Analysis of Second-Moment Budgets and Closure Models for Richtmyer-Meshkov Instability

An analysis of second moment budgets for variable density mixing induced by the interaction between a Mach 1.45 shock and subsequent re-shock with the interface between two ideal gases at high Atwood number (sulphur hexafluoride and air) is performed using high-resolution compressible Navier-Stokes simulations. The analysis first addresses the importance of the additional transport equations of second moment quantities: turbulent mass flux and density-specific-volume covariance for the closure of Reynolds-averaged Navier–Stokes (RANS) equations in this type of flow compared to single-species flows that only require Reynolds stress equations. Then, a short survey of RANS closures for Richtmyer-Meshkov instability is presented, together with an analysis of the requirements for capturing this type of flow. The analysis is further applied to the BHR-3 RANS model by [Schwarzkopf et al., 2011] and its extension with two separate length scales (decay and transport length scales) by [Schwarzkopf et al., 2016].