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

TL;DR

This study uses direct numerical simulations to analyze how Prandtl and Rayleigh numbers influence heat transport in high Rayleigh number thermal convection, finding boundary layer behaviors consistent with classical scaling laws.

Contribution

The paper provides high-Rayleigh-number simulation data showing boundary layer scaling and clarifies the effects of Prandtl number and boundary conditions on heat transport.

Findings

No increase in Nu/Ra^{1/3} with Pr or boundary condition changes.

Boundary layers follow Prandtl-Blasius scaling at high Ra.

Results challenge some experimental observations regarding heat transport scaling.

Abstract

Results from direct numerical simulation for three-dimensional Rayleigh-B\'enard convection in samples of aspect ratio $\Gamma=0.23$ and $\Gamma=0.5$ up to Rayleigh number $Ra=2\times10^{12}$ 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 $Nu/Ra^{1/3}$, 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.