejde-388	225	46	‖du(t)‖h3	‖du(t)‖h3	PROPN
ejde-388	225	47	.	.	PUNCT
ejde-388	226	1	the	the	DET
ejde-388	226	2	fitting	fitting	ADJ
ejde-388	226	3	dashed	dash	VERB
ejde-388	226	4	curve	curve	NOUN
ejde-388	226	5	is	be	AUX
ejde-388	226	6	e21.2	e21.2	NOUN
ejde-388	226	7	√	√	ADJ
ejde-388	226	8	t.	t.	NOUN
ejde-388	226	9	the	the	DET
ejde-388	226	10	simulation	simulation	NOUN
ejde-388	226	11	for	for	ADP
ejde-388	226	12	the	the	DET
ejde-388	226	13	same	same	ADJ
ejde-388	226	14	time	time	NOUN
ejde-388	226	15	period	period	NOUN
ejde-388	226	16	0	0	NUM
ejde-388	226	17	≤	≤	NUM
ejde-388	226	18	t	t	NOUN
ejde-388	226	19	≤	≤	NOUN
ejde-388	226	20	0.03	0.03	NUM
ejde-388	226	21	with	with	ADP
ejde-388	226	22	the	the	DET
ejde-388	226	23	same	same	ADJ
ejde-388	226	24	time	time	NOUN
ejde-388	226	25	step	step	NOUN
ejde-388	226	26	0.0005	0.0005	NUM
ejde-388	226	27	.	.	PUNCT
ejde-388	227	1	the	the	DET
ejde-388	227	2	super	super	ADV
ejde-388	227	3	fast	fast	ADJ
ejde-388	227	4	growth	growth	NOUN
ejde-388	227	5	of	of	ADP
ejde-388	227	6	the	the	DET
ejde-388	227	7	perturbation	perturbation	NOUN
ejde-388	227	8	is	be	AUX
ejde-388	227	9	shown	show	VERB
ejde-388	227	10	in	in	ADP
ejde-388	227	11	figure	figure	NOUN
ejde-388	227	12	7(b	7(b	NUM
ejde-388	227	13	)	)	PUNCT
ejde-388	227	14	.	.	PUNCT
ejde-388	228	1	we	we	PRON
ejde-388	228	2	conclude	conclude	VERB
ejde-388	228	3	that	that	SCONJ
ejde-388	228	4	at	at	ADP
ejde-388	228	5	any	any	DET
ejde-388	228	6	moment	moment	NOUN
ejde-388	228	7	,	,	PUNCT
ejde-388	228	8	an	an	DET
ejde-388	228	9	initial	initial	ADJ
ejde-388	228	10	perturbation	perturbation	NOUN
ejde-388	228	11	is	be	AUX
ejde-388	228	12	introduced	introduce	VERB
ejde-388	228	13	into	into	ADP
ejde-388	228	14	turbulence	turbulence	NOUN
ejde-388	228	15	,	,	PUNCT
ejde-388	228	16	it	it	PRON
ejde-388	228	17	immediately	immediately	ADV
ejde-388	228	18	goes	go	VERB
ejde-388	228	19	through	through	ADP
ejde-388	228	20	a	a	DET
ejde-388	228	21	ec	ec	PROPN
ejde-388	228	22	√	√	PROPN
ejde-388	228	23	t	t	PROPN
ejde-388	228	24	super	super	ADV
ejde-388	228	25	fast	fast	ADJ
ejde-388	228	26	amplification	amplification	NOUN
ejde-388	228	27	.	.	PUNCT
ejde-388	229	1	we	we	PRON
ejde-388	229	2	can	can	AUX
ejde-388	229	3	visualize	visualize	VERB
ejde-388	229	4	turbulence	turbulence	NOUN
ejde-388	229	5	as	as	ADP
ejde-388	229	6	a	a	DET
ejde-388	229	7	constant	constant	ADJ
ejde-388	229	8	super	super	ADV
ejde-388	229	9	fast	fast	ADJ
ejde-388	229	10	amplification	amplification	NOUN
ejde-388	229	11	of	of	ADP
ejde-388	229	12	ever	ever	ADV
ejde-388	229	13	appearing	appear	VERB
ejde-388	229	14	perturbations	perturbation	NOUN
ejde-388	229	15	.	.	PUNCT
ejde-388	230	1	now	now	ADV
ejde-388	230	2	we	we	PRON
ejde-388	230	3	choose	choose	VERB
ejde-388	230	4	more	more	ADJ
ejde-388	230	5	general	general	ADJ
ejde-388	230	6	initial	initial	ADJ
ejde-388	230	7	perturbations	perturbation	NOUN
ejde-388	230	8	to	to	ADP
ejde-388	230	9	the	the	DET
ejde-388	230	10	base	base	NOUN
ejde-388	230	11	solution	solution	NOUN
ejde-388	230	12	initial	initial	ADJ
ejde-388	230	13	condition	condition	NOUN
ejde-388	230	14	(	(	PUNCT
ejde-388	230	15	5.12)-(5.13	5.12)-(5.13	NUM
ejde-388	230	16	)	)	PUNCT
ejde-388	230	17	as	as	SCONJ
ejde-388	230	18	follows	follow	VERB
ejde-388	230	19	du1(0	du1(0	NOUN
ejde-388	230	20	)	)	PUNCT
ejde-388	231	1	=	=	PUNCT
ejde-388	231	2	∑	∑	PUNCT
ejde-388	231	3	0≤m	0≤m	PROPN
ejde-388	231	4	,	,	PUNCT
ejde-388	231	5	n≤n	n≤n	PROPN
ejde-388	231	6	amnn	amnn	VERB
ejde-388	231	7	sin(mx1	sin(mx1	PROPN
ejde-388	231	8	+	+	CCONJ
ejde-388	231	9	θ1	θ1	NOUN
ejde-388	231	10	)	)	PUNCT
ejde-388	231	11	sin(nx2	sin(nx2	PROPN
ejde-388	231	12	+	+	SYM
ejde-388	231	13	θ2	θ2	PROPN
ejde-388	231	14	)	)	PUNCT
ejde-388	231	15	,	,	PUNCT
ejde-388	231	16	(	(	PUNCT
ejde-388	231	17	5.15	5.15	NUM
ejde-388	231	18	)	)	PUNCT
ejde-388	231	19	du2(0	du2(0	NOUN
ejde-388	231	20	)	)	PUNCT
ejde-388	231	21	=	=	PUNCT
ejde-388	231	22	∑	∑	PUNCT
ejde-388	231	23	0≤m	0≤m	PROPN
ejde-388	231	24	,	,	PUNCT
ejde-388	231	25	n≤n	n≤n	PROPN
ejde-388	231	26	amnm	amnm	PROPN
ejde-388	231	27	cos(mx1	cos(mx1	PROPN
ejde-388	231	28	+	+	CCONJ
ejde-388	231	29	θ1	θ1	NOUN
ejde-388	231	30	)	)	PUNCT
ejde-388	231	31	cos(nx2	cos(nx2	PROPN
ejde-388	231	32	+	+	PROPN
ejde-388	231	33	θ2	θ2	PROPN
ejde-388	231	34	)	)	PUNCT
ejde-388	231	35	,	,	PUNCT
ejde-388	231	36	(	(	PUNCT
ejde-388	231	37	5.16	5.16	NUM
ejde-388	231	38	)	)	PUNCT
ejde-388	231	39	where	where	SCONJ
ejde-388	231	40	the	the	DET
ejde-388	231	41	parameters	parameter	NOUN
ejde-388	231	42	are	be	AUX
ejde-388	231	43	defined	define	VERB
ejde-388	231	44	in	in	ADP
ejde-388	231	45	(	(	PUNCT
ejde-388	231	46	5.12)-(5.13	5.12)-(5.13	NUM
ejde-388	231	47	)	)	PUNCT
ejde-388	231	48	.	.	PUNCT
ejde-388	232	1	when	when	SCONJ
ejde-388	232	2	n	n	X
ejde-388	232	3	=	=	SYM
ejde-388	232	4	16	16	NUM
ejde-388	232	5	,	,	PUNCT
ejde-388	232	6	8	8	NUM
ejde-388	232	7	,	,	PUNCT
ejde-388	232	8	4	4	NUM
ejde-388	232	9	,	,	PUNCT
ejde-388	232	10	2	2	NUM
ejde-388	232	11	,	,	PUNCT
ejde-388	232	12	we	we	PRON
ejde-388	232	13	have	have	VERB
ejde-388	232	14	the	the	DET
ejde-388	232	15	same	same	ADJ
ejde-388	232	16	superfast	superfast	ADJ
ejde-388	232	17	growth	growth	NOUN
ejde-388	232	18	(	(	PUNCT
ejde-388	232	19	figure	figure	NOUN
ejde-388	232	20	8)	8)	NUM
ejde-388	232	21	,	,	PUNCT
ejde-388	232	22	and	and	CCONJ
ejde-388	232	23	clearly	clearly	ADV
ejde-388	232	24	lower	low	ADJ
ejde-388	232	25	perturbation	perturbation	NOUN
ejde-388	232	26	mode	mode	NOUN
ejde-388	232	27	grows	grow	VERB
ejde-388	232	28	faster	fast	ADV
ejde-388	232	29	.	.	PUNCT
ejde-388	233	1	again	again	ADV
ejde-388	233	2	,	,	PUNCT
ejde-388	233	3	since	since	SCONJ
ejde-388	233	4	the	the	DET
ejde-388	233	5	perturbation	perturbation	NOUN
ejde-388	233	6	equations	equation	NOUN
ejde-388	233	7	are	be	AUX
ejde-388	233	8	linear	linear	ADJ
ejde-388	233	9	,	,	PUNCT
ejde-388	233	10	each	each	DET
ejde-388	233	11	initial	initial	ADJ
ejde-388	233	12	individual	individual	ADJ
ejde-388	233	13	fourier	fourier	NOUN
ejde-388	233	14	mode	mode	NOUN
ejde-388	233	15	amplifies	amplify	VERB
ejde-388	233	16	independently	independently	ADV
ejde-388	233	17	.	.	PUNCT
ejde-388	234	1	5.5	5.5	NUM
ejde-388	234	2	.	.	PUNCT
ejde-388	234	3	norm	norm	NOUN
ejde-388	234	4	independence	independence	NOUN
ejde-388	234	5	of	of	ADP
ejde-388	234	6	the	the	DET
ejde-388	234	7	short	short	ADJ
ejde-388	234	8	term	term	NOUN
ejde-388	234	9	unpredictability	unpredictability	NOUN
ejde-388	234	10	.	.	PUNCT
ejde-388	235	1	one	one	NUM
ejde-388	235	2	natural	natural	ADJ
ejde-388	235	3	question	question	NOUN
ejde-388	235	4	is	be	AUX
ejde-388	235	5	whether	whether	SCONJ
ejde-388	235	6	or	or	CCONJ
ejde-388	235	7	not	not	PART
ejde-388	235	8	the	the	DET
ejde-388	235	9	super	super	ADV
ejde-388	235	10	fast	fast	ADJ
ejde-388	235	11	amplification	amplification	NOUN
ejde-388	235	12	of	of	ADP
ejde-388	235	13	perturbations	perturbation	NOUN
ejde-388	235	14	is	be	AUX
ejde-388	235	15	due	due	ADJ
ejde-388	235	16	to	to	ADP
ejde-388	235	17	the	the	DET
ejde-388	235	18	special	special	ADJ
ejde-388	235	19	normh3	normh3	NOUN
ejde-388	235	20	.	.	PUNCT
ejde-388	236	1	we	we	PRON
ejde-388	236	2	tested	test	VERB
ejde-388	236	3	different	different	ADJ
ejde-388	236	4	norms	norm	NOUN
ejde-388	236	5	.	.	PUNCT
ejde-388	237	1	for	for	ADP
ejde-388	237	2	all	all	DET
ejde-388	237	3	the	the	DET
ejde-388	237	4	cases	case	NOUN
ejde-388	237	5	we	we	PRON
ejde-388	237	6	tested	test	VERB
ejde-388	237	7	,	,	PUNCT
ejde-388	237	8	we	we	PRON
ejde-388	237	9	observed	observe	VERB
ejde-388	237	10	12	12	NUM
ejde-388	237	11	z.	z.	PROPN
ejde-388	237	12	feng	feng	PROPN
ejde-388	237	13	,	,	PUNCT
ejde-388	237	14	y.	y.	PROPN
ejde-388	237	15	c.	c.	PROPN
ejde-388	237	16	li	li	PROPN
ejde-388	238	1	ejde-2020/104	ejde-2020/104	PROPN
ejde-388	238	2	0	0	NUM
ejde-388	238	3	0.1	0.1	NUM
ejde-388	238	4	0.2	0.2	NUM
ejde-388	238	5	0.3	0.3	NUM
ejde-388	238	6	t	t	NOUN
ejde-388	238	7	0	0	NUM
ejde-388	238	8	5	5	NUM
ejde-388	238	9	10	10	NUM
ejde-388	238	10	15	15	NUM
ejde-388	238	11	ln	ln	NOUN
ejde-388	238	12	(	(	PUNCT
ejde-388	238	13	λ	λ	NOUN
ejde-388	238	14	/λ	/λ	NOUN
ejde-388	238	15	0	0	NUM
ejde-388	238	16	)	)	PUNCT
ejde-388	238	17	0	0	NUM
ejde-388	238	18	0.1	0.1	NUM
ejde-388	238	19	0.2	0.2	NUM
ejde-388	238	20	0.3	0.3	NUM
ejde-388	238	21	t	t	NOUN
ejde-388	238	22	0	0	NUM
ejde-388	238	23	5	5	NUM
ejde-388	238	24	10	10	NUM
ejde-388	238	25	15	15	NUM
ejde-388	238	26	ln	ln	NOUN
ejde-388	238	27	(	(	PUNCT
ejde-388	238	28	λ	λ	NOUN
ejde-388	238	29	/λ	/λ	NOUN
ejde-388	238	30	0	0	NUM
ejde-388	238	31	)	)	PUNCT
ejde-388	238	32	(	(	PUNCT
ejde-388	238	33	a	a	X
ejde-388	238	34	)	)	PUNCT
ejde-388	238	35	re	re	NOUN
ejde-388	238	36	=	=	NOUN
ejde-388	238	37	1000	1000	NUM
ejde-388	238	38	,	,	PUNCT
ejde-388	238	39	k1	k1	NOUN
ejde-388	238	40	=	=	SYM
ejde-388	238	41	5	5	NUM
ejde-388	238	42	,	,	PUNCT
ejde-388	238	43	k2	k2	NOUN
ejde-388	238	44	=	=	SYM
ejde-388	238	45	4	4	NUM
ejde-388	238	46	(	(	PUNCT
ejde-388	238	47	b	b	NOUN
ejde-388	238	48	)	)	PUNCT
ejde-388	238	49	re	re	NOUN
ejde-388	238	50	=	=	NOUN
ejde-388	238	51	1000	1000	NUM
ejde-388	238	52	,	,	PUNCT
ejde-388	238	53	k1	k1	NOUN
ejde-388	238	54	=	=	SYM
ejde-388	238	55	4	4	NUM
ejde-388	238	56	,	,	PUNCT
ejde-388	238	57	k2	k2	NOUN
ejde-388	238	58	=	=	NOUN
ejde-388	238	59	3	3	NUM
ejde-388	238	60	0	0	NUM
ejde-388	238	61	0.1	0.1	NUM
ejde-388	238	62	0.2	0.2	NUM
ejde-388	238	63	0.3	0.3	NUM
ejde-388	238	64	t	t	NOUN
ejde-388	238	65	0	0	NUM
ejde-388	238	66	5	5	NUM
ejde-388	238	67	10	10	NUM
ejde-388	238	68	15	15	NUM
ejde-388	238	69	ln	ln	NOUN
ejde-388	238	70	(	(	PUNCT
ejde-388	238	71	λ	λ	NOUN
ejde-388	238	72	/λ	/λ	NOUN
ejde-388	238	73	0	0	NUM
ejde-388	238	74	)	)	PUNCT
ejde-388	238	75	0	0	NUM
ejde-388	238	76	0.1	0.1	NUM
ejde-388	238	77	0.2	0.2	NUM
ejde-388	238	78	0.3	0.3	NUM
ejde-388	238	79	t	t	NOUN
ejde-388	238	80	0	0	NUM
ejde-388	238	81	5	5	NUM
ejde-388	238	82	10	10	NUM
ejde-388	238	83	15	15	NUM
ejde-388	238	84	ln	ln	NOUN
ejde-388	238	85	(	(	PUNCT
ejde-388	238	86	λ	λ	NOUN
ejde-388	238	87	/λ	/λ	NOUN
ejde-388	238	88	0	0	NUM
ejde-388	238	89	)	)	PUNCT
ejde-388	238	90	(	(	PUNCT
ejde-388	238	91	c	c	X
ejde-388	238	92	)	)	PUNCT
ejde-388	238	93	re	re	NOUN
ejde-388	238	94	=	=	NOUN
ejde-388	238	95	1000	1000	NUM
ejde-388	238	96	,	,	PUNCT
ejde-388	238	97	k1	k1	NOUN
ejde-388	238	98	=	=	SYM
ejde-388	238	99	3	3	NUM
ejde-388	238	100	,	,	PUNCT
ejde-388	238	101	k2	k2	NOUN
ejde-388	238	102	=	=	SYM
ejde-388	238	103	2	2	NUM
ejde-388	238	104	(	(	PUNCT
ejde-388	238	105	d	d	NOUN
ejde-388	238	106	)	)	PUNCT
ejde-388	238	107	re	re	NOUN
ejde-388	238	108	=	=	NOUN
ejde-388	238	109	1000	1000	NUM
ejde-388	238	110	,	,	PUNCT
ejde-388	238	111	k1	k1	NOUN
ejde-388	238	112	=	=	SYM
ejde-388	238	113	2	2	NUM
ejde-388	238	114	,	,	PUNCT
ejde-388	238	115	k2	k2	NOUN
ejde-388	238	116	=	=	SYM
ejde-388	238	117	1	1	NUM
ejde-388	238	118	figure	figure	NOUN
ejde-388	238	119	6	6	NUM
ejde-388	238	120	.	.	PUNCT
ejde-388	239	1	the	the	DET
ejde-388	239	2	solid	solid	ADJ
ejde-388	239	3	curve	curve	NOUN
ejde-388	239	4	is	be	AUX
ejde-388	239	5	the	the	DET
ejde-388	239	6	numerical	numerical	ADJ
ejde-388	239	7	result	result	NOUN
ejde-388	239	8	of	of	ADP
ejde-388	239	9	the	the	DET
ejde-388	239	10	super	super	ADV
ejde-388	239	11	fast	fast	ADJ
ejde-388	239	12	growth	growth	NOUN
ejde-388	239	13	of	of	ADP
ejde-388	239	14	perturbations	perturbation	NOUN
ejde-388	239	15	with	with	ADP
ejde-388	239	16	initial	initial	ADJ
ejde-388	239	17	condition	condition	NOUN
ejde-388	239	18	(	(	PUNCT
ejde-388	239	19	5.7	5.7	NUM
ejde-388	239	20	)	)	PUNCT
ejde-388	239	21	with	with	ADP
ejde-388	239	22	k1	k1	NOUN
ejde-388	239	23	=	=	SYM
ejde-388	239	24	1	1	NUM
ejde-388	239	25	and	and	CCONJ
ejde-388	239	26	k2	k2	NOUN
ejde-388	239	27	=	=	NOUN
ejde-388	239	28	1	1	NUM
ejde-388	239	29	under	under	ADP
ejde-388	239	30	different	different	ADJ
ejde-388	239	31	base	base	NOUN
ejde-388	239	32	solutions	solution	NOUN
ejde-388	239	33	with	with	ADP
ejde-388	239	34	initial	initial	ADJ
ejde-388	239	35	conditions	condition	NOUN
ejde-388	239	36	given	give	VERB
ejde-388	239	37	by	by	ADP
ejde-388	239	38	(	(	PUNCT
ejde-388	239	39	5.11	5.11	NUM
ejde-388	239	40	)	)	PUNCT
ejde-388	239	41	,	,	PUNCT
ejde-388	239	42	where	where	SCONJ
ejde-388	239	43	λ(t	λ(t	NOUN
ejde-388	239	44	)	)	PUNCT
ejde-388	239	45	=	=	SYM
ejde-388	239	46	‖du(t)‖h3	‖du(t)‖h3	PROPN
ejde-388	239	47	.	.	PUNCT
ejde-388	240	1	the	the	DET
ejde-388	240	2	fitting	fitting	ADJ
ejde-388	240	3	dashed	dash	VERB
ejde-388	240	4	curve	curve	NOUN
ejde-388	240	5	is	be	AUX
ejde-388	240	6	e21.2	e21.2	NOUN
ejde-388	240	7	√	√	ADJ
ejde-388	240	8	t.	t.	NOUN
ejde-388	240	9	0	0	NUM
ejde-388	240	10	0.1	0.1	NUM
ejde-388	240	11	0.2	0.2	NUM
ejde-388	240	12	0.3	0.3	NUM
ejde-388	240	13	t	t	NOUN
ejde-388	240	14	5	5	NUM
ejde-388	240	15	10	10	NUM
ejde-388	240	16	15	15	NUM
ejde-388	240	17	20	20	NUM
ejde-388	240	18	ln	ln	NOUN
ejde-388	240	19	(	(	PUNCT
ejde-388	240	20	λ	λ	NOUN
ejde-388	240	21	/λ	/λ	NOUN
ejde-388	240	22	0	0	NUM
ejde-388	240	23	)	)	PUNCT
ejde-388	240	24	0	0	NUM
ejde-388	240	25	0.1	0.1	NUM
ejde-388	240	26	0.2	0.2	NUM
ejde-388	240	27	0.3	0.3	NUM
ejde-388	240	28	t	t	NOUN
ejde-388	240	29	5	5	NUM
ejde-388	240	30	10	10	NUM
ejde-388	240	31	15	15	NUM
ejde-388	240	32	20	20	NUM
ejde-388	240	33	ln	ln	NOUN
ejde-388	240	34	(	(	PUNCT
ejde-388	240	35	λ	λ	NOUN
ejde-388	240	36	/λ	/λ	NOUN
ejde-388	240	37	0	0	NUM
ejde-388	240	38	)	)	PUNCT
ejde-388	240	39	(	(	PUNCT
ejde-388	240	40	a	a	X
ejde-388	240	41	)	)	PUNCT
ejde-388	240	42	starts	start	NOUN
ejde-388	240	43	at	at	ADP
ejde-388	240	44	t	t	PROPN
ejde-388	240	45	=	=	SYM
ejde-388	240	46	0	0	PUNCT
ejde-388	240	47	(	(	PUNCT
ejde-388	240	48	b	b	NOUN
ejde-388	240	49	)	)	PUNCT
ejde-388	240	50	restarts	restart	NOUN
ejde-388	240	51	at	at	ADP
ejde-388	240	52	t	t	NOUN
ejde-388	240	53	=	=	SYM
ejde-388	240	54	0.03	0.03	NUM
ejde-388	240	55	figure	figure	NOUN
ejde-388	240	56	7	7	NUM
ejde-388	240	57	.	.	PUNCT
ejde-388	240	58	super	super	ADJ
ejde-388	240	59	fast	fast	ADJ
ejde-388	240	60	growths	growth	NOUN
ejde-388	240	61	of	of	ADP
ejde-388	240	62	the	the	DET
ejde-388	240	63	perturbations	perturbation	NOUN
ejde-388	240	64	with	with	ADP
ejde-388	240	65	the	the	DET
ejde-388	240	66	same	same	ADJ
ejde-388	240	67	initial	initial	ADJ
ejde-388	240	68	condition	condition	NOUN
ejde-388	240	69	(	(	PUNCT
ejde-388	240	70	5.14	5.14	NUM
ejde-388	240	71	)	)	PUNCT
ejde-388	240	72	which	which	PRON
ejde-388	240	73	is	be	AUX
ejde-388	240	74	introduced	introduce	VERB
ejde-388	240	75	at	at	ADP
ejde-388	240	76	(	(	PUNCT
ejde-388	240	77	a	a	NOUN
ejde-388	240	78	)	)	PUNCT
ejde-388	240	79	.	.	PUNCT
ejde-388	241	1	t	t	NOUN
ejde-388	241	2	=	=	SYM
ejde-388	241	3	0	0	NUM
ejde-388	241	4	,	,	PUNCT
ejde-388	241	5	and	and	CCONJ
ejde-388	241	6	(	(	PUNCT
ejde-388	241	7	b	b	NOUN
ejde-388	241	8	)	)	PUNCT
ejde-388	241	9	.	.	PUNCT
ejde-388	242	1	t	t	PROPN
ejde-388	242	2	=	=	NUM
ejde-388	242	3	0.03	0.03	NUM
ejde-388	242	4	to	to	ADP
ejde-388	242	5	the	the	DET
ejde-388	242	6	base	base	NOUN
ejde-388	242	7	solution	solution	NOUN
ejde-388	242	8	with	with	ADP
ejde-388	242	9	the	the	DET
ejde-388	242	10	initial	initial	ADJ
ejde-388	242	11	condition	condition	NOUN
ejde-388	242	12	(	(	PUNCT
ejde-388	242	13	5.12)-(5.13	5.12)-(5.13	NUM
ejde-388	242	14	)	)	PUNCT
ejde-388	242	15	,	,	PUNCT
ejde-388	242	16	where	where	SCONJ
ejde-388	242	17	λ(t	λ(t	NOUN
ejde-388	242	18	)	)	PUNCT
ejde-388	242	19	=	=	SYM
ejde-388	242	20	‖du(t)‖h3	‖du(t)‖h3	PROPN
ejde-388	242	21	.	.	PUNCT
ejde-388	243	1	that	that	SCONJ
ejde-388	243	2	the	the	DET
ejde-388	243	3	super	super	ADV
ejde-388	243	4	fast	fast	ADJ
ejde-388	243	5	growth	growth	NOUN
ejde-388	243	6	(	(	PUNCT
ejde-388	243	7	short	short	ADJ
ejde-388	243	8	term	term	NOUN
ejde-388	243	9	unpredictability	unpredictability	NOUN
ejde-388	243	10	)	)	PUNCT
ejde-388	243	11	nature	nature	NOUN
ejde-388	243	12	is	be	AUX
ejde-388	243	13	independent	independent	ADJ
ejde-388	243	14	of	of	ADP
ejde-388	243	15	ejde-2020/104	ejde-2020/104	PROPN
