Testing an analytic model for Richtmyer-Meshkov turbulent mixing widths

We discuss a model for the evolution of the turbulent mixing width after a shock or a reshock passes through the interface between two fluids of densities and inducing a velocity jump . In this model, the initial growth rate is independent of the surface finish or initial mixing width , but its duration is directly proportional to it: for , and for . Here is the Atwood number and are dimensionless, -dependent parameters measured in past Rayleigh-Taylor experiments, and is a new dimensionless parameter we introduce via . The mixing width and its derivative remain continuous at since and . We evaluate at from air/SF experiments and propose that the transition at signals isotropication of turbulence. We apply this model to the recent experiments of Jacobs et al. (Shock Waves 23:407-413, 2013) on shock and reshock, and discuss briefly the third wave causing an unstable acceleration of the interface. We also consider the experiments of Weber et al. (Phys Fluids 24:074105, 2012) and argue that their smaller growth rates reflect density gradient stabilization.