Effects of surface tension and viscosity on the growth rates of Rayleigh-Taylor and Richtmyer-Meshkov instabilities

We present an analytical model for unstable interfaces with surface tension in fluids of arbitrary viscosity. Linear and nonlinear asymptotic solutions are obtained for growth rates of Rayleigh-Taylor and Richtmyer-Meshkov instabilities. In Rayleigh-Taylor instability, both surface tension and viscosity decrease the asymptotic bubble velocity. For Richtmyer-Meshkov instability, the analysis of the model suggests a dependence of the decaying rate of the bubble velocity on the relative importance of viscosity and surface tension. Results of numerical simulations are also given, and comparisons of the solutions of the model with numerical results are in good agreement.