  Variable-density mixing in shock bubble interaction, a canonical flow of
Richtermyer-Meshkov 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 variable-density flows. 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 or increase of the mean
concentration depending on Atwood number. Further analyzing a number of
simulations for the cylindrical or spherical bubbles under a broad range of
shock Mach numbers, Reynolds numbers, and Peclet numbers, the density gradient
accelerated mixing rate exhibits weak dependent on Peclet numbers, and
identifies an Atwood number range with high mixing rate, which can be
theoretically predicted based on the mode of hyperbolic conservation violation
behavior.
