On the role of rarefaction/compression waves in Richtmyer-Meshkov instability with reshock

Abstract

Richtmyer-Meshkov instability (RMI) with reshock is characterized with the interaction between the mixing zone (MZ) and multiple waves, of which the process has not been fully understood so far. A direct numerical simulation of RMI with reshock, in which the shock initially propagates from a light fluid to a heavy one, is carried out. After the reshock, the MZ is accelerated by rarefaction and compression waves alternatively with decaying strength, during which the mixing zone is accelerated as a whole system and a mean-velocity gradient is evident in the MZ. Although the velocity field is quite complex during rarefaction/compression waves, the scaled profiles of mean volume fraction are not essentially different from those before the first rarefaction wave. A budget analysis reveals that the production of turbulent kinetic energy by the pressure and velocity gradient dominates during the first rarefaction and compression waves. The sign of the pressure-gradient production is opposite to that of the velocity-gradient production, with the amplitude of the former one being larger than that of the latter one. Rarefaction waves contribute to the turbulent motions while compression waves consume turbulence energy. The increment of MZ width is accompanied with formation of large-scale structures. These structures are stretched after the reshock, during the rarefaction waves, and compressed during the compression waves.