General Analysis of the Stability of Superposed Fluids

Abstract

An analysis is made of the stability of the interface between two compressible fluids in a gravity field when the fluids have translational velocities parallel to the interface. The effects of viscosity and surface tension are not included. The general dispersion relation is found to involve Whittaker functions and their first derivatives. Appropriate limits for these functions correspond to various physical conditions. The familiar Rayleigh-Taylor and Kelvin-Helmholtz criterions for stability are obtained in the incompressible limit. It is found that compressibility in the subsonic case decreases the range of stability. In the supersonic case, the stability found by Landau holds for only one disturbance mode. In general, stratification leads to instability of the interface for the supersonic case. A simple physical discussion of the Kelvin-Helmholtz stability problem for incompressible or compressible flow concludes the paper.