Effect of compressibility on the Rayleigh--Taylor instability

Eigenfrequencies are calculated for infinitesimal perturbations of the system consisting of two semi-infinite regions, each filled with a constant-temperature ideal polytrope stratified exponentially against gravity. The linear growth rate for the Rayleigh--Taylor instability which occurs when the density above the interface exceeds that below it is shown in the model to vary linearly with wavenumber k as k→0. The incompressible fluid result is obtained when the adiabatic index #betta# approaches infinity. For finite #betta# (i.e., compressible fluids), the growth rates are in general larger than in the incompressible case. Numerical results and limiting cases are described which illustrate this conclusion