Large-eddy simulations of the multi-mode Richtmyer–Meshkov instability and turbulent mixing under reshock

Abstract

The multi-mode Richtmyer–Meshkov instability under reshock and the induced turbulent mixing are numerically investigated by using our parallel large-eddy simulation code MVFT (multi-viscous-flow and turbulence), in which the third-order Godonov scheme is used based on the finite volume method. The one-dimensional wave diagram of wave-interface interaction is presented. The turbulent mixing zone (TMZ) width is in good agreement with experiments. The TMZ width grows in time as a power law before reshock and an exponential law after reshock. The time scaling laws of statistics show the evolution of TMZ has a statistics similarity behavior. The turbulent kinetic energy and dissipation rate, whether they are the resolved-scales or subgrid-scales, all decay with time as a power law before reshock and an exponential law after reshock, so does the enstrophy. The modal analysis shows that the evolution of TMZ is still dominated by the initial perturbation modes during a long time after the first shock. The kinetic energy and enstrophy spectra are amplified extremely by the reshock. After reshock, the energy spectrum moves toward the low wave numbers, which illustrates that larger and larger spatial structures develop in the TMZ. It is also shown that the global spectra exhibit a k−3 scaling law after the reshock and a k−3.5 scaling law at the very late times in three-dimension.