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Comparison between two- and three-dimensional Rayleigh–Bénard convection

Published online by Cambridge University Press:  04 November 2013

Erwin P. van der Poel ,
Richard J. A. M. Stevens  and
Detlef Lohse
Erwin P. van der Poel*
Affiliation:
Department of Science and Technology and J.M. Burgers Center for Fluid Dynamics, University of Twente, P.O Box 217, 7500 AE Enschede, The Netherlands
Richard J. A. M. Stevens
Affiliation:
Department of Science and Technology and J.M. Burgers Center for Fluid Dynamics, University of Twente, P.O Box 217, 7500 AE Enschede, The Netherlands Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
Detlef Lohse
Affiliation:
Department of Science and Technology and J.M. Burgers Center for Fluid Dynamics, University of Twente, P.O Box 217, 7500 AE Enschede, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

Two-dimensional and three-dimensional Rayleigh–Bénard convection is compared using results from direct numerical simulations and previous experiments. The phase diagrams for both cases are reviewed. The differences and similarities between two- and three-dimensional convection are studied using $Nu(Ra)$ for $\mathit{Pr}= 4. 38$ and $\mathit{Pr}= 0. 7$ and $Nu(Pr)$ for $Ra$ up to $1{0}^{8} $. In the $Nu(Ra)$ scaling at higher $Pr$, two- and three-dimensional convection is very similar, differing only by a constant factor up to $\mathit{Ra}= 1{0}^{10} $. In contrast, the difference is large at lower $Pr$, due to the strong roll state dependence of $Nu$ in two dimensions. The behaviour of $Nu(Pr)$ is similar in two and three dimensions at large $Pr$. However, it differs significantly around $\mathit{Pr}= 1$. The Reynolds number values are consistently higher in two dimensions and additionally converge at large $Pr$. Finally, the thermal boundary layer profiles are compared in two and three dimensions.

JFM classification

Turbulent Flows: Turbulent Flows Turbulent Flows: Turbulent convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 736 , 10 December 2013 , pp. 177 - 194
Copyright
©2013 Cambridge University Press 

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