Density dependence of a Zufiria-type model for Rayleigh–Taylor bubble fronts

Abstract

We present the analytic model for the evolution of bubbles of arbitrary density ratio in Rayleigh-Taylor and Richtmyer-Meshkov instabilities. The model is the generalization of Zufiria's potential theory, which is based on the velocity potential with a point source and previously applied only for the interface of infinite density ratio. The analytic expressions for asymptotic solutions of bubbles are obtained. The predictions from the Zufiria model agree well with the numerical results not only for the bubble velocity, but also for the bubble curvature. It is found that the asymptotic curvature of a Richtmyer-Meshkov bubble is smaller than that of a Rayleigh-Taylor bubble for all Atwood numbers.