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arXiv · 1611.09076

Dynamics of large-scale quantities in Rayleigh-Bénard convection

Ambrish Pandey·Abhishek Kumar·Anando G. Chatterjee·Mahendra K. Verma
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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 $\mathrm{Ra}^{0.3}$.

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Ambrish Pandey, Abhishek Kumar, Anando G. Chatterjee, Mahendra K. Verma. 2016-11-28. Dynamics of large-scale quantities in Rayleigh-Bénard convection. https://doi.org/10.1103/physreve.94.053106

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