Destabilizing effect of compressibility on Rayleigh–Taylor instability for fluids with fixed density profile

Abstract

Analytical solutions for the growth rate of the Rayleigh–Taylor instability (RTI) for two superimposed fluids of exponentially varying densities are obtained by variational approach, which has been introduced to solve the eigenvalue problems related to RTI for inviscid compressible fluid. In order to distinguish the effect of density profile from compressibility effects, two independent parameters have been introduced to describe the static fluid states, one (Pa) is for the variation of pressure near the interface and the other (Pb) for setting the density profile. Three factors related to the RTI growth for compressible fluids have been discussed in detail. For incompressible fluids, the only factor to affect the RTI growth is the density profile. While for compressible fluids, besides the density profile, the specific heat ratio and the interface pressure also contribute to the growth rate of RTI. Analytic dispersion relations and growth rates have been compared to numerical results. It is found that compressibility alone acts a destabilizing role for fluids with fixed density profile.