Strongly superadiabatic and stratified limits of compressible convection

Fully compressible turbulent convection beyond the Oberbeck-Boussinesq limit and anelastic regime is studied in three-dimensional numerical simulations. Superadiabaticity $\epsilon$ and dissipation number $D$, which measures the strength of stratification of adiabatic equilibria, cause two limits of compressible convection -- nearly top-down-symmetric, strongly superadiabatic and highly top-down-asymmetric, strongly stratified convection. Highest turbulent Mach numbers $M_t$ follow for a symmetric blend of these two limits which we term the fully compressible case. Particularly, the strongly stratified convection case leads to a fluctuation-reduced top layer in the convection zone, a strongly reduced global heat transfer, and differing boundary layer dynamics between top and bottom. We detect this asymmetry for growing dissipation number $D$ also in the phase plane which is spanned by the turbulent Mach number $M_t$ and the dilatation parameter $\delta$ which relates the dilatational velocity fluctuations to the solenoidal ones. A detailed analysis of the different transport currents in the fully compressible energy budget relates the low-$D$ convection cases to the standard definition of the dimensionless Nusselt number in the Oberbeck-Boussinesq limit.