Viscous dissipation and dynamics in simulations of rotating, stratified plane-layer convection

Abstract

ABSTRACT Convection in stars and planets must be maintained against viscous and Ohmic dissipation. Here, we present the first systematic investigation of viscous dissipation in simulations of rotating, density-stratified plane layers of convection. Our simulations consider an anelastic ideal gas, and employ the open-source code Dedalus. We demonstrate that when the convection is sufficiently vigorous, the integrated dissipative heating tends towards a value that is independent of viscosity or thermal diffusivity, but depends on the imposed luminosity and the stratification. We show that knowledge of the dissipation provides a bound on the magnitude of the kinetic energy flux in the convection zone. In our non-rotating cases with simple flow fields, much of the dissipation occurs near the highest possible temperatures, and the kinetic energy flux approaches this bound. In the rotating cases, although the total integrated dissipation is similar, it is much more uniformly distributed (and locally balanced by work against the stratification), with a consequently smaller kinetic energy flux. The heat transport in our rotating simulations is in good agreement with results previously obtained for 3D Boussinesq convection, and approaches the predictions of diffusion-free theory.