Compressible turbulent convection at very high Rayleigh numbers

TL;DR

This study simulates compressible turbulent convection at extremely high Rayleigh numbers, revealing classical heat transport scaling and distinct temperature and density profiles compared to Rayleigh-Bénard convection.

Contribution

It provides the first high-Rayleigh-number simulations of compressible convection showing classical Nu-Ra scaling and detailed flow characteristics.

Findings

Nu scales as Ra^{0.3}, indicating classical scaling.

Bulk temperature drops adiabatically with height.

Density decreases with height, unlike in RBC.

Abstract

Heat transport in highly turbulent convection is not well understood. In this paper, we simulate compressible convection in a box of aspect ratio 4 using computationally-efficient MacCormack-TVD finite difference method on single and multi-GPUs, and reach very high Rayleigh number ($\mathrm{Ra}$) -- $10^{15}$ in two dimensions and $10^{11}$ in three dimensions. We show that the Nusselt number $\mathrm{Nu} \propto \mathrm{Ra}^{0.3}$ (classical scaling) that differs strongly from the ultimate-regime scaling, which is $\mathrm{Nu} \propto \mathrm{Ra}^{1/2}$. The bulk temperature drops adiabatically along the vertical even for high $\mathrm{Ra}$, which is in contrast to the constant bulk temperature in Rayleigh-B\'{e}nard convection (RBC). Unlike RBC, the density decreases with height. In addition, the vertical pressure-gradient ($-dp/dz$) nearly matches the buoyancy term ($\rho g$). But, the difference, $-dp/dz-\rho g$, is equal to the nonlinear term that leads to Reynolds number $\mathrm{Re} \propto \mathrm{Ra}^{1/2}$.