Analysis of second-moments and their budgets for Richtmyer-Meshkov instability and variable-density turbulence induced by re-shock

Abstract

The nonlinear Richtmyer-Meshkov instability and mixing transition induced by a Mach 1.45 shock and subsequent re-shock at an interface between two ideal gases (sulphur hexafluoride and air) with high Atwood number are studied with second-moment analysis using data from highresolution compressible Navier-Stokes simulations. The analysis first addresses the importance of second-order moments: turbulent mass flux and density-specific-volume covariance, together with their transport equations. These quantities play an essential role on the development of Favreaveraged Reynolds stress and turbulent kinetic energy in this variable-density flow. Then, grid sensitivities and the time evolution of the second-moment quantities are investigated, followed by a detailed study of the transport equations of the second-moments using fully resolved data before re-shock. After re-shock, budgets of large-scale second-moments, which have insignificant influence from numerical regularization, are studied with the effects of subfilter-scale stress accounted. The effects of subfilter-scale stress on the budgets of large-scale second-moments with different levels of filtering are also examined.