Reflections on dissipation associated with thermal convection

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.