Rayleigh-Taylor Instability in a Compressible Fluid

TL;DR

This paper analyzes how compressibility affects Rayleigh-Taylor instability in fluids with pressure-dependent density, finding that compressibility generally reduces the instability growth rate under certain conditions.

Contribution

It provides a theoretical calculation of compressibility corrections to the Rayleigh-Taylor growth rate in compressible fluids with equal sound speeds.

Findings

Compressibility reduces the growth rate of Rayleigh-Taylor instability.

The correction is calculated to order O(g^2/k^2a^4).

Effects are significant under specific fluid conditions.

Abstract

Rayleigh-Taylor instability in a compressible fluid is reconsidered. The density is allowed to vary with pressure under the barotropy assumption. For the case with equal speeds of sound in the two superposed fluids, in order to give a non-trivial compressibility correction to the Rayleigh-Taylor growth rate, the compressibility correction is calculated to $O(g^2/k^2a^4)$. To this order, compressibility effects are found to reduce the growth rate.