Reflections on dissipation associated with thermal convection

This is the authors' abstract. We don't add key points for this paper.

Buoyancy-driven convection is modelled using the Navier–Stokes and entropy equations. It is first shown that the coefficient of heat capacity at constant pressure, cₚ , must in general depend explicitly on pressure (i.e. is not a function of temperature alone) in order to resolve a dissipation inconsistency. It is shown that energy dissipation in a statistically steady state is the time-averaged volume integral of - D P/ D t and not that of - α T(D P/ D t) . Secondly, in the framework of the anelastic equations derived with respect to the adiabatic reference state, we obtain a condition when the anelastic liquid approximation can be made, γ - 1 1 , independent of the dissipation number.