ejde-388	243	16	short	short	ADJ
ejde-388	243	17	term	term	NOUN
ejde-388	243	18	unpredictability	unpredictability	NOUN
ejde-388	243	19	13	13	NUM
ejde-388	243	20	0	0	NUM
ejde-388	243	21	0.05	0.05	NUM
ejde-388	243	22	0.1	0.1	NUM
ejde-388	243	23	0.15	0.15	NUM
ejde-388	243	24	0.2	0.2	NUM
ejde-388	243	25	0.25	0.25	NUM
ejde-388	243	26	0.3	0.3	NUM
ejde-388	243	27	t	t	NOUN
ejde-388	243	28	0	0	NUM
ejde-388	243	29	2	2	NUM
ejde-388	243	30	4	4	NUM
ejde-388	243	31	6	6	NUM
ejde-388	243	32	8	8	NUM
ejde-388	243	33	ln	ln	NOUN
ejde-388	243	34	(	(	PUNCT
ejde-388	243	35	λ	λ	NOUN
ejde-388	243	36	/λ	/λ	NOUN
ejde-388	243	37	0	0	NUM
ejde-388	243	38	)	)	PUNCT
ejde-388	243	39	0	0	NUM
ejde-388	244	1	0.05	0.05	NUM
ejde-388	244	2	0.1	0.1	NUM
ejde-388	244	3	0.15	0.15	NUM
ejde-388	244	4	0.2	0.2	NUM
ejde-388	244	5	0.25	0.25	NUM
ejde-388	244	6	0.3	0.3	NUM
ejde-388	244	7	t	t	NOUN
ejde-388	244	8	0	0	NUM
ejde-388	244	9	2	2	NUM
ejde-388	244	10	4	4	NUM
ejde-388	244	11	6	6	NUM
ejde-388	244	12	8	8	NUM
ejde-388	244	13	10	10	NUM
ejde-388	244	14	12	12	NUM
ejde-388	244	15	ln	ln	NOUN
ejde-388	244	16	(	(	PUNCT
ejde-388	244	17	λ	λ	INTJ
ejde-388	244	18	/λ	/λ	NOUN
ejde-388	244	19	0	0	NUM
ejde-388	244	20	)	)	PUNCT
ejde-388	244	21	(	(	PUNCT
ejde-388	244	22	a	a	X
ejde-388	244	23	)	)	PUNCT
ejde-388	244	24	n	n	NOUN
ejde-388	244	25	=	=	SYM
ejde-388	244	26	16	16	NUM
ejde-388	244	27	(	(	PUNCT
ejde-388	244	28	b	b	NOUN
ejde-388	244	29	)	)	PUNCT
ejde-388	244	30	n	n	NOUN
ejde-388	244	31	=	=	SYM
ejde-388	244	32	8	8	NUM
ejde-388	244	33	0	0	NUM
ejde-388	244	34	0.05	0.05	NUM
ejde-388	244	35	0.1	0.1	NUM
ejde-388	244	36	0.15	0.15	NUM
ejde-388	244	37	0.2	0.2	NUM
ejde-388	244	38	0.25	0.25	NUM
ejde-388	244	39	0.3	0.3	NUM
ejde-388	244	40	t	t	NOUN
ejde-388	244	41	2	2	NUM
ejde-388	244	42	4	4	NUM
ejde-388	244	43	6	6	NUM
ejde-388	244	44	8	8	NUM
ejde-388	244	45	10	10	NUM
ejde-388	244	46	12	12	NUM
ejde-388	244	47	14	14	NUM
ejde-388	244	48	ln	ln	ADJ
ejde-388	244	49	(	(	PUNCT
ejde-388	244	50	λ	λ	INTJ
ejde-388	244	51	/λ	/λ	NOUN
ejde-388	244	52	0	0	NUM
ejde-388	244	53	)	)	PUNCT
ejde-388	244	54	0	0	NUM
ejde-388	244	55	0.05	0.05	NUM
ejde-388	244	56	0.1	0.1	NUM
ejde-388	244	57	0.15	0.15	NUM
ejde-388	244	58	0.2	0.2	NUM
ejde-388	244	59	0.25	0.25	NUM
ejde-388	244	60	0.3	0.3	NUM
ejde-388	244	61	t	t	NOUN
ejde-388	244	62	6	6	NUM
ejde-388	244	63	8	8	NUM
ejde-388	244	64	10	10	NUM
ejde-388	244	65	12	12	NUM
ejde-388	244	66	14	14	NUM
ejde-388	244	67	16	16	NUM
ejde-388	244	68	18	18	NUM
ejde-388	244	69	ln	ln	NOUN
ejde-388	244	70	(	(	PUNCT
ejde-388	244	71	λ	λ	PROPN
ejde-388	244	72	/λ	/λ	NOUN
ejde-388	244	73	0	0	NUM
ejde-388	244	74	)	)	PUNCT
ejde-388	244	75	(	(	PUNCT
ejde-388	244	76	c	c	X
ejde-388	244	77	)	)	PUNCT
ejde-388	244	78	n	n	NOUN
ejde-388	244	79	=	=	SYM
ejde-388	244	80	4	4	NUM
ejde-388	244	81	(	(	PUNCT
ejde-388	244	82	d	d	NOUN
ejde-388	244	83	)	)	PUNCT
ejde-388	244	84	n	n	NOUN
ejde-388	244	85	=	=	SYM
ejde-388	244	86	2	2	NUM
ejde-388	244	87	figure	figure	NOUN
ejde-388	244	88	8	8	NUM
ejde-388	244	89	.	.	PUNCT
ejde-388	245	1	super	super	ADJ
ejde-388	245	2	fast	fast	ADJ
ejde-388	245	3	growths	growth	NOUN
ejde-388	245	4	of	of	ADP
ejde-388	245	5	the	the	DET
ejde-388	245	6	perturbations	perturbation	NOUN
ejde-388	245	7	with	with	ADP
ejde-388	245	8	the	the	DET
ejde-388	245	9	initial	initial	ADJ
ejde-388	245	10	condition	condition	NOUN
ejde-388	245	11	(	(	PUNCT
ejde-388	245	12	5.15)-(5.16	5.15)-(5.16	NUM
ejde-388	245	13	)	)	PUNCT
ejde-388	245	14	when	when	SCONJ
ejde-388	245	15	n	n	X
ejde-388	245	16	=	=	SYM
ejde-388	245	17	16	16	NUM
ejde-388	245	18	,	,	PUNCT
ejde-388	245	19	8	8	NUM
ejde-388	245	20	,	,	PUNCT
ejde-388	245	21	4	4	NUM
ejde-388	245	22	,	,	PUNCT
ejde-388	245	23	2	2	NUM
ejde-388	245	24	,	,	PUNCT
ejde-388	245	25	to	to	ADP
ejde-388	245	26	the	the	DET
ejde-388	245	27	base	base	NOUN
ejde-388	245	28	solution	solution	NOUN
ejde-388	245	29	with	with	ADP
ejde-388	245	30	the	the	DET
ejde-388	245	31	initial	initial	ADJ
ejde-388	245	32	condition	condition	NOUN
ejde-388	245	33	(	(	PUNCT
ejde-388	245	34	5.12)-(5.13	5.12)-(5.13	NUM
ejde-388	245	35	)	)	PUNCT
ejde-388	245	36	,	,	PUNCT
ejde-388	245	37	where	where	SCONJ
ejde-388	245	38	λ(t	λ(t	NOUN
ejde-388	245	39	)	)	PUNCT
ejde-388	245	40	=	=	SYM
ejde-388	245	41	‖du(t)‖h3	‖du(t)‖h3	PROPN
ejde-388	245	42	.	.	PUNCT
ejde-388	246	1	the	the	DET
ejde-388	246	2	norm	norm	NOUN
ejde-388	246	3	used	use	VERB
ejde-388	246	4	to	to	PART
ejde-388	246	5	measure	measure	VERB
ejde-388	246	6	the	the	DET
ejde-388	246	7	perturbation	perturbation	NOUN
ejde-388	246	8	.	.	PUNCT
ejde-388	247	1	figure	figure	NOUN
ejde-388	247	2	9	9	NUM
ejde-388	247	3	shows	show	VERB
ejde-388	247	4	the	the	DET
ejde-388	247	5	representative	representative	ADJ
ejde-388	247	6	cases	case	NOUN
ejde-388	247	7	of	of	ADP
ejde-388	247	8	h0	h0	NOUN
ejde-388	247	9	and	and	CCONJ
ejde-388	247	10	h3	h3	NOUN
ejde-388	247	11	norms	norm	NOUN
ejde-388	247	12	.	.	PUNCT
ejde-388	248	1	in	in	ADP
ejde-388	248	2	general	general	ADJ
ejde-388	248	3	,	,	PUNCT
ejde-388	248	4	norm	norm	ADJ
ejde-388	248	5	dependence	dependence	NOUN
ejde-388	248	6	is	be	AUX
ejde-388	248	7	a	a	DET
ejde-388	248	8	delicate	delicate	ADJ
ejde-388	248	9	matter	matter	NOUN
ejde-388	248	10	[	[	X
ejde-388	248	11	19	19	NUM
ejde-388	248	12	]	]	PUNCT
ejde-388	248	13	.	.	PUNCT
ejde-388	249	1	we	we	PRON
ejde-388	249	2	do	do	AUX
ejde-388	249	3	not	not	PART
ejde-388	249	4	rule	rule	VERB
ejde-388	249	5	out	out	ADP
ejde-388	249	6	special	special	ADJ
ejde-388	249	7	examples	example	NOUN
ejde-388	249	8	such	such	ADJ
ejde-388	249	9	that	that	SCONJ
ejde-388	249	10	the	the	DET
ejde-388	249	11	super	super	ADV
ejde-388	249	12	fast	fast	ADJ
ejde-388	249	13	growth	growth	NOUN
ejde-388	249	14	depends	depend	VERB
ejde-388	249	15	on	on	ADP
ejde-388	249	16	norms	norm	NOUN
ejde-388	249	17	.	.	PUNCT
ejde-388	250	1	5.6	5.6	NUM
ejde-388	250	2	.	.	PUNCT
ejde-388	251	1	an	an	DET
ejde-388	251	2	intuition	intuition	NOUN
ejde-388	251	3	on	on	ADP
ejde-388	251	4	the	the	DET
ejde-388	251	5	super	super	ADV
ejde-388	251	6	fast	fast	ADJ
ejde-388	251	7	amplification	amplification	NOUN
ejde-388	251	8	of	of	ADP
ejde-388	251	9	perturbation	perturbation	NOUN
ejde-388	251	10	.	.	PUNCT
ejde-388	252	1	take	take	VERB
ejde-388	252	2	2d	2d	NOUN
ejde-388	252	3	for	for	ADP
ejde-388	252	4	example	example	NOUN
ejde-388	252	5	,	,	PUNCT
ejde-388	252	6	following	follow	VERB
ejde-388	252	7	is	be	AUX
ejde-388	252	8	an	an	DET
ejde-388	252	9	intuition	intuition	NOUN
ejde-388	252	10	on	on	ADP
ejde-388	252	11	the	the	DET
ejde-388	252	12	super	super	ADV
ejde-388	252	13	fast	fast	ADJ
ejde-388	252	14	amplification	amplification	NOUN
ejde-388	252	15	of	of	ADP
ejde-388	252	16	perturbation	perturbation	NOUN
ejde-388	252	17	:	:	PUNCT
ejde-388	252	18	in	in	ADP
ejde-388	252	19	terms	term	NOUN
ejde-388	252	20	of	of	ADP
ejde-388	252	21	the	the	DET
ejde-388	252	22	vorticity	vorticity	NOUN
ejde-388	252	23	variable	variable	NOUN
ejde-388	252	24	ω	ω	PROPN
ejde-388	252	25	,	,	PUNCT
ejde-388	252	26	a	a	DET
ejde-388	252	27	mode	mode	NOUN
ejde-388	252	28	kb	kb	PROPN
ejde-388	252	29	=	=	SYM
ejde-388	252	30	(	(	PUNCT
ejde-388	252	31	kb1	kb1	PROPN
ejde-388	252	32	,	,	PUNCT
ejde-388	252	33	k	k	PROPN
ejde-388	252	34	b	b	PROPN
ejde-388	252	35	2	2	NUM
ejde-388	252	36	)	)	PUNCT
ejde-388	252	37	with	with	ADP
ejde-388	252	38	amplitude	amplitude	NOUN
ejde-388	252	39	ωkb	ωkb	NOUN
ejde-388	252	40	of	of	ADP
ejde-388	252	41	the	the	DET
ejde-388	252	42	base	base	NOUN
ejde-388	252	43	solution	solution	NOUN
ejde-388	252	44	and	and	CCONJ
ejde-388	252	45	a	a	DET
ejde-388	252	46	mode	mode	NOUN
ejde-388	252	47	kp	kp	PROPN
ejde-388	252	48	=	=	PUNCT
ejde-388	252	49	(	(	PUNCT
ejde-388	252	50	kp1	kp1	PROPN
ejde-388	252	51	,	,	PUNCT
ejde-388	252	52	k	k	PROPN
ejde-388	252	53	p	p	NOUN
ejde-388	252	54	2	2	NUM
ejde-388	252	55	)	)	PUNCT
ejde-388	252	56	with	with	ADP
ejde-388	252	57	amplitude	amplitude	NOUN
ejde-388	252	58	ωkp	ωkp	NUM
ejde-388	252	59	of	of	ADP
ejde-388	252	60	the	the	DET
ejde-388	252	61	perturbation	perturbation	NOUN
ejde-388	252	62	make	make	VERB
ejde-388	252	63	a	a	DET
ejde-388	252	64	contribution	contribution	NOUN
ejde-388	252	65	[	[	X
ejde-388	252	66	10	10	NUM
ejde-388	252	67	]	]	SYM
ejde-388	252	68	1	1	NUM
ejde-388	252	69	2	2	NUM
ejde-388	253	1	[	[	X
ejde-388	253	2	|kb|−2	|kb|−2	NOUN
ejde-388	253	3	−	−	PROPN
ejde-388	253	4	|kp|−2	|kp|−2	NOUN
ejde-388	253	5	]	]	X
ejde-388	253	6	∣∣∣∣kp1	∣∣∣∣kp1	PROPN
ejde-388	253	7	kb1	kb1	PROPN
ejde-388	253	8	kp2	kp2	VERB
ejde-388	253	9	kb2	kb2	PROPN
ejde-388	253	10	∣∣∣∣ωkpωkb	∣∣∣∣ωkpωkb	PROPN
ejde-388	253	11	to	to	ADP
ejde-388	253	12	the	the	DET
ejde-388	253	13	time	time	NOUN
ejde-388	253	14	derivative	derivative	NOUN
ejde-388	253	15	of	of	ADP
ejde-388	253	16	the	the	DET
ejde-388	253	17	amplitude	amplitude	NOUN
ejde-388	253	18	ωkp+kb	ωkp+kb	NOUN
ejde-388	253	19	of	of	ADP
ejde-388	253	20	the	the	DET
ejde-388	253	21	perturbation	perturbation	NOUN
ejde-388	253	22	mode	mode	NOUN
ejde-388	253	23	kp	kp	PROPN
ejde-388	254	1	+	+	CCONJ
ejde-388	254	2	kb	kb	PROPN
ejde-388	254	3	.	.	PUNCT
ejde-388	255	1	when	when	SCONJ
ejde-388	255	2	|kb|	|kb|	NOUN
ejde-388	255	3	is	be	AUX
ejde-388	255	4	much	much	ADV
ejde-388	255	5	larger	large	ADJ
ejde-388	255	6	than	than	ADP
ejde-388	255	7	kp	kp	PROPN
ejde-388	255	8	,	,	PUNCT
ejde-388	255	9	the	the	DET
ejde-388	255	10	above	above	ADJ
ejde-388	255	11	contribution	contribution	NOUN
ejde-388	255	12	is	be	AUX
ejde-388	255	13	usually	usually	ADV
ejde-388	255	14	of	of	ADP
ejde-388	255	15	the	the	DET
ejde-388	255	16	order	order	NOUN
ejde-388	255	17	|kb||ωkp	|kb||ωkp	NOUN
ejde-388	255	18	|	|	ADV
ejde-388	255	19	.	.	PUNCT
ejde-388	256	1	this	this	PRON
ejde-388	256	2	can	can	AUX
ejde-388	256	3	lead	lead	VERB
ejde-388	256	4	to	to	ADP
ejde-388	256	5	a	a	DET
ejde-388	256	6	super	super	ADJ
ejde-388	256	7	-	-	ADJ
ejde-388	256	8	fast	fast	ADJ
ejde-388	256	9	amplification	amplification	NOUN
ejde-388	256	10	of	of	ADP
ejde-388	256	11	the	the	DET
ejde-388	256	12	perturbation	perturbation	NOUN
ejde-388	256	13	in	in	ADP
ejde-388	256	14	h1	h1	PROPN
ejde-388	256	15	norm	norm	NOUN
ejde-388	256	16	(	(	PUNCT
ejde-388	256	17	i.e.	i.e.	X
ejde-388	256	18	vorticity	vorticity	NOUN
ejde-388	256	19	’s	’s	PART
ejde-388	256	20	l2	l2	PROPN
ejde-388	256	21	norm	norm	NOUN
ejde-388	256	22	)	)	PUNCT
ejde-388	256	23	.	.	PUNCT
ejde-388	257	1	the	the	DET
ejde-388	257	2	amplification	amplification	NOUN
ejde-388	257	3	of	of	ADP
ejde-388	257	4	the	the	DET
ejde-388	257	5	h3	h3	NOUN
ejde-388	257	6	norm	norm	NOUN
ejde-388	257	7	of	of	ADP
ejde-388	257	8	the	the	DET
ejde-388	257	9	perturbation	perturbation	NOUN
ejde-388	257	10	is	be	AUX
ejde-388	257	11	even	even	ADV
ejde-388	257	12	faster	fast	ADJ
ejde-388	257	13	.	.	PUNCT
ejde-388	258	1	this	this	DET
ejde-388	258	2	simple	simple	ADJ
ejde-388	258	3	intuition	intuition	NOUN
ejde-388	258	4	only	only	ADV
ejde-388	258	5	hints	hint	VERB
ejde-388	258	6	a	a	DET
ejde-388	258	7	possible	possible	ADJ
ejde-388	258	8	amplification	amplification	NOUN
ejde-388	258	9	.	.	PUNCT
ejde-388	259	1	the	the	DET
ejde-388	259	2	specific	specific	ADJ
ejde-388	259	3	temporary	temporary	ADJ
ejde-388	259	4	amplification	amplification	NOUN
ejde-388	259	5	as	as	SCONJ
ejde-388	259	6	revealed	reveal	VERB
ejde-388	259	7	via	via	ADP
ejde-388	259	8	numerical	numerical	PROPN
ejde-388	259	9	simulation	simulation	PROPN
ejde-388	259	10	is	be	AUX
ejde-388	259	11	of	of	ADP
ejde-388	259	12	the	the	DET
ejde-388	259	13	form	form	NOUN
ejde-388	259	14	ec	ec	PROPN
ejde-388	259	15	√	√	PROPN
ejde-388	259	16	t.	t.	PROPN
ejde-388	260	1	14	14	NUM
ejde-388	260	2	z.	z.	PROPN
ejde-388	260	3	feng	feng	PROPN
ejde-388	260	4	,	,	PUNCT
ejde-388	260	5	y.	y.	PROPN
ejde-388	260	6	c.	c.	PROPN
ejde-388	260	7	li	li	PROPN
ejde-388	261	1	ejde-2020/104	ejde-2020/104	PROPN
ejde-388	261	2	0	0	NUM
ejde-388	261	3	0.05	0.05	NUM
ejde-388	261	4	0.1	0.1	NUM
ejde-388	261	5	0.15	0.15	NUM
ejde-388	261	6	0.2	0.2	NUM
ejde-388	261	7	0.25	0.25	NUM
ejde-388	261	8	0.3	0.3	NUM
ejde-388	261	9	t	t	NOUN
ejde-388	261	10	6	6	NUM
ejde-388	261	11	8	8	NUM
ejde-388	261	12	10	10	NUM
ejde-388	261	13	12	12	NUM
ejde-388	261	14	14	14	NUM
ejde-388	261	15	16	16	NUM
ejde-388	261	16	ln	ln	ADJ
ejde-388	261	17	(	(	PUNCT
ejde-388	261	18	λ	λ	INTJ
ejde-388	261	19	/λ	/λ	NOUN
ejde-388	261	20	0	0	NUM
ejde-388	261	21	)	)	PUNCT
ejde-388	261	22	0	0	NUM
ejde-388	261	23	0.05	0.05	NUM
ejde-388	261	24	0.1	0.1	NUM
ejde-388	261	25	0.15	0.15	NUM
ejde-388	261	26	0.2	0.2	NUM
ejde-388	261	27	0.25	0.25	NUM
ejde-388	261	28	0.3	0.3	NUM
ejde-388	261	29	t	t	NOUN
ejde-388	261	30	7	7	NUM
ejde-388	261	31	8	8	NUM
ejde-388	261	32	9	9	NUM
ejde-388	261	33	10	10	NUM
ejde-388	261	34	11	11	NUM
ejde-388	261	35	12	12	NUM
ejde-388	261	36	ln	ln	NOUN
ejde-388	261	37	(	(	PUNCT
ejde-388	261	38	λ	λ	PROPN
ejde-388	261	39	/λ	/λ	NOUN
ejde-388	261	40	0	0	NUM
ejde-388	261	41	)	)	PUNCT
ejde-388	261	42	(	(	PUNCT
ejde-388	261	43	a	a	X
ejde-388	261	44	)	)	PUNCT
ejde-388	261	45	h3	h3	NOUN
ejde-388	261	46	norm	norm	NOUN
ejde-388	261	47	,	,	PUNCT
ejde-388	261	48	re	re	ADP
ejde-388	261	49	=	=	NOUN
ejde-388	261	50	100	100	NUM
ejde-388	261	51	(	(	PUNCT
ejde-388	261	52	b	b	NOUN
ejde-388	261	53	)	)	PUNCT
ejde-388	261	54	h3	h3	NOUN
ejde-388	261	55	norm	norm	NOUN
ejde-388	261	56	,	,	PUNCT
ejde-388	261	57	re	re	ADP
ejde-388	261	58	=	=	NOUN
ejde-388	261	59	5	5	NUM
ejde-388	261	60	0	0	NUM
ejde-388	261	61	0.05	0.05	NUM
ejde-388	261	62	0.1	0.1	NUM
ejde-388	261	63	0.15	0.15	NUM
ejde-388	261	64	0.2	0.2	NUM
ejde-388	261	65	0.25	0.25	NUM
ejde-388	261	66	0.3	0.3	NUM
ejde-388	261	67	t	t	NOUN
ejde-388	261	68	0	0	NUM
ejde-388	261	69	2	2	NUM
ejde-388	261	70	4	4	NUM
ejde-388	261	71	6	6	NUM
ejde-388	261	72	8	8	NUM
ejde-388	261	73	ln	ln	NOUN
ejde-388	261	74	(	(	PUNCT
ejde-388	261	75	λ	λ	NOUN
ejde-388	261	76	/λ	/λ	NOUN
ejde-388	261	77	0	0	NUM
ejde-388	261	78	)	)	PUNCT
ejde-388	261	79	0	0	NUM
ejde-388	261	80	0.05	0.05	NUM
ejde-388	261	81	0.1	0.1	NUM
ejde-388	261	82	0.15	0.15	NUM
ejde-388	261	83	0.2	0.2	NUM
ejde-388	261	84	0.25	0.25	NUM
ejde-388	261	85	0.3	0.3	NUM
ejde-388	261	86	t	t	NOUN
ejde-388	261	87	0	0	NUM
ejde-388	261	88	1	1	NUM
ejde-388	261	89	2	2	NUM
ejde-388	261	90	3	3	NUM
ejde-388	261	91	4	4	NUM
ejde-388	261	92	ln	ln	NOUN
ejde-388	261	93	(	(	PUNCT
ejde-388	261	94	λ	λ	NOUN
ejde-388	261	95	/λ	/λ	NOUN
ejde-388	261	96	0	0	NUM
ejde-388	261	97	)	)	PUNCT
ejde-388	261	98	(	(	PUNCT
ejde-388	261	99	c	c	X
ejde-388	261	100	)	)	PUNCT
ejde-388	261	101	h0	h0	NOUN
ejde-388	261	102	norm	norm	NOUN
ejde-388	261	103	,	,	PUNCT
ejde-388	261	104	re	re	ADP
ejde-388	261	105	=	=	NOUN
ejde-388	261	106	100	100	NUM
ejde-388	261	107	(	(	PUNCT
ejde-388	261	108	d	d	NOUN
ejde-388	261	109	)	)	PUNCT
ejde-388	261	110	h0	h0	NOUN
ejde-388	261	111	norm	norm	NOUN
ejde-388	261	112	,	,	PUNCT
ejde-388	261	113	re	re	ADP
ejde-388	261	114	=	=	SYM
ejde-388	261	115	5	5	NUM
ejde-388	261	116	figure	figure	NOUN
ejde-388	261	117	9	9	NUM
ejde-388	261	118	.	.	PUNCT
ejde-388	262	1	super	super	ADJ
ejde-388	262	2	fast	fast	ADJ
ejde-388	262	3	growths	growth	NOUN
ejde-388	262	4	of	of	ADP
ejde-388	262	5	the	the	DET
ejde-388	262	6	perturbations	perturbation	NOUN
ejde-388	262	7	measured	measure	VERB
ejde-388	262	8	in	in	ADP
ejde-388	262	9	different	different	ADJ
ejde-388	262	10	norms	norm	NOUN
ejde-388	262	11	,	,	PUNCT
ejde-388	262	12	with	with	ADP
ejde-388	262	13	the	the	DET
ejde-388	262	14	initial	initial	ADJ
ejde-388	262	15	condition	condition	NOUN
ejde-388	262	16	(	(	PUNCT
ejde-388	262	17	5.15)-(5.16	5.15)-(5.16	NUM
ejde-388	262	18	)	)	PUNCT
ejde-388	262	19	to	to	ADP
ejde-388	262	20	the	the	DET
ejde-388	262	21	base	base	NOUN
ejde-388	262	22	solution	solution	NOUN
ejde-388	262	23	with	with	ADP
ejde-388	262	24	the	the	DET
ejde-388	262	25	initial	initial	ADJ
ejde-388	262	26	condition	condition	NOUN
ejde-388	262	27	(	(	PUNCT
ejde-388	262	28	5.12)-(5.13	5.12)-(5.13	NUM
ejde-388	262	29	)	)	PUNCT
ejde-388	262	30	(	(	PUNCT
ejde-388	262	31	n	n	NOUN
