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 γ approaches ∞. For finite γ (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.