Investigation of the interface stretching within a reshocked mixing zone produced by the Richtmyer Meshkov Instability

The spatio-temporal evolution of a bi-dimensional (2D) and three-dimensional (3D) air/SF6 mixing layer issued from the development of a Richtmyer-Meshkov instability (RMI) under reshock is investigated using direct numerical simulations (DNS) at moderate Mach number (M=1.2) and high Atwood number (A=0.67). This study discusses the relevance of an original criterion based on the measurement of the gaseous interface stretching in the analysis of the mixing process. The first part of the work provides an estimation of the validity of a 2D approach in time for the retained simulation cases. To this avail, a 2D simulation for one typical parameter set is compared to its 3D counterpart. As a means of comparing the development of the mixing layer in both simulations, the classical criterion relying on the evaluation of the mixing layer thickness has been chosen. This criterion is commonly used to characterize baroclinic instability as it is intuitive and easy to compute and to analyze. However, this criterion only provides the mixing zone frontiers but does not provide information about the length scale content and its evolution on the interface. In order to tackle this issue, it is proposed to adapt a still documented criterion for the determination of the interface stretching, based on the computation of the temporal evolution of the mixing interface length for the study of various cases involving different initial interface perturbations, with reshock consideration.