Compressible turbulent convection in highly stratified adiabatic background

Buoyancy-driven turbulent convection leads to a fully compressible flow with a strong top-down asymmetry of first- and second-order statistics when the adiabatic equilibrium profiles of temperature, density and pressure decay very strongly across the convection layer. The growth of this asymmetry and the formation of an increasingly thicker stabilized sublayer with a negative mean convective heat flux at the top of the convection zone is reported here by a series highly resolved three-dimensional direct numerical simulations beyond the Oberbeck-Boussinesq and anelastic limits for dimensionless dissipation numbers $0.1 \le D\le 0.8$ at fixed Rayleigh number $Ra=10^6$ and superadiabaticity. The highly stratified compressible convection regime appears for $D > D_{\rm crit}\approx 0.65$, when density fluctuations collapse to those of pressure; it is characterized by an up to nearly 50\% reduced global turbulent heat transfer and a sparse network of focused thin thermal plumes falling through the top sublayer deep into the bulk.