Nonlinear evolution of multimode Rayleigh–Taylor instability in two and three dimensions

Abstract

The nonlinear evolution of the Rayleigh–Taylor instability from multimode initial perturbations is studied by two complementary approaches. First, a statistical-mechanics bubble-merger model is presented, that enables determination of the late-time scaling properties based on single-mode and two-bubble interaction physics. The results for Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) bubble and spike front penetrations are given, as well as scaling laws for mixing under a time-dependent driving acceleration. The second approach is a modal model, in which nonlinear mode coupling and saturation are included in an equation for effective modes that describe the mixed region. The importance of mode coupling in the generation of large structure that dominates the late stage evolution, and the relative importance of long-wavelength components in the initial perturbation spectra on the late-stage evolution are studied. Finally, multimode RT instability in three dimensions is studied by both full-scale simulations and the modal model. The effect and late-stage memory loss of different aspect ratios in the initial perturbation are demonstrated.