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The linearized Navier-Stokes equations for a system of superposed immisciblecompressible ideal fluids are analyzed. The results of the analysis reconcilethe stabilizing and destabilizing effects of compressibility reported in theliterature. It is shown that the growth rate $n$ obtained for an inviscid,compressible flow in an infinite domain is bounded by the growth rates obtainedfor the corresponding incompressible flows with uniform and exponentiallyvarying density. As the equilibrium pressure at the interface $p_\infty$increases (less compressible flow), $n$ increases towards the uniform densityresult, while as the ratio of specific heats $\gamma$ increases (lesscompressible fluid), $n$ decreases towards the exponentially varying densityincompressible flow result. This remains valid in the presence of surfacetension or for viscous fluids and the validity of the results is also discussedfor finite size domains. The critical wavenumber imposed by the presence ofsurface tension is unaffected by compressibility. However, the results showthat the surface tension modifies the sensitivity of the growth rate to adifferential change in $\gamma$ for the lower and upper fluids. For the viscouscase, the linearized equations are solved numerically for different values of$p_\infty$ and $\gamma$. It is found that the largest differences compared withthe incompressible cases are obtained at small Atwood numbers. The mostunstable mode for the compressible case is also bounded by the most unstablemodes corresponding to the two limiting incompressible cases.Comment: To appear in Physics of Fluid

Compressibility effects on the Rayleigh–Taylor instability growth between immiscible fluids