Beyond the anealstic approximation: Compressibility effects in turbulent convection

We systematically study the compressibility effects on Rayleigh-B\'{e}rnard turbulent convection for an ideal gas using DNS of fully compressible Navier-Stokes equations. Compressibility effects in convection are parametrized by the dissipation number, $D= gd/c_{p}T_{B} $ and superadiabaticity, $\epsilon= \Delta T / T_{B}$ where $T_{B}$ and $\Delta T$ correspond to the bottom plate temperature and superadiabatic temperature difference across the plates respectively. Our simulations encompass the Oberbeck-Boussinesq (OB) limit $\left( D, \epsilon \rightarrow 0 \right)$ to regimes going beyond the anelastic approximations $\left( D, \epsilon ~ \approx O(1) \right)$ starting from a Rayliegh number, $Ra \approx 10^{6}$ and fixed Prandtl number, $Pr= 0.72$. We show the symmetry breaking of the mean superadiabatic temperature with strong stratification of density. Asymmetry is also observed for compressibility parameters: the turbulent Mach number, $M_{t}= u_{rms}/ \langle c \rangle$ and dilatation, $\theta = \partial u_{i} / \partial x_{i}$. We separate compressible mechanisms responsible for symmetry breaking from incompressible non-OB ones. Analyses include the bulk statistics and scaling of Nusselt number with different compressible parameters and Rayleigh numbers.