Thermodynamic Consistency of a Pseudoincompressible Approximation for General Equations of State

In sound-proof model equations for geophysical fluid dynamics, the momentum and mechanical energy budgets decouple from the thermodynamics for adiabatic flows. In applying such models to non-adiabatic flows of fluids with general equations of state, thermodynamic consistency of the sound-proof approximations needs to be ensured. Specifically, a physically meaningful total energy conservation law should arise as an integral of adiabatic dynamics, while for diabatic flows, the effective energy source terms should be related through thermodynamic relationships to the rates of change of entropy and other pertinent internal degrees of freedom. Complementing earlier work by one of the authors on the Lipps and Hemler-type anelastic approximation, we discuss here the thermodynamic consistency of an extension of Durran's pseudo-incompressible model to moist atmospheric motions allowing for a general equation of state.