The effect of initial conditions on the nonlinear evolution of perturbed interfaces driven by strong blast waves

Abstract

In core-collapse supernovae, strong blast waves drive interfaces susceptible to Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) instabilities. In addition, perturbation growth can result from material expansion in large-scale velocity gradients behind the shock front. Laser-driven experiments are designed to produce a strongly shocked interface whose evolution is a scaled version of the unstable hydrogen-helium interface in core-collapse supernovae such as SN 1987A. The ultimate goal of this research is to develop an understanding of the effect of hydrodynamic instabilities and the resulting transition to turbulence on supernovae observables that remain as yet unexplained. In this dissertation, we present a computational study of unstable systems driven by high Mach number shock and blast waves. Using multi-physics radiation hydrodynamics codes and theoretical models, we consider the late nonlinear instability evolution of single mode, few mode, and multimode interfaces. We rely primarily on 2D calculations but present recent 3D results as well. For planar multimode systems, we show that compressibility effects preclude the emergence of a regime of self-similar instability growth independent of the initial conditions (IC's) by allowing for memory of the initial conditions to be retained in the mix-width at all times. The loss of transverse spectral information is demonstrated, however, along with the existence of a quasi-self-similar regime over short time intervals. Aspects of the IC's are shown to have a strong effect on the time to transition to the quasi-self-similar regime. With higher-dimensional blast waves, divergence restores the properties necessary for establishment of the self-similar state, but achieving it requires very high initial characteristic mode number and high Mach number for the incident blast wave. We point to recent stellar calculations that predict IC's we find incompatible with self-similarity, and emphasize the consequent importance of developing a sound understanding of the initial modal structure in the supernova progenitor. For divergent and planar systems, the time-dependence of the drive is shown to impose an "effective box size" on the systems that limits the inverse cascade to large-scales. Our model explains the weak IC-dependence of this scale observed in some supernova calculations.