Turbulence Generation by Shock Interaction with a Highly Non-Uniform Medium

An initially planar shock wave propagating into a medium of non-uniform density will be perturbed, leading to the generation of post-shock velocity perturbations. Using numerical simulations we study this phenomenon in the case of highly-non-uniform density (order-unity normalized variance, $\sigma_{\rho}/\overline{\rho} \sim 1$) and strong shocks (shock Mach numbers $\overline{M}_s \gtrsim 10$). This leads to a highly disrupted shock and a turbulent post-shock flow. We simulate this interaction for a range of shock drives and initial density configurations meant to mimic those which might be presently achieved in experiments. Theoretical considerations lead to scaling relations, which are found to reasonably predict the post-shock turbulence properties. The turbulent velocity dispersion and turbulent Mach number are found to depend on the pre-shock density dispersion and shock speed in a manner consistent with the linear Richtymer-Meshkov instability prediction. We also show a dependence of the turbulence generation on the scale of density perturbations. The post-shock pressure and density, which can be substantially reduced relative to the unperturbed case, are found to be reasonably predicted by a simplified analysis that treats the extended shock transition region as a single normal shock.
Comment: 15 pages, 10 figures