Simple potential-flow model of Rayleigh-Taylor and Richtmyer-Meshkov instabilities for all density ratios

Abstract

We generalize the Layzer-type model for unstable interfaces to the system of arbitrary density ratio. The predictions from the generalized model for bubble growth rates of Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities are in good agreement with numerical results. We present the theoretical prediction for asymptotic growth rates for RT and RM bubbles for finite density ratios in two and three dimensions.