Dynamics of large-scale quantities in Rayleigh-Bénard convection

Abstract

In this paper we estimate the relative strengths of various terms of the Rayleigh-Bénard equations. Based on these estimates and scaling analysis, we derive a general formula for the large-scale velocity, $U$, or the Péclet number that is applicable for arbitrary Rayleigh number $\mathrm{Ra}$ and Prandtl number $\mathrm{Pr}$. Our formula fits reasonably well with the earlier simulation and experimental results. Our analysis also shows that the wall-bounded convection has enhanced viscous force compared to free turbulence. We also demonstrate how correlations deviate the Nusselt number scaling from the theoretical prediction of ${\mathrm{Ra}}^{1/2}$ to the experimentally observed scaling of nearly ${\mathrm{Ra}}^{0.3}$.

8 pages, 6 figures

References in corpus (4)

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Cited by in corpus (4)

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• Large-eddy simulation of Rayleigh-Bénard convection at extreme Rayleigh numbers
• Prandtl number dependence of the small-scale properties in turbulent Rayleigh-Bénard convection
• Transient and steady convection in two dimensions