ejde-388	262	32	=	=	SYM
ejde-388	262	33	2	2	NUM
ejde-388	262	34	)	)	PUNCT
ejde-388	262	35	,	,	PUNCT
ejde-388	262	36	where	where	SCONJ
ejde-388	262	37	λ(t	λ(t	NOUN
ejde-388	262	38	)	)	PUNCT
ejde-388	262	39	=	=	SYM
ejde-388	263	1	‖du(t)‖hn	‖du(t)‖hn	X
ejde-388	263	2	(	(	PUNCT
ejde-388	263	3	n	n	NOUN
ejde-388	263	4	=	=	SYM
ejde-388	263	5	0	0	NUM
ejde-388	263	6	,	,	PUNCT
ejde-388	263	7	3	3	NUM
ejde-388	263	8	)	)	PUNCT
ejde-388	263	9	.	.	PUNCT
ejde-388	264	1	6	6	X
ejde-388	264	2	.	.	X
ejde-388	264	3	reynolds	reynold	NOUN
ejde-388	264	4	-	-	PUNCT
ejde-388	264	5	number	number	NOUN
ejde-388	264	6	dependence	dependence	NOUN
ejde-388	264	7	of	of	ADP
ejde-388	264	8	the	the	DET
ejde-388	264	9	super	super	ADV
ejde-388	264	10	fast	fast	ADJ
ejde-388	264	11	amplification	amplification	NOUN
ejde-388	264	12	of	of	ADP
ejde-388	264	13	perturbations	perturbation	NOUN
ejde-388	264	14	when	when	SCONJ
ejde-388	264	15	the	the	DET
ejde-388	264	16	initial	initial	ADJ
ejde-388	264	17	perturbations	perturbation	NOUN
ejde-388	264	18	are	be	AUX
ejde-388	264	19	of	of	ADP
ejde-388	264	20	single	single	ADJ
ejde-388	264	21	modes	mode	NOUN
ejde-388	264	22	,	,	PUNCT
ejde-388	264	23	lower	low	ADJ
ejde-388	264	24	mode	mode	NOUN
ejde-388	264	25	amplifies	amplify	VERB
ejde-388	264	26	faster	fast	ADV
ejde-388	264	27	.	.	PUNCT
ejde-388	265	1	this	this	PRON
ejde-388	265	2	does	do	AUX
ejde-388	265	3	not	not	PART
ejde-388	265	4	mean	mean	VERB
ejde-388	265	5	that	that	SCONJ
ejde-388	265	6	the	the	DET
ejde-388	265	7	lowest	low	ADJ
ejde-388	265	8	mode	mode	NOUN
ejde-388	265	9	initial	initial	ADJ
ejde-388	265	10	perturbation	perturbation	NOUN
ejde-388	265	11	is	be	AUX
ejde-388	265	12	the	the	DET
ejde-388	265	13	maximizer	maximizer	NOUN
ejde-388	265	14	in	in	ADP
ejde-388	265	15	the	the	DET
ejde-388	265	16	definition	definition	NOUN
ejde-388	265	17	(	(	PUNCT
ejde-388	265	18	5.10	5.10	NUM
ejde-388	265	19	)	)	PUNCT
ejde-388	265	20	of	of	ADP
ejde-388	265	21	the	the	DET
ejde-388	265	22	norm	norm	NOUN
ejde-388	265	23	of	of	ADP
ejde-388	265	24	the	the	DET
ejde-388	265	25	derivative	derivative	NOUN
ejde-388	265	26	of	of	ADP
ejde-388	265	27	the	the	DET
ejde-388	265	28	solution	solution	NOUN
ejde-388	265	29	map	map	NOUN
ejde-388	265	30	,	,	PUNCT
ejde-388	265	31	as	as	SCONJ
ejde-388	265	32	shown	show	VERB
ejde-388	265	33	below	below	ADV
ejde-388	265	34	.	.	PUNCT
ejde-388	266	1	let	let	VERB
ejde-388	266	2	dû(0	dû(0	NOUN
ejde-388	266	3	)	)	PUNCT
ejde-388	266	4	and	and	CCONJ
ejde-388	266	5	dũ(0	dũ(0	PROPN
ejde-388	266	6	)	)	PUNCT
ejde-388	266	7	be	be	VERB
ejde-388	266	8	two	two	NUM
ejde-388	266	9	single	single	ADJ
ejde-388	266	10	-	-	PUNCT
ejde-388	266	11	mode	mode	NOUN
ejde-388	266	12	initial	initial	ADJ
ejde-388	266	13	perturbations	perturbation	NOUN
ejde-388	266	14	:	:	PUNCT
ejde-388	266	15	‖dû(t)‖h3	‖dû(t)‖h3	PROPN
ejde-388	266	16	=	=	PUNCT
ejde-388	266	17	√	√	ADP
ejde-388	266	18	c1(t)‖dû(0)‖h3	c1(t)‖dû(0)‖h3	PROPN
ejde-388	266	19	,	,	PUNCT
ejde-388	266	20	‖dũ(t)‖h3	‖dũ(t)‖h3	PROPN
ejde-388	266	21	=	=	PUNCT
ejde-388	267	1	√	√	PROPN
ejde-388	267	2	c2(t)‖dũ(0)‖h3	c2(t)‖dũ(0)‖h3	PROPN
ejde-388	267	3	.	.	PUNCT
ejde-388	268	1	for	for	ADP
ejde-388	268	2	any	any	DET
ejde-388	268	3	fixed	fix	VERB
ejde-388	268	4	t	t	PROPN
ejde-388	268	5	>	>	X
ejde-388	268	6	0	0	NUM
ejde-388	268	7	,	,	PUNCT
ejde-388	268	8	without	without	ADP
ejde-388	268	9	loss	loss	NOUN
ejde-388	268	10	of	of	ADP
ejde-388	268	11	generality	generality	NOUN
ejde-388	268	12	,	,	PUNCT
ejde-388	268	13	assume	assume	VERB
ejde-388	268	14	that	that	SCONJ
ejde-388	268	15	c1(t	c1(t	NOUN
ejde-388	268	16	)	)	PUNCT
ejde-388	268	17	≥	≥	NOUN
ejde-388	268	18	c2(t	c2(t	NOUN
ejde-388	268	19	)	)	PUNCT
ejde-388	268	20	.	.	PUNCT
ejde-388	269	1	consider	consider	VERB
ejde-388	269	2	the	the	DET
ejde-388	269	3	initial	initial	ADJ
ejde-388	269	4	perturbations	perturbation	NOUN
ejde-388	269	5	dû(0	dû(0	NOUN
ejde-388	269	6	)	)	PUNCT
ejde-388	270	1	+	+	CCONJ
ejde-388	270	2	αdũ(0	αdũ(0	NOUN
ejde-388	270	3	)	)	PUNCT
ejde-388	270	4	,	,	PUNCT
ejde-388	270	5	where	where	SCONJ
ejde-388	270	6	α	α	NOUN
ejde-388	270	7	is	be	AUX
ejde-388	270	8	a	a	DET
ejde-388	270	9	real	real	ADJ
ejde-388	270	10	parameter	parameter	NOUN
ejde-388	270	11	,	,	PUNCT
ejde-388	270	12	‖dû(t	‖dû(t	NOUN
ejde-388	270	13	)	)	PUNCT
ejde-388	271	1	+	+	SYM
ejde-388	271	2	αdũ(t)‖2h3	αdũ(t)‖2h3	X
ejde-388	272	1	=	=	SYM
ejde-388	272	2	‖dû(t)‖2h3	‖dû(t)‖2h3	PROPN
ejde-388	272	3	+	+	SYM
ejde-388	272	4	α2‖dũ(t)‖2h3	α2‖dũ(t)‖2h3	PROPN
ejde-388	272	5	+	+	NUM
ejde-388	272	6	2α〈dû(t	2α〈dû(t	NOUN
ejde-388	272	7	)	)	PUNCT
ejde-388	272	8	,	,	PUNCT
ejde-388	272	9	dũ(t)〉h3	dũ(t)〉h3	PROPN
ejde-388	272	10	,	,	PUNCT
ejde-388	272	11	where	where	SCONJ
ejde-388	272	12	〈	〈	PROPN
ejde-388	272	13	dû(t	dû(t	X
ejde-388	272	14	)	)	PUNCT
ejde-388	272	15	,	,	PUNCT
ejde-388	272	16	dũ(t)〉h3	dũ(t)〉h3	PROPN
ejde-388	272	17	=	=	SYM
ejde-388	272	18	∫	∫	PROPN
ejde-388	272	19	∑	∑	PUNCT
ejde-388	272	20	0≤m+n≤3,`=1,2	0≤m+n≤3,`=1,2	PUNCT
ejde-388	273	1	[	[	X
ejde-388	273	2	(	(	PUNCT
ejde-388	273	3	∂	∂	NUM
ejde-388	273	4	∂x1	∂x1	NOUN
ejde-388	273	5	)	)	PUNCT
ejde-388	273	6	m	m	PROPN
ejde-388	273	7	(	(	PUNCT
ejde-388	273	8	∂	∂	NUM
ejde-388	273	9	∂x2	∂x2	NOUN
ejde-388	273	10	)	)	PUNCT
ejde-388	273	11	n	n	PRON
ejde-388	273	12	dû	dû	NOUN
ejde-388	273	13	`	`	PUNCT
ejde-388	273	14	]	]	PUNCT
ejde-388	273	15	[	[	X
ejde-388	273	16	(	(	PUNCT
ejde-388	273	17	∂	∂	NUM
ejde-388	273	18	∂x1	∂x1	NOUN
ejde-388	273	19	)	)	PUNCT
ejde-388	274	1	m	m	PROPN
ejde-388	274	2	(	(	PUNCT
ejde-388	274	3	∂	∂	NUM
ejde-388	274	4	∂x2	∂x2	NOUN
ejde-388	274	5	)	)	PUNCT
ejde-388	274	6	n	n	PRON
ejde-388	274	7	dũ	dũ	NOUN
ejde-388	274	8	`	`	PUNCT
ejde-388	274	9	]	]	PUNCT
ejde-388	275	1	dx1	dx1	PROPN
ejde-388	275	2	dx2	dx2	PROPN
ejde-388	275	3	.	.	PROPN
ejde-388	275	4	then	then	ADV
ejde-388	275	5	‖dû(t	‖dû(t	X
ejde-388	275	6	)	)	PUNCT
ejde-388	276	1	+	+	SYM
ejde-388	276	2	αdũ(t)‖2h3	αdũ(t)‖2h3	X
ejde-388	277	1	=	=	SYM
ejde-388	277	2	c1(t)‖dû(0)‖2h3	c1(t)‖dû(0)‖2h3	PROPN
ejde-388	278	1	+	+	NUM
ejde-388	278	2	α2c2(t)‖dũ(0)‖2h3	α2c2(t)‖dũ(0)‖2h3	PROPN
ejde-388	278	3	+	+	NUM
ejde-388	278	4	2α〈dû(t	2α〈dû(t	PROPN
ejde-388	278	5	)	)	PUNCT
ejde-388	278	6	,	,	PUNCT
ejde-388	278	7	dũ(t)〉h3	dũ(t)〉h3	PROPN
ejde-388	278	8	.	.	PUNCT
ejde-388	279	1	ejde-2020/104	ejde-2020/104	PROPN
ejde-388	279	2	short	short	ADJ
ejde-388	279	3	term	term	NOUN
ejde-388	279	4	unpredictability	unpredictability	NOUN
ejde-388	279	5	15	15	NUM
ejde-388	279	6	since	since	SCONJ
ejde-388	279	7	dû(0	dû(0	NOUN
ejde-388	279	8	)	)	PUNCT
ejde-388	279	9	and	and	CCONJ
ejde-388	279	10	dũ(0	dũ(0	NUM
ejde-388	279	11	)	)	PUNCT
ejde-388	279	12	are	be	AUX
ejde-388	279	13	single	single	ADJ
ejde-388	279	14	modes	mode	NOUN
ejde-388	279	15	,	,	PUNCT
ejde-388	279	16	〈	〈	PROPN
ejde-388	279	17	dû(0	dû(0	NOUN
ejde-388	279	18	)	)	PUNCT
ejde-388	279	19	,	,	PUNCT
ejde-388	279	20	dũ(0)〉h3	dũ(0)〉h3	X
ejde-388	279	21	=	=	SYM
ejde-388	279	22	0	0	NUM
ejde-388	279	23	,	,	PUNCT
ejde-388	279	24	‖dû(0	‖dû(0	NOUN
ejde-388	279	25	)	)	PUNCT
ejde-388	280	1	+	+	CCONJ
ejde-388	280	2	αdũ(0)‖2h3	αdũ(0)‖2h3	ADV
ejde-388	280	3	=	=	SYM
ejde-388	280	4	‖dû(0)‖2h3	‖dû(0)‖2h3	PUNCT
ejde-388	281	1	+	+	CCONJ
ejde-388	281	2	α2‖dũ(0)‖2h3	α2‖dũ(0)‖2h3	PROPN
ejde-388	281	3	.	.	PUNCT
ejde-388	282	1	next	next	ADV
ejde-388	282	2	we	we	PRON
ejde-388	282	3	show	show	VERB
ejde-388	282	4	that	that	SCONJ
ejde-388	282	5	for	for	ADP
ejde-388	282	6	some	some	DET
ejde-388	282	7	range	range	NOUN
ejde-388	282	8	of	of	ADP
ejde-388	282	9	the	the	DET
ejde-388	282	10	parameter	parameter	NOUN
ejde-388	282	11	α	α	NOUN
ejde-388	282	12	,	,	PUNCT
ejde-388	282	13	‖dû(t	‖dû(t	NOUN
ejde-388	282	14	)	)	PUNCT
ejde-388	282	15	+	+	NUM
ejde-388	283	1	αdũ(t)‖2h3	αdũ(t)‖2h3	NUM
ejde-388	283	2	>	>	PUNCT
ejde-388	283	3	c1(t)‖dû(0	c1(t)‖dû(0	NUM
ejde-388	283	4	)	)	PUNCT
ejde-388	284	1	+	+	CCONJ
ejde-388	284	2	αdũ(0)‖2h3	αdũ(0)‖2h3	ADV
ejde-388	284	3	,	,	PUNCT
ejde-388	284	4	(	(	PUNCT
ejde-388	284	5	6.1	6.1	NUM
ejde-388	284	6	)	)	PUNCT
ejde-388	284	7	that	that	PRON
ejde-388	284	8	is	be	AUX
ejde-388	284	9	,	,	PUNCT
ejde-388	284	10	dû(0)+αdũ(0	dû(0)+αdũ(0	ADV
ejde-388	284	11	)	)	PUNCT
ejde-388	284	12	can	can	AUX
ejde-388	284	13	amplify	amplify	VERB
ejde-388	284	14	faster	fast	ADV
ejde-388	284	15	than	than	ADP
ejde-388	284	16	both	both	DET
ejde-388	284	17	dû(0	dû(0	NOUN
ejde-388	284	18	)	)	PUNCT
ejde-388	284	19	and	and	CCONJ
ejde-388	284	20	dũ(0	dũ(0	NUM
ejde-388	284	21	)	)	PUNCT
ejde-388	284	22	.	.	PUNCT
ejde-388	285	1	the	the	DET
ejde-388	285	2	inequality	inequality	NOUN
ejde-388	285	3	(	(	PUNCT
ejde-388	285	4	6.1	6.1	NUM
ejde-388	285	5	)	)	PUNCT
ejde-388	285	6	is	be	AUX
ejde-388	285	7	equivalent	equivalent	ADJ
ejde-388	285	8	to	to	ADP
ejde-388	285	9	2	2	NUM
ejde-388	285	10	α	α	NOUN
ejde-388	285	11	〈	〈	PROPN
ejde-388	285	12	dû(t	dû(t	X
ejde-388	285	13	)	)	PUNCT
ejde-388	285	14	,	,	PUNCT
ejde-388	285	15	dũ(t)〉h3	dũ(t)〉h3	PROPN
ejde-388	285	16	>	>	X
ejde-388	285	17	(	(	PUNCT
ejde-388	285	18	c1(t)−	c1(t)−	X
ejde-388	285	19	c2(t))‖dũ(0)‖2h3	c2(t))‖dũ(0)‖2h3	PROPN
ejde-388	285	20	.	.	PUNCT
ejde-388	286	1	as	as	ADV
ejde-388	286	2	long	long	ADV
ejde-388	286	3	as	as	ADP
ejde-388	286	4	〈	〈	PROPN
ejde-388	286	5	dû(t	dû(t	X
ejde-388	286	6	)	)	PUNCT
ejde-388	286	7	,	,	PUNCT
ejde-388	286	8	dũ(t)〉h3	dũ(t)〉h3	PROPN
ejde-388	286	9	6=	6=	ADP
ejde-388	286	10	0	0	NUM
ejde-388	286	11	,	,	PUNCT
ejde-388	286	12	the	the	DET
ejde-388	286	13	inequality	inequality	NOUN
ejde-388	286	14	is	be	AUX
ejde-388	286	15	satisfied	satisfied	ADJ
ejde-388	286	16	in	in	ADP
ejde-388	286	17	certain	certain	ADJ
ejde-388	286	18	range	range	NOUN
ejde-388	286	19	of	of	ADP
ejde-388	286	20	α	α	NOUN
ejde-388	286	21	with	with	ADP
ejde-388	286	22	small	small	ADJ
ejde-388	286	23	enough	enough	ADJ
ejde-388	286	24	|α|	|α|	PROPN
ejde-388	286	25	.	.	PUNCT
ejde-388	287	1	similarly	similarly	ADV
ejde-388	287	2	,	,	PUNCT
ejde-388	287	3	in	in	ADP
ejde-388	287	4	another	another	DET
ejde-388	287	5	range	range	NOUN
ejde-388	287	6	of	of	ADP
ejde-388	287	7	α	α	NOUN
ejde-388	287	8	with	with	ADP
ejde-388	287	9	large	large	ADJ
ejde-388	287	10	enough	enough	ADJ
ejde-388	287	11	|α|	|α|	NOUN
ejde-388	287	12	,	,	PUNCT
ejde-388	287	13	such	such	ADJ
ejde-388	287	14	that	that	SCONJ
ejde-388	287	15	−2α〈dû(t	−2α〈dû(t	X
ejde-388	287	16	)	)	PUNCT
ejde-388	287	17	,	,	PUNCT
ejde-388	287	18	dũ(t)〉h3	dũ(t)〉h3	AUX
ejde-388	287	19	>	>	X
ejde-388	287	20	(	(	PUNCT
ejde-388	287	21	c1(t)−	c1(t)−	SYM
ejde-388	287	22	c2(t))‖dû(0)‖2h3	c2(t))‖dû(0)‖2h3	PROPN
ejde-388	287	23	,	,	PUNCT
ejde-388	287	24	we	we	PRON
ejde-388	287	25	have	have	VERB
ejde-388	287	26	‖dû(t	‖dû(t	NOUN
ejde-388	287	27	)	)	PUNCT
ejde-388	288	1	+	+	NUM
ejde-388	288	2	αdũ(t)‖2h3	αdũ(t)‖2h3	NUM
ejde-388	288	3	<	<	X
ejde-388	288	4	c2(t)‖dû(0	c2(t)‖dû(0	NUM
ejde-388	288	5	)	)	PUNCT
ejde-388	289	1	+	+	CCONJ
ejde-388	289	2	αdũ(0)‖2h3	αdũ(0)‖2h3	ADV
ejde-388	289	3	,	,	PUNCT
ejde-388	289	4	that	that	ADV
ejde-388	289	5	is	is	ADV
ejde-388	289	6	,	,	PUNCT
ejde-388	289	7	dû(0	dû(0	NOUN
ejde-388	289	8	)	)	PUNCT
ejde-388	290	1	+	+	CCONJ
ejde-388	290	2	αdũ(0	αdũ(0	NOUN
ejde-388	290	3	)	)	PUNCT
ejde-388	290	4	can	can	AUX
ejde-388	290	5	amplify	amplify	VERB
ejde-388	290	6	slower	slow	ADJ
ejde-388	290	7	than	than	ADP
ejde-388	290	8	both	both	DET
ejde-388	290	9	dû(0	dû(0	NOUN
ejde-388	290	10	)	)	PUNCT
ejde-388	290	11	and	and	CCONJ
ejde-388	290	12	dũ(0	dũ(0	NUM
ejde-388	290	13	)	)	PUNCT
ejde-388	290	14	.	.	PUNCT
ejde-388	291	1	let	let	VERB
ejde-388	291	2	f(α	f(α	NOUN
ejde-388	291	3	)	)	PUNCT
ejde-388	291	4	=	=	SYM
ejde-388	291	5	‖dû(t	‖dû(t	NOUN
ejde-388	291	6	)	)	PUNCT
ejde-388	292	1	+	+	CCONJ
ejde-388	292	2	αdũ(t)‖2h3	αdũ(t)‖2h3	NUM
ejde-388	292	3	‖dû(0	‖dû(0	NOUN
ejde-388	292	4	)	)	PUNCT
ejde-388	293	1	+	+	CCONJ
ejde-388	293	2	αdũ(0)‖2h3	αdũ(0)‖2h3	ADV
ejde-388	293	3	,	,	PUNCT
ejde-388	293	4	the	the	DET
ejde-388	293	5	qualitative	qualitative	ADJ
ejde-388	293	6	feature	feature	NOUN
ejde-388	293	7	of	of	ADP
ejde-388	293	8	f(α	f(α	NOUN
ejde-388	293	9	)	)	PUNCT
ejde-388	293	10	is	be	AUX
ejde-388	293	11	shown	show	VERB
ejde-388	293	12	in	in	ADP
ejde-388	293	13	figure	figure	NOUN
ejde-388	293	14	10	10	NUM
ejde-388	293	15	,	,	PUNCT
ejde-388	293	16	where	where	SCONJ
ejde-388	293	17	figure	figure	NOUN
ejde-388	293	18	10(a	10(a	NUM
ejde-388	293	19	)	)	PUNCT
ejde-388	293	20	corresponds	correspond	VERB
ejde-388	293	21	to	to	ADP
ejde-388	293	22	the	the	DET
ejde-388	293	23	case	case	NOUN
ejde-388	293	24	〈	〈	PROPN
ejde-388	293	25	dû(t	dû(t	X
ejde-388	293	26	)	)	PUNCT
ejde-388	293	27	,	,	PUNCT
ejde-388	293	28	dũ(t)〉h3	dũ(t)〉h3	PROPN
ejde-388	293	29	>	>	SYM
ejde-388	293	30	0	0	NUM
ejde-388	293	31	and	and	CCONJ
ejde-388	293	32	figure	figure	NOUN
ejde-388	293	33	10(b	10(b	NUM
ejde-388	293	34	)	)	PUNCT
ejde-388	293	35	corresponds	correspond	VERB
ejde-388	293	36	to	to	ADP
ejde-388	293	37	the	the	DET
ejde-388	293	38	case	case	NOUN
ejde-388	293	39	〈	〈	PROPN
ejde-388	293	40	dû(t	dû(t	X
ejde-388	293	41	)	)	PUNCT
ejde-388	293	42	,	,	PUNCT
ejde-388	293	43	dũ(t)〉h3	dũ(t)〉h3	PROPN
ejde-388	293	44	<	<	X
ejde-388	293	45	0	0	NUM
ejde-388	293	46	,	,	PUNCT
ejde-388	293	47	since	since	SCONJ
ejde-388	293	48	f	f	PROPN
ejde-388	293	49	′(0	′(0	PROPN
ejde-388	293	50	)	)	PUNCT
ejde-388	293	51	=	=	SYM
ejde-388	293	52	2〈dû(t	2〈dû(t	NUM
ejde-388	293	53	)	)	PUNCT
ejde-388	293	54	,	,	PUNCT
ejde-388	293	55	dũ(t)〉h3	dũ(t)〉h3	PROPN
ejde-388	293	56	‖dû(0)‖2h3	‖dû(0)‖2h3	PUNCT
ejde-388	293	57	.	.	PUNCT
ejde-388	294	1	f(α	f(α	NOUN
ejde-388	294	2	)	)	PUNCT
ejde-388	294	3	α	α	NOUN
ejde-388	294	4	•	•	NUM
ejde-388	294	5	c	c	NOUN
ejde-388	294	6	1	1	NUM
ejde-388	294	7	(	(	PUNCT
ejde-388	294	8	t	t	PROPN
ejde-388	294	9	)	)	PUNCT
ejde-388	294	10	•	•	NUM
ejde-388	294	11	c	c	NOUN
ejde-388	294	12	2	2	NUM
ejde-388	294	13	(	(	PUNCT
ejde-388	294	14	t	t	NOUN
ejde-388	294	15	)	)	PUNCT
ejde-388	294	16	α	α	PROPN
ejde-388	294	17	+	+	NOUN
ejde-388	294	18	α	α	NOUN
ejde-388	294	19	f(α	f(α	NOUN
ejde-388	294	20	)	)	PUNCT
ejde-388	294	21	α	α	NOUN
ejde-388	294	22	•	•	NOUN
ejde-388	294	23	c	c	NOUN
ejde-388	294	24	1	1	NUM
ejde-388	294	25	(	(	PUNCT
ejde-388	294	26	t	t	PROPN
ejde-388	294	27	)	)	PUNCT
ejde-388	294	28	•	•	NUM
ejde-388	294	29	c	c	NOUN
ejde-388	294	30	2	2	NUM
ejde-388	294	31	(	(	PUNCT
ejde-388	294	32	t	t	NOUN
ejde-388	294	33	)	)	PUNCT
ejde-388	294	34	α	α	PROPN
ejde-388	295	1	+	+	X
ejde-388	295	2	α	α	PROPN
ejde-388	295	3	(	(	PUNCT
ejde-388	295	4	a	a	NOUN
ejde-388	295	5	)	)	PUNCT
ejde-388	295	6	〈	〈	NOUN
ejde-388	295	7	dû(t	dû(t	X
ejde-388	295	8	)	)	PUNCT
ejde-388	295	9	,	,	PUNCT
ejde-388	295	10	dũ(t)〉h3	dũ(t)〉h3	PROPN
ejde-388	295	11	>	>	X
ejde-388	295	12	0	0	NUM
ejde-388	296	1	(	(	PUNCT
ejde-388	296	2	b	b	NOUN
ejde-388	296	3	)	)	PUNCT
ejde-388	296	4	〈	〈	NOUN
ejde-388	296	5	dû(t	dû(t	X
ejde-388	296	6	)	)	PUNCT
ejde-388	296	7	,	,	PUNCT
ejde-388	296	8	dũ(t)〉h3	dũ(t)〉h3	PROPN
ejde-388	296	9	<	<	X
ejde-388	296	10	0	0	NUM
ejde-388	296	11	figure	figure	NOUN
ejde-388	296	12	10	10	NUM
ejde-388	296	13	.	.	PUNCT
ejde-388	297	1	qualitative	qualitative	ADJ
ejde-388	297	2	feature	feature	NOUN
ejde-388	297	3	of	of	ADP
ejde-388	297	4	f(α	f(α	NOUN
ejde-388	297	5	):	):	PUNCT
ejde-388	297	6	(	(	PUNCT
ejde-388	297	7	a	a	X
ejde-388	297	8	)	)	PUNCT
ejde-388	297	9	〈	〈	NOUN
ejde-388	297	10	dû(t	dû(t	X
ejde-388	297	11	)	)	PUNCT
ejde-388	297	12	,	,	PUNCT
ejde-388	297	13	dũ(t)〉h3	dũ(t)〉h3	PROPN
ejde-388	297	14	>	>	X
ejde-388	297	15	0	0	NUM
ejde-388	297	16	,	,	PUNCT
ejde-388	297	17	and	and	CCONJ
ejde-388	297	18	(	(	PUNCT
ejde-388	297	19	b	b	X
ejde-388	297	20	)	)	PUNCT
ejde-388	297	21	〈	〈	NOUN
ejde-388	297	22	dû(t	dû(t	X
ejde-388	297	23	)	)	PUNCT
ejde-388	297	24	,	,	PUNCT
ejde-388	297	25	dũ(t)〉h3	dũ(t)〉h3	PROPN
ejde-388	297	26	<	<	X
ejde-388	297	27	0	0	NUM
ejde-388	297	28	.	.	PUNCT
ejde-388	298	1	denoting	denote	VERB
ejde-388	298	2	a	a	PRON
ejde-388	298	3	=	=	SYM
ejde-388	298	4	‖dû(0)‖2h3	‖dû(0)‖2h3	PROPN
ejde-388	298	5	,	,	PUNCT
ejde-388	298	6	b	b	X
ejde-388	298	7	=	=	SYM
