Growth of a Richtmyer-Meshkov turbulent layer after reshock

Abstract

This paper presents a numerical study of a reshocked turbulent mixing layer using high-order accurate Implicit Large-Eddy-Simulations (ILES). Existing theoretical approaches are discussed, and the theory of Youngs (detailed in Ref. 1) is extended to predict the behaviour of a reshocked mixing layer formed initially from a shock interacting with a broadband instability. The theory of Mikaelian2 is also extended to account for molecular mixing in the single-shocked layer prior to reshock. Simulations are conducted for broadband and narrowband initial perturbations and results for the growth rate of the reshocked layer and the decay rate of turbulent kinetic energy show excellent agreement with the extended theoretical approach. Reshock causes a marginal decrease in mixing parameters for the narrowband layer, but a significant increase for the broadband initial perturbation. The layer properties are observed to be very similar post-reshock, however, the growth rate exponent for the mixing layer width is higher in the broadband case, indicating that the reshocked layer still has a dependence (although weakened) on the initial conditions. These results have important implications for Unsteady Reynolds Averaged Navier Stokes modelling of such instabilities.