Two classes of Richtmyer-Meshkov instabilities: A detailed statistical look

Abstract

A single parameter numerical study of the evolution of the multimode planar Richtmyer-Meshkov instability (RMI) in a shocked/reshocked (air-SF6, Atwood number A = 0.67) configuration with a Mach number Ma = 1.5 shock is carried out. Our results demonstrate that the initial material interface morphology (for fixed Ma, A) controls the RMI evolution characteristics. Our discussion focuses on the light-to-heavy configuration with initial A > 0 and heavy-to-light reshock. Depending on the rms slope of the initial interface, ηo, there are two different instabilities: one with the classical RMI trends and another with trends suggesting a very different fluid physics which we study in detail. We use statistical metrics to demonstrate that the two different regimes are characterized by very different and self-consistent fluid physics. The response of the rate of mixing layer growth to increasing ηo is different and opposite in sign in each regime: in the high-ηo class of initial conditions, increasing ηo leads to a decrease in kinetic energy and mixing layer growth rate; and in the low-ηo class of flows, increasing ηo leads to an increase in kinetic energy and growth rate. The low ηo case corresponds to impulsive acceleration of an almost-flat thin interface, the classical small-perturbation RMI. The high-ηo regime corresponds to: (a) impulsive acceleration of a very rough initial interface, and (b) shock passage through a turbulent material interface. We additionally observe that this bipolar behavior of the turbulent field is not seen in the statistics of the material mixing field and this may invalidate closures that slave the mixing field to the turbulence. It appears that simple Reynolds-Averaged Navier-Stokes moment closure models cannot currently predict both classes of RMI. We offer speculations on the similarity of instabilities and the possibility of using high-ηo first-shocked simulations to study reshock problems. Our article describes these two instabilities as a function of ηo for fixed A and Ma; we do not propose that ηo offers a complete parameterization of the general problem.