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Fully compressible turbulent convection beyond the Oberbeck-Boussinesq limitand anelastic regime is studied in three-dimensional numerical simulations.Superadiabaticity $\epsilon$ and dissipation number $D$, which measures thestrength of stratification of adiabatic equilibria, cause two limits ofcompressible convection -- nearly top-down-symmetric, strongly superadiabaticand highly top-down-asymmetric, strongly stratified convection. Highestturbulent Mach numbers $M_t$ follow for a symmetric blend of these two limitswhich we term the fully compressible case. Particularly, the stronglystratified convection case leads to a fluctuation-reduced top layer in theconvection zone, a strongly reduced global heat transfer, and differingboundary layer dynamics between top and bottom. We detect this asymmetry forgrowing dissipation number $D$ also in the phase plane which is spanned by theturbulent Mach number $M_t$ and the dilatation parameter $\delta$ which relatesthe dilatational velocity fluctuations to the solenoidal ones. A detailedanalysis of the different transport currents in the fully compressible energybudget relates the low-$D$ convection cases to the standard definition of thedimensionless Nusselt number in the Oberbeck-Boussinesq limit.

Strongly superadiabatic and stratified limits of compressible convection