Rayleigh-Taylor mixing rates for compressible flow

We study Rayleigh-Taylor instability in both the moderately compressible and weakly compressible regimes. For the two-dimensional single mode case, we find that the dimensionless terminal velocities (and associated Froude numbers) are nearly constant over most of this region of parameter space, as the thermodynamic parameters describing the equation of state are varied. The phenomenological drag coefficient which occurs in the single mode buoyancy-drag equation is directly related to the terminal velocities and has a similar behavior. Pressure differences and interface shape, however, display significant dependence on the equation of state parameters even for the weakly compressible flows. For three-dimensional multimode mixing, we expect accordingly that density stratification rather than drag will provide the leading compressibility effect. We develop an analytical model to account for density stratification effects in multimode self-similar mixing. Our theory is consistent with and extends numerically based conclusions developed earlier which also identify density stratification as the dominant compressibility effect for multimode three-dimensional mixing.