Rigorous entropy formulation of the anelastic liquid equations in an ideal gas

Abstract

The point of this short paper is to provide a useful set of equations governing stratified convection, expressed solely in terms of two thermodynamic variables, i.e. the pressure and the entropy, and the velocity field of the flow, free from any additional assumptions about the properties of turbulence. The pressure fluctuation is entirely eliminated from the energy equation and it appears only in the momentum balance, easily removable by taking its curl. This goal is achieved through the well-known anelastic approximation and an assumption of constant thermal diffusivity coefficient. The rigorously derived system of anelastic liquid equations constitutes a useful tool for modelling the dynamics of stellar interiors.