ejde-388	298	8	‖dũ(0)‖2h3	‖dũ(0)‖2h3	PROPN
ejde-388	298	9	,	,	PUNCT
ejde-388	298	10	p	p	X
ejde-388	298	11	(	(	PUNCT
ejde-388	298	12	t	t	NOUN
ejde-388	298	13	)	)	PUNCT
ejde-388	298	14	=	=	PUNCT
ejde-388	299	1	〈	〈	PROPN
ejde-388	299	2	dû(t	dû(t	X
ejde-388	299	3	)	)	PUNCT
ejde-388	299	4	,	,	PUNCT
ejde-388	299	5	dũ(t)〉h3	dũ(t)〉h3	PROPN
ejde-388	299	6	,	,	PUNCT
ejde-388	299	7	the	the	DET
ejde-388	299	8	maximum	maximum	ADJ
ejde-388	299	9	and	and	CCONJ
ejde-388	299	10	minimum	minimum	ADJ
ejde-388	299	11	points	point	NOUN
ejde-388	299	12	of	of	ADP
ejde-388	299	13	f(α	f(α	NOUN
ejde-388	299	14	)	)	PUNCT
ejde-388	299	15	are	be	AUX
ejde-388	299	16	α±	α±	PROPN
ejde-388	299	17	=	=	SYM
ejde-388	299	18	−ab(c1(t)−	−ab(c1(t)−	PROPN
ejde-388	299	19	c2(t))±	c2(t))±	PROPN
ejde-388	299	20	√	√	PROPN
ejde-388	299	21	a2b2(c1(t)−	a2b2(c1(t)−	PROPN
ejde-388	299	22	c2(t))2	c2(t))2	NOUN
ejde-388	300	1	+	+	CCONJ
ejde-388	300	2	4abp	4abp	NUM
ejde-388	300	3	(	(	PUNCT
ejde-388	300	4	t)2	t)2	PROPN
ejde-388	300	5	2bp	2bp	NOUN
ejde-388	300	6	(	(	PUNCT
ejde-388	300	7	t	t	PROPN
ejde-388	300	8	)	)	PUNCT
ejde-388	300	9	.	.	PUNCT
ejde-388	301	1	16	16	NUM
ejde-388	301	2	z.	z.	PROPN
ejde-388	301	3	feng	feng	PROPN
ejde-388	301	4	,	,	PUNCT
ejde-388	301	5	y.	y.	PROPN
ejde-388	301	6	c.	c.	PROPN
ejde-388	301	7	li	li	PROPN
ejde-388	302	1	ejde-2020/104	ejde-2020/104	PROPN
ejde-388	303	1	in	in	ADP
ejde-388	303	2	the	the	DET
ejde-388	303	3	case	case	NOUN
ejde-388	303	4	c1(t	c1(t	NOUN
ejde-388	303	5	)	)	PUNCT
ejde-388	303	6	>	>	X
ejde-388	303	7	c2(t	c2(t	PROPN
ejde-388	303	8	)	)	PUNCT
ejde-388	303	9	,	,	PUNCT
ejde-388	303	10	when	when	SCONJ
ejde-388	303	11	|α+|	|α+|	PROPN
ejde-388	303	12	is	be	AUX
ejde-388	303	13	small	small	ADJ
ejde-388	303	14	,	,	PUNCT
ejde-388	303	15	α+	α+	X
ejde-388	303	16	≈	≈	PROPN
ejde-388	303	17	p	p	X
ejde-388	303	18	(	(	PUNCT
ejde-388	303	19	t	t	PROPN
ejde-388	303	20	)	)	PUNCT
ejde-388	303	21	(	(	PUNCT
ejde-388	303	22	c1(t)−	c1(t)−	PROPN
ejde-388	303	23	c2(t))b	c2(t))b	PROPN
ejde-388	303	24	,	,	PUNCT
ejde-388	303	25	(	(	PUNCT
ejde-388	303	26	6.2	6.2	NUM
ejde-388	303	27	)	)	PUNCT
ejde-388	303	28	when	when	SCONJ
ejde-388	303	29	|α−|	|α−|	NOUN
ejde-388	303	30	is	be	AUX
ejde-388	303	31	large	large	ADJ
ejde-388	303	32	,	,	PUNCT
ejde-388	303	33	α−	α−	ADP
ejde-388	303	34	≈	≈	PROPN
ejde-388	303	35	−	−	PROPN
ejde-388	304	1	(	(	PUNCT
ejde-388	304	2	c1(t)−	c1(t)−	X
ejde-388	304	3	c2(t))a	c2(t))a	PROPN
ejde-388	304	4	p	p	PROPN
ejde-388	304	5	(	(	PUNCT
ejde-388	304	6	t	t	PROPN
ejde-388	304	7	)	)	PUNCT
ejde-388	304	8	.	.	PUNCT
ejde-388	305	1	the	the	DET
ejde-388	305	2	key	key	ADJ
ejde-388	305	3	point	point	NOUN
ejde-388	305	4	is	be	AUX
ejde-388	305	5	that	that	SCONJ
ejde-388	305	6	if	if	SCONJ
ejde-388	305	7	〈	〈	PROPN
ejde-388	305	8	dû(0	dû(0	NOUN
ejde-388	305	9	)	)	PUNCT
ejde-388	305	10	,	,	PUNCT
ejde-388	305	11	dũ(0)〉h3	dũ(0)〉h3	X
ejde-388	305	12	=	=	SYM
ejde-388	305	13	0	0	NUM
ejde-388	305	14	and	and	CCONJ
ejde-388	305	15	〈	〈	PROPN
ejde-388	305	16	dû(t	dû(t	X
ejde-388	305	17	)	)	PUNCT
ejde-388	305	18	,	,	PUNCT
ejde-388	305	19	dũ(t)〉h3	dũ(t)〉h3	PROPN
ejde-388	305	20	6=	6=	ADP
ejde-388	305	21	0	0	NUM
ejde-388	305	22	,	,	PUNCT
ejde-388	305	23	then	then	ADV
ejde-388	305	24	there	there	PRON
ejde-388	305	25	is	be	VERB
ejde-388	305	26	a	a	DET
ejde-388	305	27	range	range	NOUN
ejde-388	305	28	of	of	ADP
ejde-388	305	29	the	the	DET
ejde-388	305	30	parameter	parameter	NOUN
ejde-388	305	31	α	α	PRON
ejde-388	305	32	such	such	ADJ
ejde-388	305	33	that	that	DET
ejde-388	305	34	dû(0	dû(0	NOUN
ejde-388	305	35	)	)	PUNCT
ejde-388	306	1	+	+	CCONJ
ejde-388	306	2	αdũ(0	αdũ(0	NOUN
ejde-388	306	3	)	)	PUNCT
ejde-388	306	4	can	can	AUX
ejde-388	306	5	amplify	amplify	VERB
ejde-388	306	6	faster	fast	ADV
ejde-388	306	7	than	than	ADP
ejde-388	306	8	both	both	DET
ejde-388	306	9	dû(0	dû(0	NOUN
ejde-388	306	10	)	)	PUNCT
ejde-388	306	11	and	and	CCONJ
ejde-388	306	12	dũ(0	dũ(0	NUM
ejde-388	306	13	)	)	PUNCT
ejde-388	306	14	.	.	PUNCT
ejde-388	307	1	by	by	ADP
ejde-388	307	2	iterating	iterate	VERB
ejde-388	307	3	the	the	DET
ejde-388	307	4	above	above	ADJ
ejde-388	307	5	argument	argument	NOUN
ejde-388	307	6	for	for	ADP
ejde-388	307	7	all	all	DET
ejde-388	307	8	the	the	DET
ejde-388	307	9	single	single	ADJ
ejde-388	307	10	fourier	fourier	NOUN
ejde-388	307	11	modes	mode	NOUN
ejde-388	307	12	,	,	PUNCT
ejde-388	307	13	adding	add	VERB
ejde-388	307	14	higher	high	ADJ
ejde-388	307	15	and	and	CCONJ
ejde-388	307	16	higher	high	ADJ
ejde-388	307	17	fourier	fourier	NOUN
ejde-388	307	18	modes	mode	NOUN
ejde-388	307	19	leads	lead	VERB
ejde-388	307	20	to	to	ADP
ejde-388	307	21	faster	fast	ADJ
ejde-388	307	22	and	and	CCONJ
ejde-388	307	23	faster	fast	ADJ
ejde-388	307	24	amplifications	amplification	NOUN
ejde-388	307	25	.	.	PUNCT
ejde-388	308	1	such	such	ADJ
ejde-388	308	2	combinations	combination	NOUN
ejde-388	308	3	of	of	ADP
ejde-388	308	4	more	more	ADJ
ejde-388	308	5	and	and	CCONJ
ejde-388	308	6	more	more	ADJ
ejde-388	308	7	fourier	fourier	NOUN
ejde-388	308	8	modes	mode	NOUN
ejde-388	308	9	amplify	amplify	VERB
ejde-388	308	10	closer	close	ADV
ejde-388	308	11	and	and	CCONJ
ejde-388	308	12	closer	close	ADJ
ejde-388	308	13	to	to	ADP
ejde-388	308	14	the	the	DET
ejde-388	308	15	supremum	supremum	ADJ
ejde-388	308	16	(	(	PUNCT
ejde-388	308	17	5.10	5.10	NUM
ejde-388	308	18	)	)	PUNCT
ejde-388	308	19	.	.	PUNCT
ejde-388	309	1	in	in	ADP
ejde-388	309	2	general	general	ADJ
ejde-388	309	3	,	,	PUNCT
ejde-388	309	4	the	the	DET
ejde-388	309	5	supremum	supremum	NOUN
ejde-388	309	6	can	can	AUX
ejde-388	309	7	not	not	PART
ejde-388	309	8	be	be	AUX
ejde-388	309	9	reached	reach	VERB
ejde-388	309	10	by	by	ADP
ejde-388	309	11	any	any	DET
ejde-388	309	12	specific	specific	ADJ
ejde-388	309	13	initial	initial	ADJ
ejde-388	309	14	perturbation	perturbation	NOUN
ejde-388	309	15	.	.	PUNCT
ejde-388	310	1	the	the	DET
ejde-388	310	2	supremum	supremum	ADJ
ejde-388	310	3	strongly	strongly	ADV
ejde-388	310	4	depends	depend	VERB
ejde-388	310	5	on	on	ADP
ejde-388	310	6	the	the	DET
ejde-388	310	7	reynolds	reynolds	PROPN
ejde-388	310	8	number	number	PROPN
ejde-388	310	9	re	re	PROPN
ejde-388	310	10	.	.	PUNCT
ejde-388	311	1	for	for	ADP
ejde-388	311	2	a	a	DET
ejde-388	311	3	specific	specific	ADJ
ejde-388	311	4	initial	initial	ADJ
ejde-388	311	5	perturbation	perturbation	NOUN
ejde-388	311	6	,	,	PUNCT
ejde-388	311	7	the	the	DET
ejde-388	311	8	reynolds	reynold	NOUN
ejde-388	311	9	-	-	PUNCT
ejde-388	311	10	number	number	NOUN
ejde-388	311	11	effect	effect	NOUN
ejde-388	311	12	is	be	AUX
ejde-388	311	13	negligible	negligible	ADJ
ejde-388	311	14	when	when	SCONJ
ejde-388	311	15	the	the	DET
ejde-388	311	16	reynolds	reynold	NOUN
ejde-388	311	17	number	number	NOUN
ejde-388	311	18	is	be	AUX
ejde-388	311	19	large	large	ADJ
ejde-388	311	20	enough	enough	ADV
ejde-388	311	21	.	.	PUNCT
ejde-388	312	1	in	in	ADP
ejde-388	312	2	fact	fact	NOUN
ejde-388	312	3	,	,	PUNCT
ejde-388	312	4	we	we	PRON
ejde-388	312	5	believe	believe	VERB
ejde-388	312	6	that	that	SCONJ
ejde-388	312	7	the	the	DET
ejde-388	312	8	square	square	ADJ
ejde-388	312	9	-	-	PUNCT
ejde-388	312	10	root	root	NOUN
ejde-388	312	11	nature	nature	NOUN
ejde-388	312	12	of	of	ADP
ejde-388	312	13	the	the	DET
ejde-388	312	14	reynolds	reynolds	PROPN
ejde-388	312	15	number	number	NOUN
ejde-388	312	16	in	in	ADP
ejde-388	312	17	(	(	PUNCT
ejde-388	312	18	3.3	3.3	NUM
ejde-388	312	19	)	)	PUNCT
ejde-388	312	20	can	can	AUX
ejde-388	312	21	only	only	ADV
ejde-388	312	22	be	be	AUX
ejde-388	312	23	realized	realize	VERB
ejde-388	312	24	by	by	ADP
ejde-388	312	25	the	the	DET
ejde-388	312	26	supremum	supremum	ADJ
ejde-388	312	27	,	,	PUNCT
ejde-388	312	28	and	and	CCONJ
ejde-388	312	29	can	can	AUX
ejde-388	312	30	not	not	PART
ejde-388	312	31	be	be	AUX
ejde-388	312	32	realized	realize	VERB
ejde-388	312	33	by	by	ADP
ejde-388	312	34	any	any	DET
ejde-388	312	35	specific	specific	ADJ
ejde-388	312	36	initial	initial	ADJ
ejde-388	312	37	perturbation	perturbation	NOUN
ejde-388	312	38	.	.	PUNCT
ejde-388	313	1	our	our	PRON
ejde-388	313	2	argument	argument	NOUN
ejde-388	313	3	here	here	ADV
ejde-388	313	4	shows	show	VERB
ejde-388	313	5	that	that	SCONJ
ejde-388	313	6	in	in	ADP
ejde-388	313	7	turbulence	turbulence	NOUN
ejde-388	313	8	,	,	PUNCT
ejde-388	313	9	neither	neither	CCONJ
ejde-388	313	10	lower	low	ADJ
ejde-388	313	11	modes	mode	NOUN
ejde-388	313	12	nor	nor	CCONJ
ejde-388	313	13	higher	high	ADJ
ejde-388	313	14	modes	mode	NOUN
ejde-388	313	15	rather	rather	ADV
ejde-388	313	16	certain	certain	ADJ
ejde-388	313	17	combinations	combination	NOUN
ejde-388	313	18	of	of	ADP
ejde-388	313	19	them	they	PRON
ejde-388	313	20	grow	grow	VERB
ejde-388	313	21	faster	fast	ADV
ejde-388	313	22	!	!	PUNCT
ejde-388	314	1	such	such	DET
ejde-388	314	2	a	a	DET
ejde-388	314	3	mechanism	mechanism	NOUN
ejde-388	314	4	manifests	manifest	NOUN
ejde-388	314	5	in	in	ADP
ejde-388	314	6	the	the	DET
ejde-388	314	7	appearance	appearance	NOUN
ejde-388	314	8	of	of	ADP
ejde-388	314	9	turbulence	turbulence	NOUN
ejde-388	314	10	.	.	PUNCT
ejde-388	315	1	7	7	X
ejde-388	315	2	.	.	X
ejde-388	315	3	3d	3d	PROPN
ejde-388	315	4	numerical	numerical	PROPN
ejde-388	315	5	simulations	simulation	NOUN
ejde-388	315	6	on	on	ADP
ejde-388	315	7	rough	rough	ADJ
ejde-388	315	8	dependence	dependence	NOUN
ejde-388	315	9	on	on	ADP
ejde-388	315	10	initial	initial	ADJ
ejde-388	315	11	data	datum	NOUN
ejde-388	315	12	in	in	ADP
ejde-388	315	13	this	this	DET
ejde-388	315	14	section	section	NOUN
ejde-388	315	15	,	,	PUNCT
ejde-388	315	16	we	we	PRON
ejde-388	315	17	will	will	AUX
ejde-388	315	18	demonstrate	demonstrate	VERB
ejde-388	315	19	numerically	numerically	ADV
ejde-388	315	20	the	the	DET
ejde-388	315	21	super	super	ADV
ejde-388	315	22	fast	fast	ADJ
ejde-388	315	23	amplification	amplification	NOUN
ejde-388	315	24	of	of	ADP
ejde-388	315	25	perturbations	perturbation	NOUN
ejde-388	315	26	to	to	ADP
ejde-388	315	27	the	the	DET
ejde-388	315	28	solutions	solution	NOUN
ejde-388	315	29	of	of	ADP
ejde-388	315	30	the	the	DET
ejde-388	315	31	3d	3d	PROPN
ejde-388	315	32	navier	navier	PROPN
ejde-388	315	33	-	-	PUNCT
ejde-388	315	34	stokes	stokes	PROPN
ejde-388	315	35	equations	equation	NOUN
ejde-388	315	36	.	.	PUNCT
ejde-388	316	1	we	we	PRON
ejde-388	316	2	will	will	AUX
ejde-388	316	3	also	also	ADV
ejde-388	316	4	show	show	VERB
ejde-388	316	5	that	that	SCONJ
ejde-388	316	6	such	such	ADJ
ejde-388	316	7	super	super	ADJ
ejde-388	316	8	fast	fast	ADJ
ejde-388	316	9	amplification	amplification	NOUN
ejde-388	316	10	of	of	ADP
ejde-388	316	11	perturbations	perturbation	NOUN
ejde-388	316	12	is	be	AUX
ejde-388	316	13	ubiquitous	ubiquitous	ADJ
ejde-388	316	14	.	.	PUNCT
ejde-388	317	1	we	we	PRON
ejde-388	317	2	numerically	numerically	ADV
ejde-388	317	3	simulate	simulate	VERB
ejde-388	317	4	the	the	DET
ejde-388	317	5	3d	3d	PROPN
ejde-388	317	6	navier	navier	NOUN
ejde-388	317	7	-	-	PUNCT
ejde-388	317	8	stokes	stokes	PROPN
ejde-388	317	9	equations	equation	NOUN
ejde-388	317	10	(	(	PUNCT
ejde-388	317	11	3.1	3.1	NUM
ejde-388	317	12	)	)	PUNCT
ejde-388	317	13	for	for	ADP
ejde-388	317	14	the	the	DET
ejde-388	317	15	base	base	NOUN
ejde-388	317	16	solutions	solution	NOUN
ejde-388	317	17	,	,	PUNCT
ejde-388	317	18	and	and	CCONJ
ejde-388	317	19	the	the	DET
ejde-388	317	20	corresponding	correspond	VERB
ejde-388	317	21	perturbation	perturbation	NOUN
ejde-388	317	22	equations	equation	NOUN
ejde-388	317	23	(	(	PUNCT
ejde-388	317	24	the	the	DET
ejde-388	317	25	same	same	ADJ
ejde-388	317	26	form	form	NOUN
ejde-388	317	27	with	with	ADP
ejde-388	317	28	(	(	PUNCT
ejde-388	317	29	5.6	5.6	NUM
ejde-388	317	30	)	)	PUNCT
ejde-388	317	31	)	)	PUNCT
ejde-388	317	32	under	under	ADP
ejde-388	317	33	the	the	DET
ejde-388	317	34	periodic	periodic	ADJ
ejde-388	317	35	boundary	boundary	ADJ
ejde-388	317	36	condition	condition	NOUN
ejde-388	317	37	with	with	ADP
ejde-388	317	38	period	period	NOUN
ejde-388	317	39	domain	domain	NOUN
ejde-388	317	40	[	[	X
ejde-388	317	41	0	0	NUM
ejde-388	317	42	,	,	PUNCT
ejde-388	317	43	2π	2π	NOUN
ejde-388	317	44	]	]	X
ejde-388	318	1	×	×	NOUN
ejde-388	319	1	[	[	X
ejde-388	319	2	0	0	NUM
ejde-388	319	3	,	,	PUNCT
ejde-388	319	4	2π]×	2π]×	NUM
ejde-388	320	1	[	[	X
ejde-388	320	2	0	0	NUM
ejde-388	320	3	,	,	PUNCT
ejde-388	320	4	2π	2π	NOUN
ejde-388	320	5	]	]	PUNCT
ejde-388	320	6	.	.	PUNCT
ejde-388	321	1	in	in	ADP
ejde-388	321	2	parallel	parallel	NOUN
ejde-388	321	3	with	with	ADP
ejde-388	321	4	the	the	DET
ejde-388	321	5	2d	2d	PROPN
ejde-388	321	6	simulations	simulation	NOUN
ejde-388	321	7	,	,	PUNCT
ejde-388	321	8	we	we	PRON
ejde-388	321	9	have	have	VERB
ejde-388	321	10	two	two	NUM
ejde-388	321	11	goals	goal	NOUN
ejde-388	321	12	:	:	PUNCT
ejde-388	321	13	first	first	ADV
ejde-388	321	14	we	we	PRON
ejde-388	321	15	want	want	VERB
ejde-388	321	16	to	to	PART
ejde-388	321	17	realized	realized	VERB
ejde-388	321	18	the	the	DET
ejde-388	321	19	super	super	ADV
ejde-388	321	20	fast	fast	ADJ
ejde-388	321	21	amplification	amplification	NOUN
ejde-388	321	22	of	of	ADP
ejde-388	321	23	perturbations	perturbation	NOUN
ejde-388	321	24	,	,	PUNCT
ejde-388	321	25	and	and	CCONJ
ejde-388	321	26	then	then	ADV
ejde-388	321	27	we	we	PRON
ejde-388	321	28	want	want	VERB
ejde-388	321	29	to	to	PART
ejde-388	321	30	show	show	VERB
ejde-388	321	31	that	that	SCONJ
ejde-388	321	32	such	such	ADJ
ejde-388	321	33	super	super	ADJ
ejde-388	321	34	fast	fast	ADJ
ejde-388	321	35	amplification	amplification	NOUN
ejde-388	321	36	of	of	ADP
ejde-388	321	37	perturbations	perturbation	NOUN
ejde-388	321	38	is	be	AUX
ejde-388	321	39	abundant	abundant	ADJ
ejde-388	321	40	among	among	ADP
ejde-388	321	41	perturbations	perturbation	NOUN
ejde-388	321	42	and	and	CCONJ
ejde-388	321	43	base	base	NOUN
ejde-388	321	44	solutions	solution	NOUN
ejde-388	321	45	.	.	PUNCT
ejde-388	322	1	again	again	ADV
ejde-388	322	2	,	,	PUNCT
ejde-388	322	3	for	for	ADP
ejde-388	322	4	such	such	ADJ
ejde-388	322	5	two	two	NUM
ejde-388	322	6	goals	goal	NOUN
ejde-388	322	7	,	,	PUNCT
ejde-388	322	8	we	we	PRON
ejde-388	322	9	are	be	AUX
ejde-388	322	10	going	go	VERB
ejde-388	322	11	to	to	PART
ejde-388	322	12	choose	choose	VERB
ejde-388	322	13	the	the	DET
ejde-388	322	14	initial	initial	ADJ
ejde-388	322	15	conditions	condition	NOUN
ejde-388	322	16	of	of	ADP
ejde-388	322	17	the	the	DET
ejde-388	322	18	base	base	NOUN
ejde-388	322	19	solutions	solution	NOUN
ejde-388	322	20	and	and	CCONJ
ejde-388	322	21	the	the	DET
ejde-388	322	22	perturbations	perturbation	NOUN
ejde-388	322	23	,	,	PUNCT
ejde-388	322	24	to	to	PART
ejde-388	322	25	be	be	AUX
ejde-388	322	26	of	of	ADP
ejde-388	322	27	the	the	DET
ejde-388	322	28	form	form	NOUN
ejde-388	322	29	of	of	ADP
ejde-388	322	30	single	single	ADJ
ejde-388	322	31	fourier	fourier	NOUN
ejde-388	322	32	modes	mode	NOUN
ejde-388	322	33	.	.	PUNCT
ejde-388	323	1	since	since	SCONJ
ejde-388	323	2	the	the	DET
ejde-388	323	3	perturbation	perturbation	NOUN
ejde-388	323	4	equations	equation	NOUN
ejde-388	323	5	are	be	AUX
ejde-388	323	6	linear	linear	ADJ
ejde-388	323	7	,	,	PUNCT
ejde-388	323	8	such	such	ADJ
ejde-388	323	9	perturbation	perturbation	NOUN
ejde-388	323	10	solutions	solution	NOUN
ejde-388	323	11	generated	generate	VERB
ejde-388	323	12	from	from	ADP
ejde-388	323	13	single	single	ADJ
ejde-388	323	14	fourier	fourier	NOUN
ejde-388	323	15	modes	mode	NOUN
ejde-388	323	16	form	form	VERB
ejde-388	323	17	a	a	DET
ejde-388	323	18	base	base	NOUN
ejde-388	323	19	of	of	ADP
ejde-388	323	20	superposition	superposition	NOUN
ejde-388	323	21	.	.	PUNCT
ejde-388	324	1	we	we	PRON
ejde-388	324	2	will	will	AUX
ejde-388	324	3	start	start	VERB
ejde-388	324	4	with	with	ADP
ejde-388	324	5	the	the	DET
ejde-388	324	6	initial	initial	ADJ
ejde-388	324	7	condition	condition	NOUN
ejde-388	324	8	for	for	ADP
ejde-388	324	9	the	the	DET
ejde-388	324	10	base	base	NOUN
ejde-388	324	11	solution	solution	NOUN
ejde-388	324	12	in	in	ADP
ejde-388	324	13	the	the	DET
ejde-388	324	14	single	single	ADJ
