Vertically coherent compressible convective flows in a layer with a high density contrast

Two-dimensional simulations are used to study compressible convection in a plane-parallel layer of ideal gas with a high density contrast across the layer. The convective flows are found to consist of rolls which are coherent throughout the entire vertical domain, similar to the results of a number of earlier investigations. Motions near the upper boundary are supersonic, though the Rayleigh number is moderate. The major effect of a high density stratification is to significantly rarefy the fluid in the upper part of the domain, hence increase its thermal diffusivity. The consequence appears to be twofold: Firstly, enhanced thermal diffusion makes non-adiabatic cooling more efficient, thus helps the flows to become supersonic more easily. Secondly, sufficient diffusion can broaden shocks to such an extent that it actually turns them into smooth transition regions.