  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.