ejde-388	324	15	-	-	PUNCT
ejde-388	324	16	mode	mode	NOUN
ejde-388	324	17	form	form	NOUN
ejde-388	324	18	u1(0	u1(0	NOUN
ejde-388	324	19	)	)	PUNCT
ejde-388	324	20	=	=	PUNCT
ejde-388	324	21	a	a	DET
ejde-388	324	22	k1	k1	NOUN
ejde-388	324	23	cos(k1x1	cos(k1x1	NOUN
ejde-388	324	24	)	)	PUNCT
ejde-388	324	25	sin(k2x2	sin(k2x2	NOUN
ejde-388	324	26	)	)	PUNCT
ejde-388	324	27	sin(k3x3	sin(k3x3	ADP
ejde-388	324	28	)	)	PUNCT
ejde-388	324	29	,	,	PUNCT
ejde-388	324	30	u2(0	u2(0	NOUN
ejde-388	324	31	)	)	PUNCT
ejde-388	324	32	=	=	PUNCT
ejde-388	324	33	a	a	DET
ejde-388	324	34	k2	k2	PROPN
ejde-388	324	35	sin(k1x1	sin(k1x1	NOUN
ejde-388	324	36	)	)	PUNCT
ejde-388	324	37	cos(k2x2	cos(k2x2	NOUN
ejde-388	324	38	)	)	PUNCT
ejde-388	324	39	sin(k3x3	sin(k3x3	ADP
ejde-388	324	40	)	)	PUNCT
ejde-388	324	41	,	,	PUNCT
ejde-388	324	42	u3(0	u3(0	PROPN
ejde-388	324	43	)	)	PUNCT
ejde-388	325	1	=	=	PRON
ejde-388	325	2	−2	−2	NOUN
ejde-388	325	3	a	a	DET
ejde-388	325	4	k3	k3	ADJ
ejde-388	325	5	sin(k1x1	sin(k1x1	NOUN
ejde-388	325	6	)	)	PUNCT
ejde-388	325	7	sin(k2x2	sin(k2x2	NOUN
ejde-388	325	8	)	)	PUNCT
ejde-388	325	9	cos(k3x3	cos(k3x3	NOUN
ejde-388	325	10	)	)	PUNCT
ejde-388	325	11	,	,	PUNCT
ejde-388	325	12	(	(	PUNCT
ejde-388	325	13	7.1	7.1	NUM
ejde-388	325	14	)	)	PUNCT
ejde-388	325	15	ejde-2020/104	ejde-2020/104	PRON
ejde-388	325	16	short	short	ADJ
ejde-388	325	17	term	term	NOUN
ejde-388	325	18	unpredictability	unpredictability	NOUN
ejde-388	325	19	17	17	NUM
ejde-388	325	20	and	and	CCONJ
ejde-388	325	21	the	the	DET
ejde-388	325	22	initial	initial	ADJ
ejde-388	325	23	condition	condition	NOUN
ejde-388	325	24	for	for	ADP
ejde-388	325	25	the	the	DET
ejde-388	325	26	perturbation	perturbation	NOUN
ejde-388	325	27	in	in	ADP
ejde-388	325	28	the	the	DET
ejde-388	325	29	single	single	ADJ
ejde-388	325	30	-	-	PUNCT
ejde-388	325	31	mode	mode	NOUN
ejde-388	325	32	form	form	NOUN
ejde-388	325	33	du1(0	du1(0	NOUN
ejde-388	325	34	)	)	PUNCT
ejde-388	325	35	=	=	PUNCT
ejde-388	325	36	a	a	DET
ejde-388	325	37	k̂1	k̂1	NOUN
ejde-388	325	38	cos(k̂1x1	cos(k̂1x1	NOUN
ejde-388	325	39	)	)	PUNCT
ejde-388	325	40	sin(k̂2x2	sin(k̂2x2	NOUN
ejde-388	325	41	)	)	PUNCT
ejde-388	325	42	sin(k̂3x3	sin(k̂3x3	NUM
ejde-388	325	43	)	)	PUNCT
ejde-388	325	44	,	,	PUNCT
ejde-388	325	45	du2(0	du2(0	NOUN
ejde-388	325	46	)	)	PUNCT
ejde-388	325	47	=	=	PUNCT
ejde-388	326	1	a	a	DET
ejde-388	326	2	k̂2	k̂2	PROPN
ejde-388	326	3	sin(k̂1x1	sin(k̂1x1	NOUN
ejde-388	326	4	)	)	PUNCT
ejde-388	326	5	cos(k̂2x2	cos(k̂2x2	NOUN
ejde-388	326	6	)	)	PUNCT
ejde-388	326	7	sin(k̂3x3	sin(k̂3x3	NUM
ejde-388	326	8	)	)	PUNCT
ejde-388	326	9	,	,	PUNCT
ejde-388	326	10	du3(0	du3(0	NOUN
ejde-388	326	11	)	)	PUNCT
ejde-388	326	12	=	=	PUNCT
ejde-388	326	13	−2	−2	NOUN
ejde-388	326	14	a	a	DET
ejde-388	326	15	k̂3	k̂3	NOUN
ejde-388	326	16	sin(k̂1x1	sin(k̂1x1	NOUN
ejde-388	326	17	)	)	PUNCT
ejde-388	326	18	sin(k̂2x2	sin(k̂2x2	NOUN
ejde-388	326	19	)	)	PUNCT
ejde-388	326	20	cos(k̂3x3	cos(k̂3x3	NUM
ejde-388	326	21	)	)	PUNCT
ejde-388	326	22	.	.	PUNCT
ejde-388	327	1	(	(	PUNCT
ejde-388	327	2	7.2	7.2	NUM
ejde-388	327	3	)	)	PUNCT
ejde-388	327	4	after	after	SCONJ
ejde-388	327	5	we	we	PRON
ejde-388	327	6	simulate	simulate	VERB
ejde-388	327	7	these	these	DET
ejde-388	327	8	single	single	ADJ
ejde-388	327	9	-	-	PUNCT
ejde-388	327	10	mode	mode	NOUN
ejde-388	327	11	cases	case	NOUN
ejde-388	327	12	,	,	PUNCT
ejde-388	327	13	we	we	PRON
ejde-388	327	14	will	will	AUX
ejde-388	327	15	simulate	simulate	VERB
ejde-388	327	16	more	more	ADV
ejde-388	327	17	realistic	realistic	ADJ
ejde-388	327	18	situations	situation	NOUN
ejde-388	327	19	in	in	ADP
ejde-388	327	20	the	the	DET
ejde-388	327	21	turbulence	turbulence	NOUN
ejde-388	327	22	regime	regime	NOUN
ejde-388	327	23	.	.	PUNCT
ejde-388	328	1	7.1	7.1	NUM
ejde-388	328	2	.	.	PUNCT
ejde-388	328	3	fixed	fix	VERB
ejde-388	328	4	base	base	NOUN
ejde-388	328	5	solution	solution	NOUN
ejde-388	328	6	and	and	CCONJ
ejde-388	328	7	different	different	ADJ
ejde-388	328	8	perturbations	perturbation	NOUN
ejde-388	328	9	.	.	PUNCT
ejde-388	329	1	to	to	PART
ejde-388	329	2	show	show	VERB
ejde-388	329	3	the	the	DET
ejde-388	329	4	abundance	abundance	NOUN
ejde-388	329	5	of	of	ADP
ejde-388	329	6	the	the	DET
ejde-388	329	7	super	super	ADV
ejde-388	329	8	fast	fast	ADJ
ejde-388	329	9	amplification	amplification	NOUN
ejde-388	329	10	among	among	ADP
ejde-388	329	11	perturbations	perturbation	NOUN
ejde-388	329	12	,	,	PUNCT
ejde-388	329	13	we	we	PRON
ejde-388	329	14	choose	choose	VERB
ejde-388	329	15	in	in	ADP
ejde-388	329	16	(	(	PUNCT
ejde-388	329	17	7.1)-(7.2	7.1)-(7.2	NUM
ejde-388	329	18	)	)	PUNCT
ejde-388	329	19	that	that	PRON
ejde-388	329	20	re	re	VERB
ejde-388	329	21	=	=	NOUN
ejde-388	329	22	1000	1000	NUM
ejde-388	329	23	,	,	PUNCT
ejde-388	329	24	a	a	DET
ejde-388	329	25	=	=	SYM
ejde-388	329	26	20	20	NUM
ejde-388	329	27	,	,	PUNCT
ejde-388	329	28	k1	k1	NOUN
ejde-388	329	29	=	=	SYM
ejde-388	329	30	6	6	NUM
ejde-388	329	31	,	,	PUNCT
ejde-388	329	32	k2	k2	NOUN
ejde-388	329	33	=	=	SYM
ejde-388	329	34	5	5	NUM
ejde-388	329	35	,	,	PUNCT
ejde-388	329	36	k3	k3	VERB
ejde-388	329	37	=	=	NOUN
ejde-388	329	38	1	1	NUM
ejde-388	329	39	,	,	PUNCT
ejde-388	329	40	a	a	DET
ejde-388	329	41	=	=	SYM
ejde-388	329	42	0.1	0.1	NUM
ejde-388	329	43	,	,	PUNCT
ejde-388	329	44	(	(	PUNCT
ejde-388	329	45	7.3	7.3	NUM
ejde-388	329	46	)	)	PUNCT
ejde-388	329	47	and	and	CCONJ
ejde-388	329	48	time	time	NOUN
ejde-388	329	49	step	step	NOUN
ejde-388	329	50	∆t	∆t	PROPN
ejde-388	329	51	=	=	SYM
ejde-388	329	52	0.0001	0.0001	NUM
ejde-388	329	53	.	.	NOUN
ejde-388	329	54	0	0	NUM
ejde-388	330	1	0.01	0.01	NUM
ejde-388	330	2	0.02	0.02	NUM
ejde-388	330	3	0.03	0.03	NUM
ejde-388	330	4	0.04	0.04	NUM
ejde-388	330	5	0.05	0.05	NUM
ejde-388	330	6	0.06	0.06	NUM
ejde-388	330	7	t	t	NOUN
ejde-388	330	8	0	0	NUM
ejde-388	330	9	2	2	NUM
ejde-388	330	10	4	4	NUM
ejde-388	330	11	6	6	NUM
ejde-388	330	12	8	8	NUM
ejde-388	330	13	10	10	NUM
ejde-388	330	14	12	12	NUM
ejde-388	330	15	ln	ln	NOUN
ejde-388	330	16	(	(	PUNCT
ejde-388	330	17	λ	λ	INTJ
ejde-388	330	18	/λ	/λ	NOUN
ejde-388	330	19	0	0	NUM
ejde-388	330	20	)	)	PUNCT
ejde-388	330	21	0	0	NUM
ejde-388	331	1	0.01	0.01	NUM
ejde-388	331	2	0.02	0.02	NUM
ejde-388	331	3	0.03	0.03	NUM
ejde-388	331	4	0.04	0.04	NUM
ejde-388	331	5	0.05	0.05	NUM
ejde-388	331	6	0.06	0.06	NUM
ejde-388	331	7	t	t	NOUN
ejde-388	331	8	0	0	NUM
ejde-388	331	9	2	2	NUM
ejde-388	331	10	4	4	NUM
ejde-388	331	11	6	6	NUM
ejde-388	331	12	8	8	NUM
ejde-388	331	13	ln	ln	NOUN
ejde-388	331	14	(	(	PUNCT
ejde-388	331	15	λ	λ	NOUN
ejde-388	331	16	/λ	/λ	NOUN
ejde-388	331	17	0	0	NUM
ejde-388	331	18	)	)	PUNCT
ejde-388	331	19	(	(	PUNCT
ejde-388	331	20	a	a	X
ejde-388	331	21	)	)	PUNCT
ejde-388	331	22	k̂1	k̂1	NOUN
ejde-388	331	23	=	=	NOUN
ejde-388	331	24	1	1	NUM
ejde-388	331	25	,	,	PUNCT
ejde-388	331	26	k̂2	k̂2	X
ejde-388	331	27	=	=	SYM
ejde-388	331	28	1	1	NUM
ejde-388	331	29	,	,	PUNCT
ejde-388	331	30	k̂3	k̂3	NOUN
ejde-388	331	31	=	=	SYM
ejde-388	331	32	1	1	NUM
ejde-388	331	33	(	(	PUNCT
ejde-388	331	34	b	b	NOUN
ejde-388	331	35	)	)	PUNCT
ejde-388	331	36	k̂1	k̂1	NOUN
ejde-388	331	37	=	=	NOUN
ejde-388	331	38	2	2	NUM
ejde-388	331	39	,	,	PUNCT
ejde-388	331	40	k̂2	k̂2	X
ejde-388	331	41	=	=	SYM
ejde-388	331	42	2	2	NUM
ejde-388	331	43	,	,	PUNCT
ejde-388	331	44	k̂3	k̂3	NOUN
ejde-388	331	45	=	=	SYM
ejde-388	331	46	2	2	NUM
ejde-388	331	47	0	0	NUM
ejde-388	331	48	0.01	0.01	NUM
ejde-388	331	49	0.02	0.02	NUM
ejde-388	331	50	0.03	0.03	NUM
ejde-388	331	51	0.04	0.04	NUM
ejde-388	331	52	0.05	0.05	NUM
ejde-388	331	53	0.06	0.06	NUM
ejde-388	331	54	t	t	NOUN
ejde-388	331	55	0	0	NUM
ejde-388	331	56	2	2	NUM
ejde-388	331	57	4	4	NUM
ejde-388	331	58	6	6	NUM
ejde-388	331	59	ln	ln	NOUN
ejde-388	331	60	(	(	PUNCT
ejde-388	331	61	λ	λ	NOUN
ejde-388	331	62	/λ	/λ	NOUN
ejde-388	331	63	0	0	NUM
ejde-388	331	64	)	)	PUNCT
ejde-388	331	65	(	(	PUNCT
ejde-388	331	66	c	c	X
ejde-388	331	67	)	)	PUNCT
ejde-388	331	68	k̂1	k̂1	NOUN
ejde-388	331	69	=	=	NOUN
ejde-388	331	70	3	3	NUM
ejde-388	331	71	,	,	PUNCT
ejde-388	331	72	k̂2	k̂2	X
ejde-388	331	73	=	=	SYM
ejde-388	331	74	3	3	NUM
ejde-388	331	75	,	,	PUNCT
ejde-388	331	76	k̂3	k̂3	NOUN
ejde-388	331	77	=	=	SYM
ejde-388	331	78	3	3	NUM
ejde-388	331	79	figure	figure	NOUN
ejde-388	331	80	11	11	NUM
ejde-388	331	81	.	.	PUNCT
ejde-388	332	1	super	super	ADJ
ejde-388	332	2	fast	fast	ADJ
ejde-388	332	3	growth	growth	NOUN
ejde-388	332	4	of	of	ADP
ejde-388	332	5	the	the	DET
ejde-388	332	6	perturbations	perturbation	NOUN
ejde-388	332	7	of	of	ADP
ejde-388	332	8	different	different	ADJ
ejde-388	332	9	modes	mode	NOUN
ejde-388	332	10	in	in	ADP
ejde-388	332	11	3d	3d	NUM
ejde-388	332	12	with	with	ADP
ejde-388	332	13	parameters	parameter	NOUN
ejde-388	332	14	(	(	PUNCT
ejde-388	332	15	7.3	7.3	NUM
ejde-388	332	16	)	)	PUNCT
ejde-388	332	17	.	.	PUNCT
ejde-388	333	1	figure	figure	NOUN
ejde-388	333	2	11	11	NUM
ejde-388	333	3	shows	show	VERB
ejde-388	333	4	the	the	DET
ejde-388	333	5	super	super	ADV
ejde-388	333	6	fast	fast	ADJ
ejde-388	333	7	growth	growth	NOUN
ejde-388	333	8	of	of	ADP
ejde-388	333	9	the	the	DET
ejde-388	333	10	perturbations	perturbation	NOUN
ejde-388	333	11	of	of	ADP
ejde-388	333	12	different	different	ADJ
ejde-388	333	13	modes	mode	NOUN
ejde-388	333	14	where	where	SCONJ
ejde-388	333	15	λ(t	λ(t	NOUN
ejde-388	333	16	)	)	PUNCT
ejde-388	333	17	is	be	AUX
ejde-388	333	18	defined	define	VERB
ejde-388	333	19	in	in	ADP
ejde-388	333	20	(	(	PUNCT
ejde-388	333	21	5.9	5.9	NUM
ejde-388	333	22	)	)	PUNCT
ejde-388	333	23	.	.	PUNCT
ejde-388	334	1	we	we	PRON
ejde-388	334	2	arrive	arrive	VERB
ejde-388	334	3	at	at	ADP
ejde-388	334	4	the	the	DET
ejde-388	334	5	same	same	ADJ
ejde-388	334	6	conclusion	conclusion	NOUN
ejde-388	334	7	as	as	ADP
ejde-388	334	8	in	in	ADP
ejde-388	334	9	2d	2d	NOUN
ejde-388	334	10	,	,	PUNCT
ejde-388	334	11	that	that	ADV
ejde-388	334	12	is	is	ADV
ejde-388	334	13	,	,	PUNCT
ejde-388	334	14	lower	low	ADJ
ejde-388	334	15	wave	wave	NOUN
ejde-388	334	16	number	number	NOUN
ejde-388	334	17	perturbations	perturbation	NOUN
ejde-388	334	18	have	have	VERB
ejde-388	334	19	faster	fast	ADJ
ejde-388	334	20	super	super	ADJ
ejde-388	334	21	fast	fast	ADJ
ejde-388	334	22	growth	growth	NOUN
ejde-388	334	23	,	,	PUNCT
ejde-388	334	24	and	and	CCONJ
ejde-388	334	25	such	such	ADJ
ejde-388	334	26	super	super	ADJ
ejde-388	334	27	fast	fast	ADJ
ejde-388	334	28	growth	growth	NOUN
ejde-388	334	29	is	be	AUX
ejde-388	334	30	abundant	abundant	ADJ
ejde-388	334	31	among	among	ADP
ejde-388	334	32	perturbations	perturbation	NOUN
ejde-388	334	33	.	.	PUNCT
ejde-388	335	1	18	18	NUM
ejde-388	335	2	z.	z.	PROPN
ejde-388	335	3	feng	feng	PROPN
ejde-388	335	4	,	,	PUNCT
ejde-388	335	5	y.	y.	PROPN
ejde-388	335	6	c.	c.	PROPN
ejde-388	335	7	li	li	PROPN
ejde-388	336	1	ejde-2020/104	ejde-2020/104	PROPN
ejde-388	336	2	7.2	7.2	NUM
ejde-388	336	3	.	.	PUNCT
ejde-388	336	4	fixed	fix	VERB
ejde-388	336	5	perturbation	perturbation	NOUN
ejde-388	336	6	and	and	CCONJ
ejde-388	336	7	different	different	ADJ
ejde-388	336	8	base	base	NOUN
ejde-388	336	9	solutions	solution	NOUN
ejde-388	336	10	.	.	PUNCT
ejde-388	337	1	to	to	PART
ejde-388	337	2	show	show	VERB
ejde-388	337	3	the	the	DET
ejde-388	337	4	abundance	abundance	NOUN
ejde-388	337	5	of	of	ADP
ejde-388	337	6	the	the	DET
ejde-388	337	7	super	super	ADV
ejde-388	337	8	fast	fast	ADJ
ejde-388	337	9	amplification	amplification	NOUN
ejde-388	337	10	among	among	ADP
ejde-388	337	11	base	base	NOUN
ejde-388	337	12	solutions	solution	NOUN
ejde-388	337	13	,	,	PUNCT
ejde-388	337	14	we	we	PRON
ejde-388	337	15	choose	choose	VERB
ejde-388	337	16	in	in	ADP
ejde-388	337	17	(	(	PUNCT
ejde-388	337	18	7.1)-(7.2	7.1)-(7.2	NUM
ejde-388	337	19	)	)	PUNCT
ejde-388	337	20	that	that	PRON
ejde-388	337	21	re	re	VERB
ejde-388	337	22	=	=	NOUN
ejde-388	337	23	1000	1000	NUM
ejde-388	337	24	,	,	PUNCT
ejde-388	337	25	a	a	DET
ejde-388	337	26	=	=	SYM
ejde-388	337	27	20	20	NUM
ejde-388	337	28	,	,	PUNCT
ejde-388	337	29	k̂1	k̂1	NOUN
ejde-388	337	30	=	=	SYM
ejde-388	337	31	1	1	NUM
ejde-388	337	32	,	,	PUNCT
ejde-388	337	33	k̂2	k̂2	X
ejde-388	338	1	=	=	SYM
ejde-388	338	2	1	1	NUM
ejde-388	338	3	,	,	PUNCT
ejde-388	338	4	k̂3	k̂3	NOUN
ejde-388	338	5	=	=	SYM
ejde-388	338	6	1	1	NUM
ejde-388	338	7	,	,	PUNCT
ejde-388	338	8	a	a	DET
ejde-388	338	9	=	=	SYM
ejde-388	338	10	0.1	0.1	NUM
ejde-388	338	11	,	,	PUNCT
ejde-388	338	12	(	(	PUNCT
ejde-388	338	13	7.4	7.4	NUM
ejde-388	338	14	)	)	PUNCT
ejde-388	338	15	and	and	CCONJ
ejde-388	338	16	time	time	NOUN
ejde-388	338	17	step	step	NOUN
ejde-388	338	18	∆t	∆t	PROPN
ejde-388	338	19	=	=	SYM
ejde-388	338	20	0.0001	0.0001	NUM
ejde-388	338	21	.	.	NOUN
ejde-388	338	22	0	0	NUM
ejde-388	338	23	0.01	0.01	NUM
ejde-388	338	24	0.02	0.02	NUM
ejde-388	338	25	0.03	0.03	NUM
ejde-388	338	26	0.04	0.04	NUM
ejde-388	338	27	0.05	0.05	NUM
ejde-388	338	28	0.06	0.06	NUM
ejde-388	338	29	t	t	NOUN
ejde-388	338	30	0	0	NUM
ejde-388	338	31	2	2	NUM
ejde-388	338	32	4	4	NUM
ejde-388	338	33	6	6	NUM
ejde-388	338	34	8	8	NUM
ejde-388	338	35	10	10	NUM
ejde-388	338	36	12	12	NUM
ejde-388	338	37	ln	ln	NOUN
ejde-388	338	38	(	(	PUNCT
ejde-388	338	39	λ	λ	INTJ
ejde-388	338	40	/λ	/λ	NOUN
ejde-388	338	41	0	0	NUM
ejde-388	338	42	)	)	PUNCT
ejde-388	338	43	0	0	NUM
ejde-388	339	1	0.01	0.01	NUM
ejde-388	339	2	0.02	0.02	NUM
ejde-388	339	3	0.03	0.03	NUM
ejde-388	339	4	0.04	0.04	NUM
ejde-388	339	5	0.05	0.05	NUM
ejde-388	339	6	0.06	0.06	NUM
ejde-388	339	7	t	t	NOUN
ejde-388	339	8	0	0	NUM
ejde-388	339	9	2	2	NUM
ejde-388	339	10	4	4	NUM
ejde-388	339	11	6	6	NUM
ejde-388	339	12	8	8	NUM
ejde-388	339	13	10	10	NUM
ejde-388	339	14	ln	ln	NOUN
ejde-388	339	15	(	(	PUNCT
ejde-388	339	16	λ	λ	NOUN
ejde-388	339	17	/λ	/λ	NOUN
ejde-388	339	18	0	0	NUM
ejde-388	339	19	)	)	PUNCT
ejde-388	339	20	(	(	PUNCT
ejde-388	339	21	a	a	X
ejde-388	339	22	)	)	PUNCT
ejde-388	339	23	k1	k1	NOUN
ejde-388	339	24	=	=	SYM
ejde-388	339	25	6	6	NUM
ejde-388	339	26	,	,	PUNCT
ejde-388	339	27	k2	k2	NOUN
ejde-388	339	28	=	=	SYM
ejde-388	339	29	5	5	NUM
ejde-388	339	30	,	,	PUNCT
ejde-388	339	31	k3	k3	VERB
ejde-388	339	32	=	=	SYM
ejde-388	339	33	1	1	NUM
ejde-388	339	34	(	(	PUNCT
ejde-388	339	35	b	b	NOUN
ejde-388	339	36	)	)	PUNCT
ejde-388	339	37	k1	k1	NOUN
ejde-388	339	38	=	=	SYM
ejde-388	339	39	7	7	NUM
ejde-388	339	40	,	,	PUNCT
ejde-388	339	41	k2	k2	NOUN
ejde-388	339	42	=	=	SYM
ejde-388	339	43	6	6	NUM
ejde-388	339	44	,	,	PUNCT
ejde-388	339	45	k3	k3	VERB
ejde-388	339	46	=	=	NOUN
ejde-388	339	47	2	2	NUM
ejde-388	339	48	0	0	NUM
ejde-388	339	49	0.01	0.01	NUM
ejde-388	339	50	0.02	0.02	NUM
ejde-388	339	51	0.03	0.03	NUM
ejde-388	339	52	0.04	0.04	NUM
ejde-388	339	53	0.05	0.05	NUM
ejde-388	339	54	0.06	0.06	NUM
ejde-388	339	55	t	t	NOUN
ejde-388	339	56	0	0	NUM
ejde-388	339	57	2	2	NUM
ejde-388	339	58	4	4	NUM
ejde-388	339	59	6	6	NUM
ejde-388	339	60	8	8	NUM
ejde-388	339	61	10	10	NUM
ejde-388	339	62	ln	ln	NOUN
ejde-388	339	63	(	(	PUNCT
ejde-388	339	64	λ	λ	NOUN
ejde-388	339	65	/λ	/λ	NOUN
ejde-388	339	66	0	0	NUM
ejde-388	339	67	)	)	PUNCT
ejde-388	339	68	(	(	PUNCT
ejde-388	339	69	c	c	X
ejde-388	339	70	)	)	PUNCT
ejde-388	339	71	k1	k1	NOUN
ejde-388	339	72	=	=	SYM
ejde-388	339	73	8	8	NUM
ejde-388	339	74	,	,	PUNCT
ejde-388	339	75	k2	k2	NOUN
ejde-388	339	76	=	=	SYM
ejde-388	339	77	7	7	NUM
ejde-388	339	78	,	,	PUNCT
ejde-388	339	79	k3	k3	VERB
ejde-388	339	80	=	=	SYM
ejde-388	339	81	3	3	NUM
ejde-388	339	82	figure	figure	NOUN
ejde-388	339	83	12	12	NUM
ejde-388	339	84	.	.	PUNCT
ejde-388	340	1	super	super	ADJ
ejde-388	340	2	fast	fast	ADJ
ejde-388	340	3	growth	growth	NOUN
ejde-388	340	4	of	of	ADP
ejde-388	340	5	the	the	DET
ejde-388	340	6	perturbation	perturbation	NOUN
ejde-388	340	7	under	under	ADP
ejde-388	340	8	different	different	ADJ
ejde-388	340	9	base	base	NOUN
ejde-388	340	10	solutions	solution	NOUN
ejde-388	340	11	in	in	ADP
ejde-388	340	12	3d	3d	NUM
ejde-388	340	13	with	with	ADP
ejde-388	340	14	parameters	parameter	NOUN
ejde-388	340	15	(	(	PUNCT
ejde-388	340	16	7.4	7.4	NUM
ejde-388	340	17	)	)	PUNCT
ejde-388	340	18	.	.	PUNCT
