Unstable normal mode for Rayleigh–Taylor instability in viscous fluids

Abstract

The character of the growth rates of the normal modes for Rayleigh–Taylor instability of superposed incompressible, viscous fluids is analyzed in terms of appropriately scaled dimensionless parameters and a particularly simple representation of the Rayleigh–Taylor dispersion relation. The chief feature that emerges is that the scaled growth rate is remarkably insensitive to the values of fluid densities and viscosities. To within a few percent, the physical growth rate depends only on the surface tension, the density-weighted average viscosity, and the effective acceleration. Approximate formulae for the most unstable wavenumber and the corresponding maximum growth rate are given.