Mixing transition in a shocked variable-density flow

Abstract

We measure two-dimensional velocity and density fluctuations in a shock-driven heavy gas curtain for three different incident Mach numbers (M = 1.21, 1.36, and 1.50) and a fixed initial perturbation. We study the time evolution of the velocity and density fields and observe two different mixing transitions in this unsteady flow. The first transition is caused by small-scale mixing in vortex cores, while the second transition is related to increased homogenization across the mixing layer and a drive towards isotropy. By measuring the anisotropy of the velocity fluctuations and the evolution of the turbulent kinetic energy, we are able to assess the anisotropy of the flow. For the first time in Richtmyer-Meshkov (RM) flows, we measure and compare turbulent length scales derived from both the density and velocity field measurements, and we find ratios of Liepmann-Taylor to inner-viscous scales (λL/λν) that are inconsistent with those found using Reynolds number scaling based on circulation, ReΓ, or based on turbulent kinetic energy, ReK. At late times, ReK better reflects the decay of the mixing field than Reynolds numbers that are based upon mixing width or circulation. We also estimate the time evolution of dissipation and Kolmogorov scales for the first time in RM flows. When we estimate the Taylor microscale (λT) for our experiments using both density and velocity, the density microscale agrees well with the relationship λT=10δRe−1/2 where Re = ReK and δ is the mixing layer width, but the velocity-based Taylor microscale follows a new scaling of λT = 10δRe−1/2.