Compressibility effects on the Rayleigh-Taylor instability between miscible fluids

Abstract

The linear Rayleigh-Taylor problem for two miscible compressible viscous fluids is solved for the first time. A wide range of parameter values is investigated. Two main parameters govern this instability: the stratification parameter —attached to the hydrostatic equilibrium— and the compressibility parameters —attached to the fluids. For increasing values of the stratification, the flow is stabilized, whereas for increasing values of the compressibility parameters the flow is destabilized. Diffusions (viscosity, thermal conduction and species) introduced a cut-off wave number beyond which the flow is marginally stable. These conclusions usually hold in the nonlinear single-mode regime, except when compressibilities are equal. In this case linear and nonlinear growth rates are in opposite order.