Simulations and model of the nonlinear Richtmyer-Meshkov instability

The nonlinear evolution of the Richtmyer-Meshkov (RM) instability is investigated using numerical simulations with the FLASH code in two dimensions. The purpose of the simulations is to develop an empirical nonlinear model of the RM instability that is applicable to inertial confinement fusion (ICF) and ejecta formation, namely, at large Atwood number A and scaled initial amplitude kh(o) (k equivalent to wave number) of the perturbation. The FLASH code is first validated with a variety of RM experiments that evolve well into the nonlinear regime. They reveal that bubbles stagnate when they grow by an increment of 2/k and that spikes accelerate for A>0.5 due to higher harmonics that focus them. These results are then compared with a variety of nonlinear models that are based on potential flow. We find that the models agree with simulations for moderate values of A < 0.9 and kh(o)< 1, but not for the larger values that characterize ICF and ejecta formation. We thus develop a new nonlinear empirical model that captures the simulation results consistent with potential flow for a broader range of A and kh(o). Our hope is that such empirical models concisely capture the RM simulations and inspire more rigorous solutions.