Effects of Initial Condition Spectral Content on Shock Driven Turbulent Mixing

Abstract: The mixing of materials due to the Richtmyer-Meshkov instability and the ensuing turbulent behavior is of intense interest in a variety of physical systems including inertial confinement fusion, combustion, and the final stages of stellar evolution. Extensive numerical and laboratory studies of shock-driven mixing have demonstrated the rich behavior associated with the onset of turbulence due to the shocks. Here we report on progress in understanding shock-driven mixing at interfaces between fluids of differing densities through 3D numerical simulations using the RAGE code in the implicit large eddy simulation context. We consider a shock tube configuration with a band of high density gas (SF$_6$) embedded in low density gas (air). Shocks with a Mach number of 1.26 are passed through SF$_6$ bands, resulting in transition to turbulence driven by the Richtmyer-Meshkov instability. The system is followed as a rarefaction wave and a reflected secondary shock from the back wall pass through the SF$_6$ band. We apply a variety of initial perturbations to the interfaces between the two fluids in which the physical standard deviation, wave number range, and the spectral slope of the perturbations are held constant, but the number of modes initially present is varied. By thus decreasing the density of initial spectral modes of the interface, we find that we can achieve as much as 25\% less total mixing at late times. This has potential direct implications for the treatment of initial conditions applied to material interfaces in both 3D and reduced dimensionality simulation models.