ejde-388	341	1	figure	figure	NOUN
ejde-388	341	2	12	12	NUM
ejde-388	341	3	shows	show	VERB
ejde-388	341	4	the	the	DET
ejde-388	341	5	super	super	ADV
ejde-388	341	6	fast	fast	ADJ
ejde-388	341	7	growth	growth	NOUN
ejde-388	341	8	of	of	ADP
ejde-388	341	9	the	the	DET
ejde-388	341	10	perturbation	perturbation	NOUN
ejde-388	341	11	under	under	ADP
ejde-388	341	12	different	different	ADJ
ejde-388	341	13	base	base	NOUN
ejde-388	341	14	solutions	solution	NOUN
ejde-388	341	15	with	with	ADP
ejde-388	341	16	initial	initial	ADJ
ejde-388	341	17	conditions	condition	NOUN
ejde-388	341	18	of	of	ADP
ejde-388	341	19	the	the	DET
ejde-388	341	20	form	form	NOUN
ejde-388	341	21	(	(	PUNCT
ejde-388	341	22	7.1	7.1	NUM
ejde-388	341	23	)	)	PUNCT
ejde-388	341	24	,	,	PUNCT
ejde-388	341	25	where	where	SCONJ
ejde-388	341	26	λ(t	λ(t	NOUN
ejde-388	341	27	)	)	PUNCT
ejde-388	341	28	is	be	AUX
ejde-388	341	29	defined	define	VERB
ejde-388	341	30	in	in	ADP
ejde-388	341	31	(	(	PUNCT
ejde-388	341	32	5.9	5.9	NUM
ejde-388	341	33	)	)	PUNCT
ejde-388	341	34	.	.	PUNCT
ejde-388	342	1	we	we	PRON
ejde-388	342	2	arrive	arrive	VERB
ejde-388	342	3	at	at	ADP
ejde-388	342	4	the	the	DET
ejde-388	342	5	same	same	ADJ
ejde-388	342	6	conclusion	conclusion	NOUN
ejde-388	342	7	as	as	ADP
ejde-388	342	8	in	in	ADP
ejde-388	342	9	2d	2d	NOUN
ejde-388	342	10	,	,	PUNCT
ejde-388	342	11	that	that	ADV
ejde-388	342	12	is	is	ADV
ejde-388	342	13	,	,	PUNCT
ejde-388	342	14	the	the	DET
ejde-388	342	15	perturbation	perturbation	NOUN
ejde-388	342	16	of	of	ADP
ejde-388	342	17	higher	high	ADJ
ejde-388	342	18	mode	mode	NOUN
ejde-388	342	19	base	base	NOUN
ejde-388	342	20	solutions	solution	NOUN
ejde-388	342	21	has	have	VERB
ejde-388	342	22	faster	fast	ADV
ejde-388	342	23	super	super	ADJ
ejde-388	342	24	fast	fast	ADJ
ejde-388	342	25	growth	growth	NOUN
ejde-388	342	26	,	,	PUNCT
ejde-388	342	27	and	and	CCONJ
ejde-388	342	28	such	such	ADJ
ejde-388	342	29	super	super	ADJ
ejde-388	342	30	fast	fast	ADJ
ejde-388	342	31	growth	growth	NOUN
ejde-388	342	32	is	be	AUX
ejde-388	342	33	abundant	abundant	ADJ
ejde-388	342	34	among	among	ADP
ejde-388	342	35	base	base	NOUN
ejde-388	342	36	solutions	solution	NOUN
ejde-388	342	37	.	.	PUNCT
ejde-388	343	1	clearly	clearly	ADV
ejde-388	343	2	,	,	PUNCT
ejde-388	343	3	the	the	DET
ejde-388	343	4	super	super	ADV
ejde-388	343	5	fast	fast	ADJ
ejde-388	343	6	amplification	amplification	NOUN
ejde-388	343	7	of	of	ADP
ejde-388	343	8	perturbations	perturbation	NOUN
ejde-388	343	9	is	be	AUX
ejde-388	343	10	a	a	DET
ejde-388	343	11	generic	generic	ADJ
ejde-388	343	12	phenomenon	phenomenon	NOUN
ejde-388	343	13	that	that	PRON
ejde-388	343	14	is	be	AUX
ejde-388	343	15	independent	independent	ADJ
ejde-388	343	16	of	of	ADP
ejde-388	343	17	spatial	spatial	ADJ
ejde-388	343	18	dimensions	dimension	NOUN
ejde-388	343	19	,	,	PUNCT
ejde-388	343	20	and	and	CCONJ
ejde-388	343	21	is	be	AUX
ejde-388	343	22	ubiquitous	ubiquitous	ADJ
ejde-388	343	23	.	.	PUNCT
ejde-388	344	1	7.3	7.3	NUM
ejde-388	344	2	.	.	PUNCT
ejde-388	344	3	turbulence	turbulence	NOUN
ejde-388	344	4	regime	regime	NOUN
ejde-388	344	5	.	.	PUNCT
ejde-388	345	1	in	in	ADP
ejde-388	345	2	this	this	DET
ejde-388	345	3	subsection	subsection	NOUN
ejde-388	345	4	,	,	PUNCT
ejde-388	345	5	we	we	PRON
ejde-388	345	6	shall	shall	AUX
ejde-388	345	7	simulate	simulate	VERB
ejde-388	345	8	more	more	ADV
ejde-388	345	9	realistic	realistic	ADJ
ejde-388	345	10	situations	situation	NOUN
ejde-388	345	11	of	of	ADP
ejde-388	345	12	base	base	NOUN
ejde-388	345	13	solutions	solution	NOUN
ejde-388	345	14	in	in	ADP
ejde-388	345	15	the	the	DET
ejde-388	345	16	turbulence	turbulence	NOUN
ejde-388	345	17	regime	regime	NOUN
ejde-388	345	18	.	.	PUNCT
ejde-388	346	1	we	we	PRON
ejde-388	346	2	start	start	VERB
ejde-388	346	3	with	with	ADP
ejde-388	346	4	base	base	NOUN
ejde-388	346	5	solution	solution	NOUN
ejde-388	346	6	’s	’s	PART
ejde-388	346	7	ejde-2020/104	ejde-2020/104	PROPN
ejde-388	346	8	short	short	ADJ
ejde-388	346	9	term	term	NOUN
ejde-388	346	10	unpredictability	unpredictability	NOUN
ejde-388	346	11	19	19	NUM
ejde-388	346	12	initial	initial	ADJ
ejde-388	346	13	condition	condition	NOUN
ejde-388	346	14	in	in	ADP
ejde-388	346	15	the	the	DET
ejde-388	346	16	form	form	NOUN
ejde-388	346	17	u1(0	u1(0	NOUN
ejde-388	346	18	)	)	PUNCT
ejde-388	346	19	=	=	SYM
ejde-388	347	1	16∑	16∑	NUM
ejde-388	348	1	l=1	l=1	NOUN
ejde-388	348	2	16∑	16∑	PROPN
ejde-388	349	1	m=1	m=1	PROPN
ejde-388	349	2	16∑	16∑	NUM
ejde-388	349	3	n=1	n=1	PROPN
ejde-388	349	4	almnmn	almnmn	VERB
ejde-388	349	5	cos(lx1	cos(lx1	PROPN
ejde-388	349	6	+	+	CCONJ
ejde-388	349	7	φ1lmn	φ1lmn	NOUN
ejde-388	349	8	)	)	PUNCT
ejde-388	349	9	×	×	NOUN
ejde-388	349	10	sin(mx2	sin(mx2	ADJ
ejde-388	349	11	+	+	NUM
ejde-388	349	12	φ2lmn	φ2lmn	NUM
ejde-388	349	13	)	)	PUNCT
ejde-388	349	14	sin(nx3	sin(nx3	PROPN
ejde-388	349	15	+	+	NUM
ejde-388	349	16	φ3lmn	φ3lmn	NOUN
ejde-388	349	17	)	)	PUNCT
ejde-388	349	18	,	,	PUNCT
ejde-388	349	19	u2(0	u2(0	NOUN
ejde-388	349	20	)	)	PUNCT
ejde-388	349	21	=	=	SYM
ejde-388	350	1	16∑	16∑	NUM
ejde-388	351	1	l=1	l=1	NOUN
ejde-388	351	2	16∑	16∑	PROPN
ejde-388	352	1	m=1	m=1	PROPN
ejde-388	352	2	16∑	16∑	NUM
ejde-388	352	3	n=1	n=1	PROPN
ejde-388	352	4	almnln	almnln	VERB
ejde-388	352	5	sin(lx1	sin(lx1	NOUN
ejde-388	352	6	+	+	NUM
ejde-388	352	7	φ1lmn	φ1lmn	NOUN
ejde-388	352	8	)	)	PUNCT
ejde-388	352	9	×	×	NOUN
ejde-388	352	10	cos(mx2	cos(mx2	ADJ
ejde-388	352	11	+	+	NUM
ejde-388	352	12	φ2lmn	φ2lmn	NUM
ejde-388	352	13	)	)	PUNCT
ejde-388	352	14	sin(nx3	sin(nx3	PROPN
ejde-388	352	15	+	+	NUM
ejde-388	352	16	φ3lmn	φ3lmn	NOUN
ejde-388	352	17	)	)	PUNCT
ejde-388	352	18	,	,	PUNCT
ejde-388	352	19	u3(0	u3(0	PROPN
ejde-388	352	20	)	)	PUNCT
ejde-388	353	1	=	=	SYM
ejde-388	353	2	−2	−2	NOUN
ejde-388	354	1	16∑	16∑	NUM
ejde-388	355	1	l=1	l=1	NOUN
ejde-388	355	2	16∑	16∑	PROPN
ejde-388	356	1	m=1	m=1	PROPN
ejde-388	356	2	16∑	16∑	NUM
ejde-388	356	3	n=1	n=1	PROPN
ejde-388	356	4	almnlm	almnlm	NOUN
ejde-388	356	5	sin(lx1	sin(lx1	ADV
ejde-388	356	6	+	+	CCONJ
ejde-388	356	7	φ1lmn	φ1lmn	NOUN
ejde-388	356	8	)	)	PUNCT
ejde-388	356	9	×	×	NOUN
ejde-388	356	10	sin(mx2	sin(mx2	ADJ
ejde-388	356	11	+	+	NUM
ejde-388	356	12	φ2lmn	φ2lmn	NUM
ejde-388	356	13	)	)	PUNCT
ejde-388	356	14	cos(nx3	cos(nx3	PROPN
ejde-388	356	15	+	+	NUM
ejde-388	356	16	φ3lmn	φ3lmn	NOUN
ejde-388	356	17	)	)	PUNCT
ejde-388	356	18	,	,	PUNCT
ejde-388	356	19	(	(	PUNCT
ejde-388	356	20	7.5	7.5	NUM
ejde-388	356	21	)	)	PUNCT
ejde-388	356	22	and	and	CCONJ
ejde-388	356	23	the	the	DET
ejde-388	356	24	initial	initial	ADJ
ejde-388	356	25	condition	condition	NOUN
ejde-388	356	26	for	for	ADP
ejde-388	356	27	the	the	DET
ejde-388	356	28	perturbation	perturbation	NOUN
ejde-388	356	29	in	in	ADP
ejde-388	356	30	the	the	DET
ejde-388	356	31	form	form	NOUN
ejde-388	356	32	du1(0	du1(0	NOUN
ejde-388	356	33	)	)	PUNCT
ejde-388	356	34	=	=	PUNCT
ejde-388	357	1	n∑	n∑	NOUN
ejde-388	358	1	l=1	l=1	PROPN
ejde-388	358	2	n∑	n∑	PROPN
ejde-388	358	3	m=1	m=1	PROPN
ejde-388	358	4	n∑	n∑	NOUN
ejde-388	358	5	n=1	n=1	PROPN
ejde-388	358	6	blmnmn	blmnmn	VERB
ejde-388	358	7	cos(lx1	cos(lx1	PROPN
ejde-388	358	8	+	+	CCONJ
ejde-388	358	9	φ1lmn	φ1lmn	NOUN
ejde-388	358	10	)	)	PUNCT
ejde-388	358	11	×	×	NOUN
ejde-388	358	12	sin(mx2	sin(mx2	ADJ
ejde-388	358	13	+	+	NUM
ejde-388	358	14	φ2lmn	φ2lmn	NUM
ejde-388	358	15	)	)	PUNCT
ejde-388	358	16	sin(nx3	sin(nx3	PROPN
ejde-388	358	17	+	+	NUM
ejde-388	358	18	φ3lmn	φ3lmn	NOUN
ejde-388	358	19	)	)	PUNCT
ejde-388	358	20	,	,	PUNCT
ejde-388	358	21	du2(0	du2(0	NOUN
ejde-388	358	22	)	)	PUNCT
ejde-388	358	23	=	=	SYM
ejde-388	359	1	n∑	n∑	NOUN
ejde-388	360	1	l=1	l=1	PROPN
ejde-388	360	2	n∑	n∑	PROPN
ejde-388	360	3	m=1	m=1	PROPN
ejde-388	360	4	n∑	n∑	PROPN
ejde-388	360	5	n=1	n=1	PROPN
ejde-388	360	6	blmnln	blmnln	VERB
ejde-388	360	7	sin(lx1	sin(lx1	ADV
ejde-388	360	8	+	+	SYM
ejde-388	360	9	φ1lmn	φ1lmn	NOUN
ejde-388	360	10	)	)	PUNCT
ejde-388	360	11	×	×	NOUN
ejde-388	360	12	cos(mx2	cos(mx2	ADJ
ejde-388	360	13	+	+	NUM
ejde-388	360	14	φ2lmn	φ2lmn	NUM
ejde-388	360	15	)	)	PUNCT
ejde-388	360	16	sin(nx3	sin(nx3	PROPN
ejde-388	360	17	+	+	NUM
ejde-388	360	18	φ3lmn	φ3lmn	NOUN
ejde-388	360	19	)	)	PUNCT
ejde-388	360	20	,	,	PUNCT
ejde-388	360	21	du3(0	du3(0	NOUN
ejde-388	360	22	)	)	PUNCT
ejde-388	360	23	=	=	SYM
ejde-388	361	1	−2	−2	NOUN
ejde-388	361	2	n∑	n∑	NOUN
ejde-388	362	1	l=1	l=1	PROPN
ejde-388	362	2	n∑	n∑	NOUN
ejde-388	362	3	m=1	m=1	PROPN
ejde-388	362	4	n∑	n∑	NOUN
ejde-388	362	5	n=1	n=1	PROPN
ejde-388	362	6	blmnlm	blmnlm	PROPN
ejde-388	362	7	sin(lx1	sin(lx1	PROPN
ejde-388	362	8	+	+	NUM
ejde-388	362	9	φ1lmn	φ1lmn	NOUN
ejde-388	362	10	)	)	PUNCT
ejde-388	362	11	×	×	NOUN
ejde-388	362	12	sin(mx2	sin(mx2	ADJ
ejde-388	362	13	+	+	NUM
ejde-388	362	14	φ2lmn	φ2lmn	NUM
ejde-388	362	15	)	)	PUNCT
ejde-388	363	1	cos(nx3	cos(nx3	PROPN
ejde-388	363	2	+	+	NUM
ejde-388	363	3	φ3lmn	φ3lmn	NOUN
ejde-388	363	4	)	)	PUNCT
ejde-388	363	5	,	,	PUNCT
ejde-388	363	6	(	(	PUNCT
ejde-388	363	7	7.6	7.6	NUM
ejde-388	363	8	)	)	PUNCT
ejde-388	363	9	where	where	SCONJ
ejde-388	363	10	almn	almn	NOUN
ejde-388	363	11	=	=	PROPN
ejde-388	363	12	0.0005a	0.0005a	PROPN
ejde-388	363	13	,	,	PUNCT
ejde-388	363	14	blmn	blmn	NOUN
ejde-388	363	15	=	=	NOUN
ejde-388	363	16	0.00001a	0.00001a	NOUN
ejde-388	363	17	,	,	PUNCT
ejde-388	363	18	a	a	PRON
ejde-388	363	19	is	be	AUX
ejde-388	363	20	a	a	DET
ejde-388	363	21	random	random	ADJ
ejde-388	363	22	variable	variable	NOUN
ejde-388	363	23	following	follow	VERB
ejde-388	363	24	the	the	DET
ejde-388	363	25	standard	standard	ADJ
ejde-388	363	26	gaussian	gaussian	ADJ
ejde-388	363	27	distribution	distribution	NOUN
ejde-388	363	28	,	,	PUNCT
ejde-388	363	29	φjlmn	φjlmn	NOUN
ejde-388	363	30	=	=	SYM
ejde-388	363	31	2πφ	2πφ	NOUN
ejde-388	363	32	(	(	PUNCT
ejde-388	363	33	j	j	NOUN
ejde-388	363	34	=	=	SYM
ejde-388	363	35	1	1	NUM
ejde-388	363	36	,	,	PUNCT
ejde-388	363	37	2	2	NUM
ejde-388	363	38	,	,	PUNCT
ejde-388	363	39	3	3	NUM
ejde-388	363	40	)	)	PUNCT
ejde-388	363	41	,	,	PUNCT
ejde-388	363	42	and	and	CCONJ
ejde-388	363	43	φ	φ	PROPN
ejde-388	363	44	is	be	AUX
ejde-388	363	45	a	a	DET
ejde-388	363	46	random	random	ADJ
ejde-388	363	47	variable	variable	NOUN
ejde-388	363	48	following	follow	VERB
ejde-388	363	49	the	the	DET
ejde-388	363	50	uniform	uniform	ADJ
ejde-388	363	51	distribution	distribution	NOUN
ejde-388	363	52	over	over	ADP
ejde-388	363	53	(	(	PUNCT
ejde-388	363	54	0	0	NUM
ejde-388	363	55	,	,	PUNCT
ejde-388	363	56	1	1	NUM
ejde-388	363	57	)	)	PUNCT
ejde-388	363	58	.	.	PUNCT
ejde-388	364	1	this	this	DET
ejde-388	364	2	type	type	NOUN
ejde-388	364	3	of	of	ADP
ejde-388	364	4	initial	initial	ADJ
ejde-388	364	5	conditions	condition	NOUN
ejde-388	364	6	put	put	VERB
ejde-388	364	7	the	the	DET
ejde-388	364	8	base	base	NOUN
ejde-388	364	9	flow	flow	NOUN
ejde-388	364	10	into	into	ADP
ejde-388	364	11	the	the	DET
ejde-388	364	12	turbulence	turbulence	NOUN
ejde-388	364	13	regime	regime	NOUN
ejde-388	364	14	.	.	PUNCT
ejde-388	365	1	we	we	PRON
ejde-388	365	2	choose	choose	VERB
ejde-388	365	3	the	the	DET
ejde-388	365	4	reynolds	reynolds	PROPN
ejde-388	365	5	number	number	NOUN
ejde-388	365	6	re	re	NOUN
ejde-388	365	7	=	=	NOUN
ejde-388	365	8	1000	1000	NUM
ejde-388	365	9	,	,	PUNCT
ejde-388	365	10	and	and	CCONJ
ejde-388	365	11	we	we	PRON
ejde-388	365	12	run	run	VERB
ejde-388	365	13	the	the	DET
ejde-388	365	14	simulation	simulation	NOUN
ejde-388	365	15	with	with	ADP
ejde-388	365	16	time	time	NOUN
ejde-388	365	17	step	step	NOUN
ejde-388	365	18	0.0001	0.0001	NUM
ejde-388	365	19	.	.	PUNCT
ejde-388	366	1	when	when	SCONJ
ejde-388	366	2	n	n	X
ejde-388	366	3	=	=	SYM
ejde-388	366	4	16	16	NUM
ejde-388	366	5	,	,	PUNCT
ejde-388	366	6	8	8	NUM
ejde-388	366	7	,	,	PUNCT
ejde-388	366	8	4	4	NUM
ejde-388	366	9	,	,	PUNCT
ejde-388	366	10	2	2	NUM
ejde-388	366	11	,	,	PUNCT
ejde-388	366	12	we	we	PRON
ejde-388	366	13	have	have	VERB
ejde-388	366	14	the	the	DET
ejde-388	366	15	same	same	ADJ
ejde-388	366	16	super	super	ADV
ejde-388	366	17	fast	fast	ADJ
ejde-388	366	18	growth	growth	NOUN
ejde-388	366	19	(	(	PUNCT
ejde-388	366	20	figure	figure	NOUN
ejde-388	366	21	13	13	NUM
ejde-388	366	22	)	)	PUNCT
ejde-388	366	23	,	,	PUNCT
ejde-388	366	24	and	and	CCONJ
ejde-388	366	25	clearly	clearly	ADV
ejde-388	366	26	lower	low	ADJ
ejde-388	366	27	perturbation	perturbation	NOUN
ejde-388	366	28	mode	mode	NOUN
ejde-388	366	29	grows	grow	VERB
ejde-388	366	30	faster	fast	ADV
ejde-388	366	31	.	.	PUNCT
ejde-388	367	1	we	we	PRON
ejde-388	367	2	would	would	AUX
ejde-388	367	3	like	like	VERB
ejde-388	367	4	to	to	PART
ejde-388	367	5	reiterate	reiterate	VERB
ejde-388	367	6	that	that	SCONJ
ejde-388	367	7	each	each	DET
ejde-388	367	8	initial	initial	ADJ
ejde-388	367	9	individual	individual	ADJ
ejde-388	367	10	fourier	fourier	NOUN
ejde-388	367	11	mode	mode	NOUN
ejde-388	367	12	amplifies	amplify	VERB
ejde-388	367	13	independently	independently	ADV
ejde-388	367	14	.	.	PUNCT
ejde-388	368	1	finally	finally	ADV
ejde-388	368	2	,	,	PUNCT
ejde-388	368	3	we	we	PRON
ejde-388	368	4	would	would	AUX
ejde-388	368	5	also	also	ADV
ejde-388	368	6	like	like	VERB
ejde-388	368	7	to	to	PART
ejde-388	368	8	reiterate	reiterate	VERB
ejde-388	368	9	that	that	SCONJ
ejde-388	368	10	the	the	DET
ejde-388	368	11	super	super	ADV
ejde-388	368	12	fast	fast	ADJ
ejde-388	368	13	amplification	amplification	NOUN
ejde-388	368	14	phenomenon	phenomenon	NOUN
ejde-388	368	15	is	be	AUX
ejde-388	368	16	a	a	DET
ejde-388	368	17	generic	generic	ADJ
ejde-388	368	18	fact	fact	NOUN
ejde-388	368	19	of	of	ADP
ejde-388	368	20	fluids	fluid	NOUN
ejde-388	368	21	,	,	PUNCT
ejde-388	368	22	and	and	CCONJ
ejde-388	368	23	is	be	AUX
ejde-388	368	24	ubiquitous	ubiquitous	ADJ
ejde-388	368	25	.	.	PUNCT
ejde-388	369	1	microscopically	microscopically	ADV
ejde-388	369	2	,	,	PUNCT
ejde-388	369	3	navier	navier	NOUN
ejde-388	369	4	-	-	PUNCT
ejde-388	369	5	stokes	stokes	PROPN
ejde-388	369	6	equations	equation	NOUN
ejde-388	369	7	model	model	NOUN
ejde-388	369	8	fluid	fluid	NOUN
ejde-388	369	9	flows	flow	VERB
ejde-388	369	10	well	well	ADV
ejde-388	369	11	.	.	PUNCT
ejde-388	370	1	thus	thus	ADV
ejde-388	370	2	,	,	PUNCT
ejde-388	370	3	the	the	DET
ejde-388	370	4	super	super	ADV
ejde-388	370	5	fast	fast	ADJ
ejde-388	370	6	amplification	amplification	NOUN
ejde-388	370	7	phenomenon	phenomenon	NOUN
ejde-388	370	8	of	of	ADP
ejde-388	370	9	navier	navier	NOUN
ejde-388	370	10	-	-	PUNCT
ejde-388	370	11	stokes	stoke	NOUN
ejde-388	370	12	equations	equation	NOUN
ejde-388	370	13	reveals	reveal	VERB
ejde-388	370	14	the	the	DET
ejde-388	370	15	same	same	ADJ
ejde-388	370	16	phenomenon	phenomenon	NOUN
ejde-388	370	17	in	in	ADP
ejde-388	370	18	physical	physical	ADJ
ejde-388	370	19	fluid	fluid	ADJ
ejde-388	370	20	flows	flow	NOUN
ejde-388	370	21	.	.	PUNCT
ejde-388	371	1	conclusions	conclusion	NOUN
ejde-388	371	2	.	.	PUNCT
ejde-388	372	1	through	through	ADP
ejde-388	372	2	numerical	numerical	ADJ
ejde-388	372	3	simulations	simulation	NOUN
ejde-388	372	4	,	,	PUNCT
ejde-388	372	5	we	we	PRON
ejde-388	372	6	showed	show	VERB
ejde-388	372	7	the	the	DET
ejde-388	372	8	super	super	ADV
ejde-388	372	9	fast	fast	ADJ
ejde-388	372	10	growth	growth	NOUN
ejde-388	372	11	of	of	ADP
ejde-388	372	12	perturbations	perturbation	NOUN
ejde-388	372	13	(	(	PUNCT
ejde-388	372	14	rough	rough	ADJ
ejde-388	372	15	dependence	dependence	NOUN
ejde-388	372	16	upon	upon	SCONJ
ejde-388	372	17	initial	initial	ADJ
ejde-388	372	18	data	datum	NOUN
ejde-388	372	19	)	)	PUNCT
ejde-388	372	20	in	in	ADP
ejde-388	372	21	high	high	ADJ
ejde-388	372	22	reynolds	reynold	NOUN
ejde-388	372	23	number	number	NOUN
ejde-388	372	24	fluid	fluid	NOUN
ejde-388	372	25	flows	flow	NOUN
ejde-388	372	26	.	.	PUNCT
ejde-388	373	1	we	we	PRON
ejde-388	373	2	also	also	ADV
ejde-388	373	3	showed	show	VERB
ejde-388	373	4	the	the	DET
ejde-388	373	5	abundance	abundance	NOUN
ejde-388	373	6	of	of	ADP
ejde-388	373	7	such	such	ADJ
ejde-388	373	8	super	super	ADJ
ejde-388	373	9	fast	fast	ADJ
ejde-388	373	10	growth	growth	NOUN
