Reflections on dissipation associated with thermal convection

TL;DR

This paper discusses the derivation of viscous dissipation expressions in thermal convection, corrects a previous error regarding the applicability of the anelastic liquid equation, and clarifies the theoretical framework involved.

Contribution

It provides a corrected analysis of dissipation in convective flows and clarifies the conditions under which the anelastic liquid approximation is valid.

Findings

Corrected the expression for viscous dissipation in convective flows

Identified the invalidity of the previous condition for the anelastic liquid equation

Published a corrigendum explaining the error and its resolution

Abstract

This paper was originally published in June 2013 in JFM (vol. 725). There was one result concerning an expression of viscous dissipation in convective flows and a second result on the condition of applicability of the anelastic liquid equation ($\gamma - 1 \ll 1$). We then found that this second result was wrong and the explanation why this is so was published as a corrigendum in July 2014 in JFM (vol. 751). In a few words, the origin of the error is that we have derived an expression for dissipation in the framework of the exact equations and subsequently used it in the framework of the anelastic models. Here we have included the original article, followed by its corrigendum.