The magnitude of viscous dissipation in strongly stratified two-dimensional convection

TL;DR

This study uses numerical simulations to show that in strongly stratified convective systems, viscous dissipation can produce more heat than the system radiates, potentially affecting stellar and planetary dynamics.

Contribution

The paper provides a theoretical and numerical analysis demonstrating that viscous dissipation can surpass the emitted luminosity in strongly stratified convection, a previously underappreciated effect.

Findings

Dissipative heating can exceed the system's luminosity.

The ratio of dissipation to luminosity depends only on layer depth and thermal scale height.

This ratio is independent of diffusivities.

Abstract

Convection in astrophysical systems must be maintained against dissipation. Although the effects of dissipation are often assumed to be negligible, theory suggests that in strongly stratified convecting fluids, the dissipative heating rate can exceed the luminosity carried by convection. Here we explore this possibility using a series of numerical simulations. We consider two-dimensional numerical models of hydrodynamic convection in a Cartesian layer under the anelastic approximation and demonstrate that the dissipative heating rate can indeed exceed the imposed luminosity. We establish a theoretical expression for the ratio of the dissipative heating rate to the luminosity emerging at the upper boundary, in terms only of the depth of the layer and the thermal scale height. In particular, we show that this ratio is independent of the diffusivities and confirm this with a series of numerical simulations. Our results suggest that dissipative heating may significantly alter the internal dynamics of stars and planets.