ejde-388	373	11	among	among	ADP
ejde-388	373	12	perturbations	perturbation	NOUN
ejde-388	373	13	and	and	CCONJ
ejde-388	373	14	base	base	NOUN
ejde-388	373	15	solutions	solution	NOUN
ejde-388	373	16	in	in	ADP
ejde-388	373	17	support	support	NOUN
ejde-388	373	18	of	of	ADP
ejde-388	373	19	our	our	PRON
ejde-388	373	20	theory	theory	NOUN
ejde-388	373	21	that	that	SCONJ
ejde-388	373	22	fully	fully	ADV
ejde-388	373	23	developed	develop	VERB
ejde-388	373	24	turbulence	turbulence	NOUN
ejde-388	373	25	is	be	AUX
ejde-388	373	26	caused	cause	VERB
ejde-388	373	27	and	and	CCONJ
ejde-388	373	28	maintained	maintain	VERB
ejde-388	373	29	by	by	ADP
ejde-388	373	30	such	such	ADJ
ejde-388	373	31	super	super	ADJ
ejde-388	373	32	fast	fast	ADJ
ejde-388	373	33	growth	growth	NOUN
ejde-388	373	34	of	of	ADP
ejde-388	373	35	perturbations	perturbation	NOUN
ejde-388	373	36	.	.	PUNCT
ejde-388	374	1	such	such	ADJ
ejde-388	374	2	super	super	ADJ
ejde-388	374	3	fast	fast	ADJ
ejde-388	374	4	amplification	amplification	NOUN
ejde-388	374	5	of	of	ADP
ejde-388	374	6	perturbations	perturbation	NOUN
ejde-388	374	7	is	be	AUX
ejde-388	374	8	ubiquitous	ubiquitous	ADJ
ejde-388	374	9	in	in	ADP
ejde-388	374	10	turbulence	turbulence	NOUN
ejde-388	374	11	.	.	PUNCT
ejde-388	375	1	20	20	NUM
ejde-388	375	2	z.	z.	PROPN
ejde-388	375	3	feng	feng	PROPN
ejde-388	375	4	,	,	PUNCT
ejde-388	375	5	y.	y.	PROPN
ejde-388	375	6	c.	c.	PROPN
ejde-388	375	7	li	li	PROPN
ejde-388	376	1	ejde-2020/104	ejde-2020/104	PROPN
ejde-388	376	2	0	0	NUM
ejde-388	376	3	0.01	0.01	NUM
ejde-388	376	4	0.02	0.02	NUM
ejde-388	376	5	0.03	0.03	NUM
ejde-388	376	6	0.04	0.04	NUM
ejde-388	376	7	0.05	0.05	NUM
ejde-388	376	8	0.06	0.06	NUM
ejde-388	376	9	t	t	NOUN
ejde-388	376	10	0	0	NUM
ejde-388	376	11	1	1	NUM
ejde-388	376	12	2	2	NUM
ejde-388	376	13	3	3	NUM
ejde-388	376	14	ln	ln	NOUN
ejde-388	376	15	(	(	PUNCT
ejde-388	376	16	λ	λ	NOUN
ejde-388	376	17	/λ	/λ	NOUN
ejde-388	376	18	0	0	NUM
ejde-388	376	19	)	)	PUNCT
ejde-388	376	20	0	0	NUM
ejde-388	377	1	0.01	0.01	NUM
ejde-388	377	2	0.02	0.02	NUM
ejde-388	377	3	0.03	0.03	NUM
ejde-388	377	4	0.04	0.04	NUM
ejde-388	377	5	0.05	0.05	NUM
ejde-388	377	6	0.06	0.06	NUM
ejde-388	377	7	t	t	NOUN
ejde-388	377	8	0	0	NUM
ejde-388	377	9	1	1	NUM
ejde-388	377	10	2	2	NUM
ejde-388	377	11	3	3	NUM
ejde-388	377	12	4	4	NUM
ejde-388	377	13	5	5	NUM
ejde-388	377	14	ln	ln	NOUN
ejde-388	377	15	(	(	PUNCT
ejde-388	377	16	λ	λ	NOUN
ejde-388	377	17	/λ	/λ	NOUN
ejde-388	377	18	0	0	NUM
ejde-388	377	19	)	)	PUNCT
ejde-388	377	20	(	(	PUNCT
ejde-388	377	21	a	a	X
ejde-388	377	22	)	)	PUNCT
ejde-388	377	23	n	n	NOUN
ejde-388	377	24	=	=	SYM
ejde-388	377	25	16	16	NUM
ejde-388	377	26	(	(	PUNCT
ejde-388	377	27	b	b	NOUN
ejde-388	377	28	)	)	PUNCT
ejde-388	377	29	n	n	NOUN
ejde-388	377	30	=	=	SYM
ejde-388	377	31	8	8	NUM
ejde-388	377	32	0	0	NUM
ejde-388	377	33	0.01	0.01	NUM
ejde-388	377	34	0.02	0.02	NUM
ejde-388	377	35	0.03	0.03	NUM
ejde-388	377	36	0.04	0.04	NUM
ejde-388	377	37	0.05	0.05	NUM
ejde-388	377	38	0.06	0.06	NUM
ejde-388	377	39	t	t	NOUN
ejde-388	377	40	0	0	NUM
ejde-388	377	41	2	2	NUM
ejde-388	377	42	4	4	NUM
ejde-388	377	43	6	6	NUM
ejde-388	377	44	8	8	NUM
ejde-388	377	45	ln	ln	NOUN
ejde-388	377	46	(	(	PUNCT
ejde-388	377	47	λ	λ	NOUN
ejde-388	377	48	/λ	/λ	NOUN
ejde-388	377	49	0	0	NUM
ejde-388	377	50	)	)	PUNCT
ejde-388	377	51	0	0	NUM
ejde-388	377	52	0.01	0.01	NUM
ejde-388	377	53	0.02	0.02	NUM
ejde-388	377	54	0.03	0.03	NUM
ejde-388	377	55	0.04	0.04	NUM
ejde-388	377	56	0.05	0.05	NUM
ejde-388	377	57	0.06	0.06	NUM
ejde-388	377	58	t	t	NOUN
ejde-388	377	59	0	0	NUM
ejde-388	377	60	2	2	NUM
ejde-388	377	61	4	4	NUM
ejde-388	377	62	6	6	NUM
ejde-388	377	63	8	8	NUM
ejde-388	377	64	ln	ln	NOUN
ejde-388	377	65	(	(	PUNCT
ejde-388	377	66	λ	λ	NOUN
ejde-388	377	67	/λ	/λ	NOUN
ejde-388	377	68	0	0	NUM
ejde-388	377	69	)	)	PUNCT
ejde-388	377	70	(	(	PUNCT
ejde-388	377	71	c	c	X
ejde-388	377	72	)	)	PUNCT
ejde-388	377	73	n	n	NOUN
ejde-388	377	74	=	=	SYM
ejde-388	377	75	4	4	NUM
ejde-388	377	76	(	(	PUNCT
ejde-388	377	77	d	d	NOUN
ejde-388	377	78	)	)	PUNCT
ejde-388	377	79	n	n	NOUN
ejde-388	377	80	=	=	SYM
ejde-388	377	81	2	2	NUM
ejde-388	377	82	figure	figure	NOUN
ejde-388	377	83	13	13	NUM
ejde-388	377	84	.	.	PUNCT
ejde-388	378	1	super	super	ADJ
ejde-388	378	2	fast	fast	ADJ
ejde-388	378	3	growths	growth	NOUN
ejde-388	378	4	of	of	ADP
ejde-388	378	5	the	the	DET
ejde-388	378	6	perturbations	perturbation	NOUN
ejde-388	378	7	with	with	ADP
ejde-388	378	8	the	the	DET
ejde-388	378	9	initial	initial	ADJ
ejde-388	378	10	condition	condition	NOUN
ejde-388	378	11	(	(	PUNCT
ejde-388	378	12	7.6	7.6	NUM
ejde-388	378	13	)	)	PUNCT
ejde-388	378	14	when	when	SCONJ
ejde-388	378	15	n	n	X
ejde-388	378	16	=	=	SYM
ejde-388	378	17	16	16	NUM
ejde-388	378	18	,	,	PUNCT
ejde-388	378	19	8	8	NUM
ejde-388	378	20	,	,	PUNCT
ejde-388	378	21	4	4	NUM
ejde-388	378	22	,	,	PUNCT
ejde-388	378	23	2	2	NUM
ejde-388	378	24	,	,	PUNCT
ejde-388	378	25	to	to	ADP
ejde-388	378	26	the	the	DET
ejde-388	378	27	base	base	NOUN
ejde-388	378	28	solution	solution	NOUN
ejde-388	378	29	with	with	ADP
ejde-388	378	30	the	the	DET
ejde-388	378	31	initial	initial	ADJ
ejde-388	378	32	condition	condition	NOUN
ejde-388	378	33	(	(	PUNCT
ejde-388	378	34	7.5	7.5	NUM
ejde-388	378	35	)	)	PUNCT
ejde-388	378	36	,	,	PUNCT
ejde-388	378	37	where	where	SCONJ
ejde-388	378	38	λ(t	λ(t	NOUN
ejde-388	378	39	)	)	PUNCT
ejde-388	378	40	=	=	SYM
ejde-388	378	41	‖du(t)‖h3	‖du(t)‖h3	PROPN
ejde-388	378	42	.	.	PUNCT
ejde-388	379	1	references	reference	NOUN
ejde-388	379	2	[	[	X
ejde-388	379	3	1	1	X
ejde-388	379	4	]	]	X
ejde-388	379	5	y.	y.	PROPN
ejde-388	379	6	duguet	duguet	PROPN
ejde-388	379	7	,	,	PUNCT
ejde-388	379	8	p.	p.	NOUN
ejde-388	379	9	schlatter	schlatter	PROPN
ejde-388	379	10	,	,	PUNCT
ejde-388	379	11	d.	d.	PROPN
ejde-388	379	12	henningson	henningson	PROPN
ejde-388	379	13	;	;	PUNCT
ejde-388	379	14	formation	formation	NOUN
ejde-388	379	15	of	of	ADP
ejde-388	379	16	turbulent	turbulent	ADJ
ejde-388	379	17	patterns	pattern	NOUN
ejde-388	379	18	near	near	ADP
ejde-388	379	19	the	the	DET
ejde-388	379	20	onset	onset	NOUN
ejde-388	379	21	of	of	ADP
ejde-388	379	22	transition	transition	NOUN
ejde-388	379	23	in	in	ADP
ejde-388	379	24	plane	plane	NOUN
ejde-388	379	25	couette	couette	NOUN
ejde-388	379	26	flow	flow	NOUN
ejde-388	379	27	,	,	PUNCT
ejde-388	379	28	j.	j.	PROPN
ejde-388	379	29	fluid	fluid	PROPN
ejde-388	379	30	mech	mech	NOUN
ejde-388	379	31	.	.	PUNCT
ejde-388	379	32	,	,	PUNCT
ejde-388	379	33	650	650	NUM
ejde-388	379	34	(	(	PUNCT
ejde-388	379	35	2010	2010	NUM
ejde-388	379	36	)	)	PUNCT
ejde-388	379	37	,	,	PUNCT
ejde-388	379	38	119	119	NUM
ejde-388	379	39	-	-	SYM
ejde-388	379	40	129	129	NUM
ejde-388	379	41	.	.	PUNCT
ejde-388	380	1	[	[	X
ejde-388	380	2	2	2	X
ejde-388	380	3	]	]	PUNCT
ejde-388	380	4	j.	j.	PROPN
ejde-388	380	5	gibson	gibson	PROPN
ejde-388	380	6	,	,	PUNCT
ejde-388	380	7	t.	t.	PROPN
ejde-388	380	8	schneider	schneider	PROPN
ejde-388	380	9	;	;	PUNCT
ejde-388	380	10	homoclinic	homoclinic	ADJ
ejde-388	380	11	snaking	snaking	NOUN
ejde-388	380	12	in	in	ADP
ejde-388	380	13	plane	plane	NOUN
ejde-388	380	14	couette	couette	NOUN
ejde-388	380	15	flow	flow	NOUN
ejde-388	380	16	:	:	PUNCT
ejde-388	380	17	bending	bend	VERB
ejde-388	380	18	,	,	PUNCT
ejde-388	380	19	skewing	skew	VERB
ejde-388	380	20	and	and	CCONJ
ejde-388	380	21	finite	finite	ADJ
ejde-388	380	22	-	-	PUNCT
ejde-388	380	23	size	size	NOUN
ejde-388	380	24	effects	effect	NOUN
ejde-388	380	25	,	,	PUNCT
ejde-388	380	26	j.	j.	PROPN
ejde-388	380	27	fluid	fluid	PROPN
ejde-388	380	28	mech	mech	NOUN
ejde-388	380	29	.	.	PUNCT
ejde-388	380	30	,	,	PUNCT
ejde-388	380	31	794	794	NUM
ejde-388	380	32	(	(	PUNCT
ejde-388	380	33	2016	2016	NUM
ejde-388	380	34	)	)	PUNCT
ejde-388	380	35	,	,	PUNCT
ejde-388	380	36	530	530	NUM
ejde-388	380	37	-	-	SYM
ejde-388	380	38	551	551	NUM
ejde-388	380	39	.	.	PUNCT
ejde-388	381	1	[	[	X
ejde-388	381	2	3	3	X
ejde-388	381	3	]	]	X
ejde-388	381	4	h.	h.	PROPN
ejde-388	381	5	inci	inci	PROPN
ejde-388	381	6	;	;	PUNCT
ejde-388	381	7	on	on	ADP
ejde-388	381	8	the	the	DET
ejde-388	381	9	regularity	regularity	NOUN
ejde-388	381	10	of	of	ADP
ejde-388	381	11	the	the	DET
ejde-388	381	12	solution	solution	NOUN
ejde-388	381	13	map	map	NOUN
ejde-388	381	14	of	of	ADP
ejde-388	381	15	the	the	DET
ejde-388	381	16	incompressible	incompressible	ADJ
ejde-388	381	17	euler	euler	NOUN
ejde-388	381	18	equation	equation	NOUN
ejde-388	381	19	,	,	PUNCT
ejde-388	381	20	dynamics	dynamic	NOUN
ejde-388	381	21	of	of	ADP
ejde-388	381	22	pde	pde	NOUN
ejde-388	381	23	,	,	PUNCT
ejde-388	381	24	12	12	NUM
ejde-388	381	25	,	,	PUNCT
ejde-388	381	26	no.2	no.2	PROPN
ejde-388	381	27	(	(	PUNCT
ejde-388	381	28	2015	2015	NUM
ejde-388	381	29	)	)	PUNCT
ejde-388	381	30	,	,	PUNCT
ejde-388	381	31	97	97	NUM
ejde-388	381	32	-	-	SYM
ejde-388	381	33	113	113	NUM
ejde-388	381	34	,	,	PUNCT
ejde-388	381	35	arxiv	arxiv	NOUN
ejde-388	381	36	:	:	PUNCT
ejde-388	381	37	1301.5997	1301.5997	ADJ
ejde-388	381	38	.	.	PUNCT
ejde-388	382	1	[	[	X
ejde-388	382	2	4	4	X
ejde-388	382	3	]	]	PUNCT
ejde-388	382	4	t.	t.	PROPN
ejde-388	382	5	kato	kato	PROPN
ejde-388	382	6	;	;	PUNCT
ejde-388	382	7	nonstationary	nonstationary	ADJ
ejde-388	382	8	flows	flow	NOUN
ejde-388	382	9	of	of	ADP
ejde-388	382	10	viscous	viscous	ADJ
ejde-388	382	11	and	and	CCONJ
ejde-388	382	12	ideal	ideal	ADJ
ejde-388	382	13	fluids	fluid	NOUN
ejde-388	382	14	in	in	ADP
ejde-388	382	15	r3	r3	PROPN
ejde-388	382	16	,	,	PUNCT
ejde-388	382	17	j.	j.	PROPN
ejde-388	382	18	funct	funct	PROPN
ejde-388	382	19	.	.	PUNCT
ejde-388	383	1	anal	anal	PROPN
ejde-388	383	2	.	.	PROPN
ejde-388	383	3	,	,	PUNCT
ejde-388	383	4	9	9	NUM
ejde-388	383	5	(	(	PUNCT
ejde-388	383	6	1972	1972	NUM
ejde-388	383	7	)	)	PUNCT
ejde-388	383	8	,	,	PUNCT
ejde-388	383	9	296	296	NUM
ejde-388	383	10	-	-	SYM
ejde-388	383	11	305	305	NUM
ejde-388	383	12	.	.	PUNCT
ejde-388	384	1	[	[	X
ejde-388	384	2	5	5	X
ejde-388	384	3	]	]	PUNCT
ejde-388	384	4	t.	t.	PROPN
ejde-388	384	5	kato	kato	PROPN
ejde-388	384	6	;	;	PUNCT
ejde-388	384	7	quasi	quasi	ADJ
ejde-388	384	8	-	-	ADJ
ejde-388	384	9	linear	linear	ADJ
ejde-388	384	10	equations	equation	NOUN
ejde-388	384	11	of	of	ADP
ejde-388	384	12	evolution	evolution	NOUN
ejde-388	384	13	,	,	PUNCT
ejde-388	384	14	with	with	ADP
ejde-388	384	15	applications	application	NOUN
ejde-388	384	16	to	to	ADP
ejde-388	384	17	partial	partial	ADJ
ejde-388	384	18	differential	differential	NOUN
ejde-388	384	19	equations	equation	NOUN
ejde-388	384	20	,	,	PUNCT
ejde-388	384	21	lect	lect	PROPN
ejde-388	384	22	.	.	PUNCT
ejde-388	384	23	notes	note	NOUN
ejde-388	384	24	in	in	ADP
ejde-388	384	25	math	math	NOUN
ejde-388	384	26	.	.	PUNCT
ejde-388	384	27	,	,	PUNCT
ejde-388	384	28	springer	springer	NOUN
ejde-388	384	29	,	,	PUNCT
ejde-388	384	30	448	448	NUM
ejde-388	384	31	(	(	PUNCT
ejde-388	384	32	1975	1975	NUM
ejde-388	384	33	)	)	PUNCT
ejde-388	384	34	,	,	PUNCT
ejde-388	384	35	25	25	NUM
ejde-388	384	36	-	-	SYM
ejde-388	384	37	70	70	NUM
ejde-388	384	38	.	.	PUNCT
ejde-388	385	1	[	[	X
ejde-388	385	2	6	6	NUM
ejde-388	385	3	]	]	PUNCT
ejde-388	385	4	g.	g.	PROPN
ejde-388	385	5	kawahara	kawahara	PROPN
ejde-388	385	6	,	,	PUNCT
ejde-388	385	7	s.	s.	PROPN
ejde-388	385	8	kida	kida	PROPN
ejde-388	385	9	;	;	PUNCT
ejde-388	385	10	periodic	periodic	ADJ
ejde-388	385	11	motion	motion	NOUN
ejde-388	385	12	embedded	embed	VERB
ejde-388	385	13	in	in	ADP
ejde-388	385	14	plane	plane	NOUN
ejde-388	385	15	couette	couette	NOUN
ejde-388	385	16	turbulence	turbulence	NOUN
ejde-388	385	17	:	:	PUNCT
ejde-388	385	18	regeneration	regeneration	NOUN
ejde-388	385	19	cycle	cycle	NOUN
ejde-388	385	20	and	and	CCONJ
ejde-388	385	21	burst	burst	NOUN
ejde-388	385	22	,	,	PUNCT
ejde-388	385	23	j.	j.	PROPN
ejde-388	385	24	fluid	fluid	PROPN
ejde-388	385	25	mech	mech	NOUN
ejde-388	385	26	.	.	PUNCT
ejde-388	385	27	,	,	PUNCT
ejde-388	385	28	449	449	NUM
ejde-388	385	29	(	(	PUNCT
ejde-388	385	30	2001	2001	NUM
ejde-388	385	31	)	)	PUNCT
ejde-388	385	32	,	,	PUNCT
ejde-388	385	33	291	291	NUM
ejde-388	385	34	-	-	SYM
ejde-388	385	35	300	300	NUM
ejde-388	385	36	.	.	PUNCT
ejde-388	386	1	[	[	X
ejde-388	386	2	7	7	X
ejde-388	386	3	]	]	X
ejde-388	386	4	g.	g.	PROPN
ejde-388	386	5	kawahara	kawahara	PROPN
ejde-388	386	6	,	,	PUNCT
ejde-388	386	7	m.	m.	NOUN
ejde-388	386	8	uhlmann	uhlmann	PROPN
ejde-388	386	9	,	,	PUNCT
ejde-388	386	10	l.	l.	PROPN
ejde-388	386	11	van	van	PROPN
ejde-388	386	12	veen	veen	PROPN
ejde-388	386	13	;	;	PUNCT
ejde-388	386	14	the	the	DET
ejde-388	386	15	significance	significance	NOUN
ejde-388	386	16	of	of	ADP
ejde-388	386	17	simple	simple	ADJ
ejde-388	386	18	invariant	invariant	ADJ
ejde-388	386	19	solutions	solution	NOUN
ejde-388	386	20	in	in	ADP
ejde-388	386	21	turbulent	turbulent	ADJ
ejde-388	386	22	flows	flow	NOUN
ejde-388	386	23	,	,	PUNCT
ejde-388	386	24	ann	ann	PROPN
ejde-388	386	25	.	.	PROPN
ejde-388	386	26	rev	rev	PROPN
ejde-388	386	27	.	.	PROPN
ejde-388	386	28	fluid	fluid	ADJ
ejde-388	386	29	mech	mech	NOUN
ejde-388	386	30	.	.	PUNCT
ejde-388	386	31	,	,	PUNCT
ejde-388	386	32	44	44	NUM
ejde-388	386	33	(	(	PUNCT
ejde-388	386	34	2012	2012	NUM
ejde-388	386	35	)	)	PUNCT
ejde-388	386	36	,	,	PUNCT
ejde-388	386	37	203	203	NUM
ejde-388	386	38	-	-	SYM
ejde-388	386	39	225	225	NUM
ejde-388	386	40	.	.	PUNCT
ejde-388	387	1	[	[	X
ejde-388	387	2	8	8	X
ejde-388	387	3	]	]	PUNCT
ejde-388	387	4	t.	t.	PROPN
ejde-388	387	5	kreilos	kreilos	PROPN
ejde-388	387	6	,	,	PUNCT
ejde-388	387	7	b.	b.	PROPN
ejde-388	387	8	eckhardt	eckhardt	PROPN
ejde-388	387	9	;	;	PUNCT
ejde-388	387	10	periodic	periodic	ADJ
ejde-388	387	11	orbits	orbit	NOUN
ejde-388	387	12	near	near	ADP
ejde-388	387	13	onset	onset	NOUN
ejde-388	387	14	of	of	ADP
ejde-388	387	15	chaos	chaos	NOUN
ejde-388	387	16	in	in	ADP
ejde-388	387	17	plane	plane	NOUN
ejde-388	387	18	couette	couette	NOUN
ejde-388	387	19	flow	flow	NOUN
ejde-388	387	20	,	,	PUNCT
ejde-388	387	21	chaos	chaos	NOUN
ejde-388	387	22	,	,	PUNCT
ejde-388	387	23	22	22	NUM
ejde-388	387	24	(	(	PUNCT
ejde-388	387	25	2012	2012	NUM
ejde-388	387	26	)	)	PUNCT
ejde-388	387	27	,	,	PUNCT
ejde-388	387	28	047505	047505	NUM
ejde-388	387	29	.	.	PUNCT
ejde-388	388	1	[	[	X
ejde-388	388	2	9	9	NUM
ejde-388	388	3	]	]	X
ejde-388	388	4	g.	g.	PROPN
ejde-388	388	5	leonov	leonov	PROPN
ejde-388	388	6	,	,	PUNCT
ejde-388	388	7	n.	n.	PROPN
ejde-388	388	8	kuznetsov	kuznetsov	PROPN
ejde-388	388	9	;	;	PUNCT
ejde-388	388	10	time	time	NOUN
ejde-388	388	11	-	-	PUNCT
ejde-388	388	12	varying	vary	VERB
ejde-388	388	13	linearization	linearization	NOUN
ejde-388	388	14	and	and	CCONJ
ejde-388	388	15	the	the	DET
ejde-388	388	16	perron	perron	PROPN
ejde-388	388	17	effects	effect	NOUN
ejde-388	388	18	,	,	PUNCT
ejde-388	388	19	international	international	ADJ
ejde-388	388	20	journal	journal	NOUN
ejde-388	388	21	of	of	ADP
ejde-388	388	22	bifurcation	bifurcation	NOUN
ejde-388	388	23	and	and	CCONJ
ejde-388	388	24	chaos	chaos	NOUN
ejde-388	388	25	,	,	PUNCT
ejde-388	388	26	17	17	NUM
ejde-388	388	27	,	,	PUNCT
ejde-388	388	28	no.4	no.4	PROPN
ejde-388	388	29	(	(	PUNCT
ejde-388	388	30	2007	2007	NUM
ejde-388	388	31	)	)	PUNCT
ejde-388	388	32	,	,	PUNCT
ejde-388	388	33	1079	1079	NUM
ejde-388	388	34	-	-	SYM
ejde-388	388	35	1107	1107	NUM
ejde-388	388	36	.	.	PUNCT
ejde-388	389	1	[	[	X
ejde-388	389	2	10	10	NUM
ejde-388	389	3	]	]	X
ejde-388	389	4	y.	y.	PROPN
ejde-388	389	5	li	li	PROPN
ejde-388	389	6	,	,	PUNCT
ejde-388	389	7	;	;	PUNCT
ejde-388	389	8	on	on	ADP
ejde-388	389	9	2d	2d	PROPN
ejde-388	389	10	euler	euler	PROPN
ejde-388	389	11	equations	equation	NOUN
ejde-388	389	12	:	:	PUNCT
ejde-388	389	13	part	part	NOUN
ejde-388	389	14	i.	i.	NOUN
ejde-388	389	15	on	on	ADP
ejde-388	389	16	the	the	DET
ejde-388	389	17	energy	energy	NOUN
ejde-388	389	18	-	-	PUNCT
ejde-388	389	19	casimir	casimir	NOUN
ejde-388	389	20	stabilities	stability	NOUN
ejde-388	389	21	and	and	CCONJ
ejde-388	389	22	the	the	DET
ejde-388	389	23	spectra	spectra	NOUN
ejde-388	389	24	for	for	ADP
ejde-388	389	25	linearized	linearize	VERB
