14th International Symposium on Particle Image Velocimetry – ISPIV 2021
August 1–5, 2021

Rayleigh-Bénard convection in air: out-of-plane
vorticity from stereoscopic PIV measurements

V. Valori1∗, A. Thieme1, C. Cierpka1, J. Schumacher1,2

1 Technische Universität Ilmenau, Institute of Thermodynamics and Fluid Mechanics, D-98684 Ilmenau,
Germany

2 New York University, Tandon School of Engineering, New York City, NY 11201, USA
∗ valentina.valori@tu-ilmenau.de

Abstract
We present results from stereoscopic PIV measurements in a Rayleigh-Bénard convection (RBC) cell filled
with (compressed) air at Rayleigh numbers: Ra = 1.5× 104,2× 104,1× 105,2× 105,5× 105, and Prandtl
number Pr ' 0.7. The three largest Rayleigh numbers are obtained pressurising the whole set-up including
cameras and objective lenses, up to 4.5 bars.
The main goal of this study is to reproduce DNS data that are acquired at the same Rayleigh numbers to
study far-tail events of the out-of-plane vorticity component (ωz).
The measurements are performed in a RBC cell with aspect ratio Γ = W/H = 10, where W is the width
and H = 3 cm is the height of the domain. The cell is equipped with a transparent bottom plate heated by a
thin oxide layer (for details see Kästner et al. (2018)), which allows us to measure 3C2D velocity fields on
a horizontal plane at mid height of the cell. The RBC cell set-up is inserted in the SCALEX facility of TU
Ilmenau, a pressure vessel with several optical accesses that can be pressurised up to 10 bars.

-10 -5 0 5 10

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(a) stereo PIV

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(b) DNS

Figure 1: PDFs of ωz from stereo PIV and DNS data at Ra = 1.5×104,2×104,1×105,2×105,5×105

The experiments aim firstly at improving the quality of previous measurements performed in the same
set-up [Kästner et al. (2018), Cierpka et al. (2019)], regarding the accuracy of the out-of-plane velocity
component. This has been realised by positioning the cameras at a larger stereo angle (about 25◦), which
is possible by placing them inside the pressure vessel. Major challenges of the current measurements are
caused by optical distortions due to the temperature gradients that are typical for thermal convection (see
Valori (2018), Valori et al. (2019)).



1900 1950 2000 2050 2100

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(a) Time evolution of ωz at (xe,ye) (b) Spatial structutre at the time of the extreme event

Figure 2: Visualization of an extreme event of ωz at Ra= 2.5×105 from a time evolution serie at the position
of the extreme event (xe,ye) and a snapshot of ωz. σ indicates the standard deviation and Tf f the free fall
time of the flow. Arrows in plot (b) show the in-plane velocity.

Probability Density Functions (PDFs) of ωz from stereo PIV experiments and from DNS data are shown
respectively in figure 1(a) and 1(b) for all Rayleigh numbers studied. We can observe that for both kind of
data the tails of the PDF becomes wider while increasing the Rayleigh number, which may be connected
to intermittency. This crossover from Gaussian to intermittent statistic was recently studied in Valori and
Schumacher (2021) from DNS. Figure2(a) shows the temporal evolution of ωz at the position of its largest
(extreme) value at Ra = 2.5× 105, while figure2(b) shows the spatial distribution of ωz at the time of its
extreme event in the experiments.
The experimental results are able to reproduce well the statistics of DNS data of the same flow, and allow
the study of extreme events of ωz.

Acknowledgements
The work is supported by the Priority Programme DFG-SPP 1881 on Turbulent Superstructures of the
Deutsche Forschungsgemeinschaft, and the ConVext Marie Skłodowska-Curie Project Number 101024531
funded by the European Union.

References
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of convection in large aspect ratio Rayleigh-Bénard cells in air and sulfur-hexafluoride. Experimental
Thermal and Fluid Science 109:109841

Kästner C, Resagk C, Westphalen J, Junghähnel M, Cierpka C, and Schumacher J (2018) Assessment of
horizontal velocity fields in square thermal convection cells with large aspect ratio. Experiments in Fluids
59:171

Valori V (2018) Rayleigh-Bénard convection of a supercritical fluid. doctoral thesis. Delft University of
Technology

Valori V, Elsinga GE, Rohde M, Westerweel J, and van der Hagen THJJ (2019) Particle image velocimetry
measurements of a thermally convective supercritical fluid. Experiments in Fluids 60:143

Valori V and Schumacher J (2021) Connecting boundary layer dynamics with extreme bulk dissipation
events in Rayleigh-Bénard flow. Europhysics Letters, in press