Fully compressible convection for planetary mantles

SUMMARY The numerical simulations of convection inside the mantle Earth or terrestrial planets have been based on approximate equations fluid dynamics. A common approximation is neglect inertia term which certainly reasonable as Reynolds number silicate mantles, their inverse Prandtl number, are infinitesimally small. However various other simplifications made we discuss in this paper. crudest that can be done Boussinesq (BA) where parameters constant and variations density only included buoyancy assumed to proportional temperature with a thermal expansivity. pressure related physical consequences (mostly presence an adiabatic gradient dissipation) usually accounted for by using anelastic (AA) initially developed astrophysical atmospheric situations. BA AA cases provide simplified but self-consistent systems differential equations. Intermediate approximations also geophysical literature although they invariably associated theoretical inconsistencies (non-conservation total energy, non-conservation statistically steady state heat flow depth, momentum entropy implying inconsistent dissipations). We show that, infinite case, solving fully compressible (FC) realistic equation (EoS) however not much more difficult numerically challenging than cases. compare statistical properties Boussinesq, FC 2-D simulations. point inconsistency when two capacities constant. suggest at high Rayleigh profile dissipation convective directly surface flux. Our results mostly discussed framework EoS used flexible enough applied icy inner core.