ejde-388	389	26	2d	2d	NUM
ejde-388	389	27	euler	euler	NOUN
ejde-388	389	28	equations	equation	NOUN
ejde-388	389	29	,	,	PUNCT
ejde-388	389	30	journal	journal	NOUN
ejde-388	389	31	of	of	ADP
ejde-388	389	32	mathematical	mathematical	ADJ
ejde-388	389	33	physics	physics	NOUN
ejde-388	389	34	,	,	PUNCT
ejde-388	389	35	41	41	NUM
ejde-388	389	36	,	,	PUNCT
ejde-388	389	37	no	no	INTJ
ejde-388	389	38	.	.	NOUN
ejde-388	389	39	2	2	NUM
ejde-388	389	40	(	(	PUNCT
ejde-388	389	41	2000	2000	NUM
ejde-388	389	42	)	)	PUNCT
ejde-388	389	43	,	,	PUNCT
ejde-388	389	44	728	728	NUM
ejde-388	389	45	-	-	SYM
ejde-388	389	46	758	758	NUM
ejde-388	389	47	.	.	PUNCT
ejde-388	390	1	[	[	X
ejde-388	390	2	11	11	NUM
ejde-388	390	3	]	]	X
ejde-388	390	4	y.	y.	PROPN
ejde-388	390	5	li	li	PROPN
ejde-388	390	6	;	;	PUNCT
ejde-388	390	7	major	major	ADJ
ejde-388	390	8	open	open	ADJ
ejde-388	390	9	problems	problem	NOUN
ejde-388	390	10	in	in	ADP
ejde-388	390	11	chaos	chaos	NOUN
ejde-388	390	12	theory	theory	NOUN
ejde-388	390	13	,	,	PUNCT
ejde-388	390	14	turbulence	turbulence	NOUN
ejde-388	390	15	and	and	CCONJ
ejde-388	390	16	nonlinear	nonlinear	ADJ
ejde-388	390	17	dynamics	dynamic	NOUN
ejde-388	390	18	,	,	PUNCT
ejde-388	390	19	dynamics	dynamic	NOUN
ejde-388	390	20	of	of	ADP
ejde-388	390	21	pde	pde	PROPN
ejde-388	390	22	10	10	NUM
ejde-388	390	23	,	,	PUNCT
ejde-388	390	24	no	no	INTJ
ejde-388	390	25	.	.	NOUN
ejde-388	390	26	4	4	NUM
ejde-388	390	27	(	(	PUNCT
ejde-388	390	28	2013	2013	NUM
ejde-388	390	29	)	)	PUNCT
ejde-388	390	30	,	,	PUNCT
ejde-388	390	31	379	379	NUM
ejde-388	390	32	-	-	SYM
ejde-388	390	33	392	392	NUM
ejde-388	390	34	.	.	PUNCT
ejde-388	391	1	[	[	X
ejde-388	391	2	12	12	NUM
ejde-388	391	3	]	]	X
ejde-388	391	4	y.	y.	PROPN
ejde-388	391	5	li	li	PROPN
ejde-388	391	6	;	;	PUNCT
ejde-388	391	7	the	the	DET
ejde-388	391	8	distinction	distinction	NOUN
ejde-388	391	9	of	of	ADP
ejde-388	391	10	turbulence	turbulence	NOUN
ejde-388	391	11	from	from	ADP
ejde-388	391	12	chaos	chaos	NOUN
ejde-388	391	13	rough	rough	ADJ
ejde-388	391	14	dependence	dependence	NOUN
ejde-388	391	15	on	on	ADP
ejde-388	391	16	initial	initial	ADJ
ejde-388	391	17	data	datum	NOUN
ejde-388	391	18	,	,	PUNCT
ejde-388	391	19	electronic	electronic	ADJ
ejde-388	391	20	journal	journal	NOUN
ejde-388	391	21	of	of	ADP
ejde-388	391	22	differential	differential	ADJ
ejde-388	391	23	equations	equation	NOUN
ejde-388	391	24	2014	2014	NUM
ejde-388	391	25	,	,	PUNCT
ejde-388	391	26	no	no	INTJ
ejde-388	391	27	.	.	NOUN
ejde-388	391	28	104	104	NUM
ejde-388	391	29	(	(	PUNCT
ejde-388	391	30	2014	2014	NUM
ejde-388	391	31	)	)	PUNCT
ejde-388	391	32	,	,	PUNCT
ejde-388	391	33	1	1	NUM
ejde-388	391	34	-	-	SYM
ejde-388	391	35	8	8	NUM
ejde-388	391	36	.	.	PUNCT
ejde-388	392	1	[	[	X
ejde-388	392	2	13	13	NUM
ejde-388	392	3	]	]	X
ejde-388	392	4	y.	y.	PROPN
ejde-388	392	5	li	li	PROPN
ejde-388	392	6	,	,	PUNCT
ejde-388	392	7	;	;	PUNCT
ejde-388	392	8	rough	rough	ADJ
ejde-388	392	9	dependence	dependence	NOUN
ejde-388	392	10	upon	upon	SCONJ
ejde-388	392	11	initial	initial	ADJ
ejde-388	392	12	data	datum	NOUN
ejde-388	392	13	exemplified	exemplify	VERB
ejde-388	392	14	by	by	ADP
ejde-388	392	15	explicit	explicit	ADJ
ejde-388	392	16	solutions	solution	NOUN
ejde-388	392	17	and	and	CCONJ
ejde-388	392	18	the	the	DET
ejde-388	392	19	effect	effect	NOUN
ejde-388	392	20	of	of	ADP
ejde-388	392	21	viscosity	viscosity	NOUN
ejde-388	392	22	,	,	PUNCT
ejde-388	392	23	nonlinearity	nonlinearity	NOUN
ejde-388	392	24	30	30	NUM
ejde-388	392	25	(	(	PUNCT
ejde-388	392	26	2017	2017	NUM
ejde-388	392	27	)	)	PUNCT
ejde-388	392	28	,	,	PUNCT
ejde-388	392	29	1097	1097	NUM
ejde-388	392	30	-	-	SYM
ejde-388	392	31	1108	1108	NUM
ejde-388	392	32	,	,	PUNCT
ejde-388	392	33	arxiv:1506.05498	arxiv:1506.05498	ADV
ejde-388	392	34	.	.	PUNCT
ejde-388	393	1	ejde-2020/104	ejde-2020/104	PRON
ejde-388	393	2	short	short	ADJ
ejde-388	393	3	term	term	NOUN
ejde-388	393	4	unpredictability	unpredictability	NOUN
ejde-388	393	5	21	21	NUM
ejde-388	393	6	[	[	X
ejde-388	393	7	14	14	NUM
ejde-388	393	8	]	]	X
ejde-388	393	9	y.	y.	PROPN
ejde-388	393	10	li	li	PROPN
ejde-388	393	11	;	;	PUNCT
ejde-388	393	12	linear	linear	ADJ
ejde-388	393	13	hydrodynamic	hydrodynamic	ADJ
ejde-388	393	14	stability	stability	NOUN
ejde-388	393	15	,	,	PUNCT
ejde-388	393	16	notices	notice	NOUN
ejde-388	393	17	of	of	ADP
ejde-388	393	18	the	the	DET
ejde-388	393	19	ams	am	NOUN
ejde-388	393	20	65	65	NUM
ejde-388	393	21	,	,	PUNCT
ejde-388	393	22	no	no	INTJ
ejde-388	393	23	.	.	NOUN
ejde-388	393	24	10	10	NUM
ejde-388	393	25	(	(	PUNCT
ejde-388	393	26	2018	2018	NUM
ejde-388	393	27	)	)	PUNCT
ejde-388	393	28	,	,	PUNCT
ejde-388	393	29	1255	1255	NUM
ejde-388	393	30	-	-	SYM
ejde-388	393	31	1259	1259	NUM
ejde-388	393	32	.	.	PUNCT
ejde-388	394	1	[	[	X
ejde-388	394	2	15	15	NUM
ejde-388	394	3	]	]	X
ejde-388	394	4	y.	y.	PROPN
ejde-388	394	5	li	li	PROPN
ejde-388	394	6	,	,	PUNCT
ejde-388	394	7	z.	z.	PROPN
ejde-388	394	8	lin	lin	PROPN
ejde-388	394	9	;	;	PUNCT
ejde-388	394	10	a	a	DET
ejde-388	394	11	resolution	resolution	NOUN
ejde-388	394	12	of	of	ADP
ejde-388	394	13	the	the	DET
ejde-388	394	14	sommerfeld	sommerfeld	ADJ
ejde-388	394	15	paradox	paradox	NOUN
ejde-388	394	16	,	,	PUNCT
ejde-388	394	17	siam	siam	PROPN
ejde-388	394	18	j.	j.	PROPN
ejde-388	394	19	math	math	PROPN
ejde-388	394	20	.	.	PUNCT
ejde-388	395	1	anal	anal	PROPN
ejde-388	395	2	.	.	PROPN
ejde-388	395	3	,	,	PUNCT
ejde-388	395	4	43	43	NUM
ejde-388	395	5	,	,	PUNCT
ejde-388	395	6	no.4	no.4	PROPN
ejde-388	395	7	(	(	PUNCT
ejde-388	395	8	2011	2011	NUM
ejde-388	395	9	)	)	PUNCT
ejde-388	395	10	,	,	PUNCT
ejde-388	395	11	1923	1923	NUM
ejde-388	395	12	-	-	SYM
ejde-388	395	13	1954	1954	NUM
ejde-388	395	14	.	.	PUNCT
ejde-388	396	1	[	[	X
ejde-388	396	2	16	16	NUM
ejde-388	396	3	]	]	X
ejde-388	396	4	d.	d.	PROPN
ejde-388	396	5	lucas	lucas	PROPN
ejde-388	396	6	,	,	PUNCT
ejde-388	396	7	r.	r.	PROPN
ejde-388	396	8	kerswell	kerswell	PROPN
ejde-388	396	9	;	;	PUNCT
ejde-388	396	10	recurrent	recurrent	ADJ
ejde-388	396	11	flow	flow	NOUN
ejde-388	396	12	analysis	analysis	NOUN
ejde-388	396	13	in	in	ADP
ejde-388	396	14	spatiotemporally	spatiotemporally	ADV
ejde-388	396	15	chaotic	chaotic	ADJ
ejde-388	396	16	2	2	NUM
ejde-388	396	17	-	-	PUNCT
ejde-388	396	18	dimensional	dimensional	ADJ
ejde-388	396	19	kolmogorov	kolmogorov	ADJ
ejde-388	396	20	flow	flow	NOUN
ejde-388	396	21	,	,	PUNCT
ejde-388	396	22	phys	phy	NOUN
ejde-388	396	23	.	.	PUNCT
ejde-388	397	1	fluids	fluid	NOUN
ejde-388	397	2	,	,	PUNCT
ejde-388	397	3	27	27	NUM
ejde-388	397	4	(	(	PUNCT
ejde-388	397	5	2015	2015	NUM
ejde-388	397	6	)	)	PUNCT
ejde-388	397	7	,	,	PUNCT
ejde-388	397	8	045106	045106	NUM
ejde-388	397	9	.	.	PUNCT
ejde-388	398	1	[	[	X
ejde-388	398	2	17	17	NUM
ejde-388	398	3	]	]	PUNCT
ejde-388	398	4	l.	l.	PROPN
ejde-388	398	5	van	van	PROPN
ejde-388	398	6	veen	veen	PROPN
ejde-388	398	7	,	,	PUNCT
ejde-388	398	8	g.	g.	PROPN
ejde-388	398	9	kawahara	kawahara	PROPN
ejde-388	398	10	;	;	PUNCT
ejde-388	398	11	homoclinic	homoclinic	ADJ
ejde-388	398	12	tangle	tangle	NOUN
ejde-388	398	13	on	on	ADP
ejde-388	398	14	the	the	DET
ejde-388	398	15	edge	edge	NOUN
ejde-388	398	16	of	of	ADP
ejde-388	398	17	shear	shear	NOUN
ejde-388	398	18	turbulence	turbulence	NOUN
ejde-388	398	19	,	,	PUNCT
ejde-388	398	20	phys	phy	NOUN
ejde-388	398	21	.	.	PUNCT
ejde-388	399	1	rev	rev	PROPN
ejde-388	399	2	.	.	PROPN
ejde-388	399	3	lett	lett	PROPN
ejde-388	399	4	.	.	PROPN
ejde-388	399	5	,	,	PUNCT
ejde-388	399	6	107	107	NUM
ejde-388	399	7	(	(	PUNCT
ejde-388	399	8	2011	2011	NUM
ejde-388	399	9	)	)	PUNCT
ejde-388	399	10	,	,	PUNCT
ejde-388	399	11	114501	114501	NUM
ejde-388	399	12	.	.	PUNCT
ejde-388	400	1	[	[	X
ejde-388	400	2	18	18	NUM
ejde-388	400	3	]	]	X
ejde-388	400	4	d.	d.	PROPN
ejde-388	400	5	viswanath	viswanath	PROPN
ejde-388	400	6	;	;	PUNCT
ejde-388	400	7	recurrent	recurrent	ADJ
ejde-388	400	8	motions	motion	NOUN
ejde-388	400	9	within	within	ADP
ejde-388	400	10	plane	plane	NOUN
ejde-388	400	11	couette	couette	NOUN
ejde-388	400	12	turbulence	turbulence	NOUN
ejde-388	400	13	,	,	PUNCT
ejde-388	400	14	j.	j.	PROPN
ejde-388	400	15	fluid	fluid	PROPN
ejde-388	400	16	mech	mech	NOUN
ejde-388	400	17	.	.	PUNCT
ejde-388	401	1	580	580	NUM
ejde-388	401	2	(	(	PUNCT
ejde-388	401	3	2007	2007	NUM
ejde-388	401	4	)	)	PUNCT
ejde-388	401	5	,	,	PUNCT
ejde-388	401	6	339	339	NUM
ejde-388	401	7	-	-	SYM
ejde-388	401	8	358	358	NUM
ejde-388	401	9	.	.	PUNCT
ejde-388	402	1	[	[	X
ejde-388	402	2	19	19	NUM
ejde-388	402	3	]	]	X
ejde-388	402	4	v.	v.	X
ejde-388	402	5	yudovich	yudovich	PROPN
ejde-388	402	6	;	;	PUNCT
ejde-388	402	7	on	on	ADP
ejde-388	402	8	the	the	DET
ejde-388	402	9	loss	loss	NOUN
ejde-388	402	10	of	of	ADP
ejde-388	402	11	smoothness	smoothness	NOUN
ejde-388	402	12	of	of	ADP
ejde-388	402	13	the	the	DET
ejde-388	402	14	solutions	solution	NOUN
ejde-388	402	15	of	of	ADP
ejde-388	402	16	the	the	DET
ejde-388	402	17	euler	euler	PROPN
ejde-388	402	18	equations	equation	NOUN
ejde-388	402	19	and	and	CCONJ
ejde-388	402	20	the	the	DET
ejde-388	402	21	inherent	inherent	ADJ
ejde-388	402	22	instability	instability	NOUN
ejde-388	402	23	of	of	ADP
ejde-388	402	24	flows	flow	NOUN
ejde-388	402	25	of	of	ADP
ejde-388	402	26	an	an	DET
ejde-388	402	27	ideal	ideal	ADJ
ejde-388	402	28	fluid	fluid	NOUN
ejde-388	402	29	,	,	PUNCT
ejde-388	402	30	chaos	chaos	NOUN
ejde-388	402	31	,	,	PUNCT
ejde-388	402	32	10	10	NUM
ejde-388	402	33	,	,	PUNCT
ejde-388	402	34	no	no	INTJ
ejde-388	402	35	.	.	NOUN
ejde-388	402	36	3	3	NUM
ejde-388	402	37	(	(	PUNCT
ejde-388	402	38	2000	2000	NUM
ejde-388	402	39	)	)	PUNCT
ejde-388	402	40	,	,	PUNCT
ejde-388	402	41	705	705	NUM
ejde-388	402	42	-	-	SYM
ejde-388	402	43	719	719	NUM
ejde-388	402	44	.	.	PUNCT
ejde-388	402	45	zaichun	zaichun	PROPN
ejde-388	402	46	feng	feng	PROPN
ejde-388	402	47	department	department	PROPN
ejde-388	402	48	of	of	ADP
ejde-388	402	49	mechanical	mechanical	ADJ
ejde-388	402	50	and	and	CCONJ
ejde-388	402	51	aerospace	aerospace	NOUN
ejde-388	402	52	engineering	engineering	NOUN
ejde-388	402	53	,	,	PUNCT
ejde-388	402	54	university	university	PROPN
ejde-388	402	55	of	of	ADP
ejde-388	402	56	missouri	missouri	PROPN
ejde-388	402	57	,	,	PUNCT
ejde-388	402	58	columbia	columbia	PROPN
ejde-388	402	59	,	,	PUNCT
ejde-388	402	60	mo	mo	PROPN
ejde-388	402	61	65211	65211	NUM
ejde-388	402	62	,	,	PUNCT
ejde-388	402	63	usa	usa	PROPN
ejde-388	402	64	email	email	NOUN
ejde-388	402	65	address	address	NOUN
ejde-388	402	66	:	:	PUNCT
ejde-388	402	67	fengf@missouri.edu	fengf@missouri.edu	PROPN
ejde-388	402	68	y.	y.	PROPN
ejde-388	402	69	charles	charles	PROPN
ejde-388	402	70	li	li	PROPN
ejde-388	402	71	department	department	PROPN
ejde-388	402	72	of	of	ADP
ejde-388	402	73	mathematics	mathematics	PROPN
ejde-388	402	74	,	,	PUNCT
ejde-388	402	75	university	university	PROPN
ejde-388	402	76	of	of	ADP
ejde-388	402	77	missouri	missouri	PROPN
ejde-388	402	78	,	,	PUNCT
ejde-388	402	79	columbia	columbia	PROPN
ejde-388	402	80	,	,	PUNCT
ejde-388	402	81	mo	mo	PROPN
ejde-388	402	82	65211	65211	NUM
ejde-388	402	83	,	,	PUNCT
ejde-388	402	84	usa	usa	PROPN
ejde-388	402	85	email	email	NOUN
ejde-388	402	86	address	address	NOUN
ejde-388	402	87	:	:	PUNCT
ejde-388	402	88	liyan@missouri.edu	liyan@missouri.edu	PROPN
ejde-388	402	89	,	,	PUNCT
ejde-388	402	90	http://faculty.missouri.edu/∼liyan	http://faculty.missouri.edu/∼liyan	ADJ
ejde-388	402	91	1	1	NUM
ejde-388	402	92	.	.	PUNCT
ejde-388	402	93	introduction	introduction	NOUN
ejde-388	402	94	2	2	NUM
ejde-388	402	95	.	.	PUNCT
ejde-388	402	96	chaos	chaos	NOUN
ejde-388	402	97	–	–	PUNCT
ejde-388	402	98	sensitive	sensitive	ADJ
ejde-388	402	99	dependence	dependence	NOUN
ejde-388	402	100	on	on	ADP
ejde-388	402	101	initial	initial	ADJ
ejde-388	402	102	data	datum	NOUN
ejde-388	402	103	3	3	NUM
ejde-388	402	104	.	.	PUNCT
ejde-388	402	105	high	high	ADJ
ejde-388	402	106	reynolds	reynolds	PROPN
ejde-388	402	107	number	number	NOUN
ejde-388	402	108	turbulence	turbulence	NOUN
ejde-388	402	109	–	–	PUNCT
ejde-388	402	110	rough	rough	ADJ
ejde-388	402	111	dependence	dependence	NOUN
ejde-388	402	112	on	on	ADP
ejde-388	402	113	initial	initial	ADJ
ejde-388	402	114	data	datum	NOUN
ejde-388	402	115	4	4	NUM
ejde-388	402	116	.	.	PUNCT
ejde-388	403	1	classical	classical	ADJ
ejde-388	403	2	hydrodynamic	hydrodynamic	ADJ
ejde-388	403	3	instability	instability	NOUN
ejde-388	403	4	–	–	PUNCT
ejde-388	403	5	directional	directional	ADJ
ejde-388	403	6	derivative	derivative	ADJ
ejde-388	403	7	5	5	NUM
ejde-388	403	8	.	.	X
ejde-388	403	9	2d	2d	PROPN
ejde-388	403	10	numerical	numerical	ADJ
ejde-388	403	11	simulations	simulation	NOUN
ejde-388	403	12	on	on	ADP
ejde-388	403	13	rough	rough	ADJ
ejde-388	403	14	dependence	dependence	NOUN
ejde-388	403	15	on	on	ADP
ejde-388	403	16	initial	initial	ADJ
ejde-388	403	17	data	datum	NOUN
ejde-388	403	18	5.1	5.1	NUM
ejde-388	403	19	.	.	PUNCT
ejde-388	404	1	a	a	DET
ejde-388	404	2	fundamental	fundamental	ADJ
ejde-388	404	3	problem	problem	NOUN
ejde-388	404	4	in	in	ADP
ejde-388	404	5	the	the	DET
ejde-388	404	6	numerical	numerical	ADJ
ejde-388	404	7	simulations	simulation	NOUN
ejde-388	404	8	5.2	5.2	NUM
ejde-388	404	9	.	.	PUNCT
ejde-388	405	1	fixed	fix	VERB
ejde-388	405	2	base	base	NOUN
ejde-388	405	3	solution	solution	NOUN
ejde-388	405	4	and	and	CCONJ
ejde-388	405	5	different	different	ADJ
ejde-388	405	6	perturbations	perturbation	NOUN
ejde-388	405	7	5.3	5.3	NUM
ejde-388	405	8	.	.	PUNCT
ejde-388	406	1	fixed	fix	VERB
ejde-388	406	2	perturbation	perturbation	NOUN
ejde-388	406	3	and	and	CCONJ
ejde-388	406	4	different	different	ADJ
ejde-388	406	5	base	base	NOUN
ejde-388	406	6	solutions	solution	NOUN
ejde-388	406	7	5.4	5.4	NUM
ejde-388	406	8	.	.	PUNCT
ejde-388	407	1	turbulence	turbulence	NOUN
ejde-388	407	2	regime	regime	VERB
ejde-388	407	3	5.5	5.5	NUM
ejde-388	407	4	.	.	PUNCT
ejde-388	408	1	norm	norm	NOUN
ejde-388	408	2	independence	independence	NOUN
ejde-388	408	3	of	of	ADP
ejde-388	408	4	the	the	DET
ejde-388	408	5	short	short	ADJ
ejde-388	408	6	term	term	NOUN
ejde-388	408	7	unpredictability	unpredictability	NOUN
ejde-388	408	8	5.6	5.6	NUM
ejde-388	408	9	.	.	PUNCT
ejde-388	409	1	an	an	DET
ejde-388	409	2	intuition	intuition	NOUN
ejde-388	409	3	on	on	ADP
ejde-388	409	4	the	the	DET
ejde-388	409	5	super	super	ADV
ejde-388	409	6	fast	fast	ADJ
ejde-388	409	7	amplification	amplification	NOUN
ejde-388	409	8	of	of	ADP
ejde-388	409	9	perturbation	perturbation	NOUN
ejde-388	409	10	6	6	NUM
ejde-388	409	11	.	.	PUNCT
ejde-388	410	1	reynolds	reynold	NOUN
ejde-388	410	2	-	-	PUNCT
ejde-388	410	3	number	number	NOUN
ejde-388	410	4	dependence	dependence	NOUN
ejde-388	410	5	of	of	ADP
ejde-388	410	6	the	the	DET
ejde-388	410	7	super	super	ADV
ejde-388	410	8	fast	fast	ADJ
ejde-388	410	9	amplification	amplification	NOUN
ejde-388	410	10	of	of	ADP
ejde-388	410	11	perturbations	perturbation	NOUN
ejde-388	410	12	7	7	NUM
ejde-388	410	13	.	.	PUNCT
ejde-388	410	14	3d	3d	PROPN
ejde-388	410	15	numerical	numerical	PROPN
ejde-388	410	16	simulations	simulation	NOUN
ejde-388	410	17	on	on	ADP
ejde-388	410	18	rough	rough	ADJ
ejde-388	410	19	dependence	dependence	NOUN
ejde-388	410	20	on	on	ADP
ejde-388	410	21	initial	initial	ADJ
ejde-388	410	22	data	datum	NOUN
ejde-388	410	23	7.1	7.1	NUM
ejde-388	410	24	.	.	PUNCT
ejde-388	411	1	fixed	fix	VERB
ejde-388	411	2	base	base	NOUN
ejde-388	411	3	solution	solution	NOUN
ejde-388	411	4	and	and	CCONJ
ejde-388	411	5	different	different	ADJ
ejde-388	411	6	perturbations	perturbation	NOUN
ejde-388	411	7	7.2	7.2	NUM
ejde-388	411	8	.	.	PUNCT
ejde-388	412	1	fixed	fix	VERB
ejde-388	412	2	perturbation	perturbation	NOUN
ejde-388	412	3	and	and	CCONJ
ejde-388	412	4	different	different	ADJ
ejde-388	412	5	base	base	NOUN
ejde-388	412	6	solutions	solution	NOUN
ejde-388	412	7	7.3	7.3	NUM
ejde-388	412	8	.	.	PUNCT
ejde-388	413	1	turbulence	turbulence	NOUN
ejde-388	413	2	regime	regime	NOUN
ejde-388	413	3	conclusions	conclusion	NOUN
ejde-388	413	4	references	reference	NOUN