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Turbulent Rayleigh–Bénard convection for a Prandtl number of 0.67

Published online by Cambridge University Press:  23 November 2009

GUENTER AHLERS ,
EBERHARD BODENSCHATZ ,
DENIS FUNFSCHILLING  and
JAMES HOGG
GUENTER AHLERS*
Affiliation:
Department of Physics, University of California, Santa Barbara, CA 93106, USA
EBERHARD BODENSCHATZ
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Goettingen, Germany
DENIS FUNFSCHILLING
Affiliation:
LSGC CNRS–GROUPE ENSIC, BP 451, 54001 Nancy Cedex, France
JAMES HOGG
Affiliation:
Department of Physics, University of California, Santa Barbara, CA 93106, USA
*
†Email address for correspondence: guenter@physics.ucsb.edu
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Abstract

For the Rayleigh-number range 107 ≲ Ra ≲ 1011 we report measurements of the Nusselt number Nu and of properties of the large-scale circulation (LSC) for cylindrical samples of helium gas (Prandtl number Pr = 0.674) that have aspect ratio Γ ≡ D/L = 0.50 (D and L are the diameter and the height respectively) and are heated from below. The results for Nu are consistent with recent direct numerical simulations. We measured the amplitude δ of the azimuthal temperature variation induced by the LSC at the sidewall, and the LSC circulation-plane orientation θ0, at three vertical positions. For the entire Ra range the LSC involves a convection roll that is coherent over the height of the system. However, this structure frequently collapses completely at irregular time intervals and then reorganizes from the incoherent flow. At small δ the probability distribution p(δ) increases linearly from zero; for Γ = 1 and Pr = 4.38 this increase is exponential. No evidence of a two-roll structure, with one above the other, was observed. This differs from recent direct numerical simulations for Γ = 0.5 and Pr = 0.7, where a one-roll LSC was found to exist only for Ra ≲ 109 to 1010, and from measurements for Γ = 0.5 and Pr ≃ 5, where one- and two-roll structures were observed with transitions between them at random time intervals.

JFM classification

Convection: Convection

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Papers
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Journal of Fluid Mechanics , Volume 641 , 25 December 2009 , pp. 157 - 167
Copyright
Copyright © Cambridge University Press 2009

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References

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