Prandtl and Rayleigh number dependence of heat transport in high Rayleigh number thermal convection

Abstract

Results from direct numerical simulation for three-dimensional Rayleigh-Bénard convection in samples of aspect ratio $\Gamma =0.23$ and $\Gamma =0.5$ up to Rayleigh number $Ra=2\times 10^{12}$ are presented. The broad range of Prandtl numbers $0.5<Pr<10$ is considered. In contrast to some experiments, we do not see any increase in $Nu/R{a}^{1/3}$, neither due to $Pr$ number effects, nor due to a constant heat flux boundary condition at the bottom plate instead of constant temperature boundary conditions. Even at these very high $Ra$, both the thermal and kinetic boundary layer thicknesses obey Prandtl-Blasius scaling.

9 pages, 7 figures

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