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 Richtermyer-Meshkov instability, is studied by high-resolution simulation. While scalar mixing is mainly controlled by dissipation, 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 show that the widely-accepted hyperbolic conservation of first moment of concentration in scalar mixing is violated in variable density mixing. We combine the compositional advection diffusion equation and divergence relation for miscible flows to provide evidence that the existence of density gradient accelerated dissipation and redistributed diffusion contributes to the anomalous decrease of mean concentration of species. Analyzing a number of simulations for a broad range of shock Mach number and Reynolds number, density gradient accelerated mixing rate exhibits, in the regime of Pelect number concerned, nearly independent of Pelect number, which paves a new way to understand variable density effect on the connection between global and local mixing behavior.