Scaling behavior of density gradient accelerated mixing rate in shock bubble interaction

Abstract

Variable-density mixing in shock bubble interaction, a canonical flow of so-called RichtermyerMeshkov instability, is studied by the high-resolution simulation. While the dissipation mainly controls the passive scalar mixing rate, an objective definition of variable-density mixing rate characterizing the macroscopic mixing formation is still lacking, and the fundamental behavior of mixing rate evolution is not yet well understood. Here, we first show that the variable-density mixing of shock bubble interaction is distinctly different from the previous observations in the passive scalar mixing. The widely-accepted hyperbolic conservation of the first moment of concentration in the scalar mixing, i.e., the conservation of the mean concentration, is violated in shock bubble interaction. We further combine the compositional transport equation and the divergence relation for the miscible flows to provide the evidence that the existence of density gradient accelerated mixing rate, decomposed by the accelerated dissipation term and redistributed diffusion term, contributes to the anomalous decrease of the mean concentration of species. Further analyzing a number of simulations for a broad range of shock Mach numbers, Reynolds numbers, and Peclet numbers, the density gradient accelerated mixing rate exhibits nearly independent of the dimensionless numbers, which paves a new way to understand the variable-density effect on the connection between global and local mixing behavior.