Scaling laws of nonlinear Rayleigh-Taylor and Richtmyer-Meshkov instabilities in two and three dimensions

The late-time nonlinear evolution of the Rayleigh-Taylor (RT) and Richtmyer -Meshkov (RM) instabilities for random initial perturbations is investigate d using a statistical mechanics model based on single-mode and bubble-compe tition physics at all Atwood numbers (A) and full numerical simulations in two and three dimensions. It is shown that the RT mixing zone bubble and sp ike fronts evolve as h similar to alpha .A.gt(2) with different values of a for the bubble and spike fronts. The RM mixing zone fronts evolve as h sim ilar to t(theta) with different values of theta for bubbles and spikes. Sim ilar analysis yields a linear growth with time of the Kelvin-Helmholtz mixi ng zone. The dependence of the RT and RM scaling parameters on A and the di mensionality will be discussed. The 3D predictions are found to be in good agreement with recent Linear Electric Motor (LEM) experiments. (C) 2000 Aca demie des sciences/Editions scientifiques et medicales Elsevier SAS.