Vortex model and simulations for Rayleigh-Taylor and Richtmyer-Meshkov instabilities.

The vortex method is applied to simulations of Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities. The numerical results from the vortex method agree well with analytic solutions and other numerical results. The bubble velocity in the RT instability converges to a constant limit, and in the RM instability, the bubble and spike have decaying growth rates, except for the spike of infinite density ratio.

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

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.