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2008•arXiv (Cornell University)Open access

Rayleigh-Taylor Instability in a Compressible Fluid

Bhimsen K. Shivamoggi

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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.

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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.

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Available 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.

Key concepts: Rayleigh–Taylor instability, Compressibility, Instability, Compressible flow, Rayleigh scattering, Richtmyer–Meshkov instability, Mechanics, Physics

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