Thierry Alboussiere, Yanick Ricard
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, c_p, 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 - alpha 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, gamma -1 << 1, independent of the dissipation number.
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http://arxiv.org/abs/1210.5421
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