Scale invariant mixing rates of hydrodynamically unstable interfaces

Abstract

The late time evolution and structure of 2D Rayleigh-Taylor and Richtmyer-Meshkov bubble fronts is calculated, using a new statistical merger model based on the potential flow equations. The merger model dynamics are shown to reach a scale invariant reigme. It is found that the Rayleigh-Taylor front reaches a constant acceleration, growing as 0.05${\mathit{gt}}^{2}$, while the Richtmyer-Meshkov front grows as ${\mathit{at}}^{0.4}$ where a depends on the initial perturbation. The model results are in good agreement with experiments and simulations.