Reflections on dissipation associated with thermal convection
Résumé
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 -DP/Dt and not that of -αT(DP/Dt). 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. © 2013 Cambridge University Press.