Vortex dynamics of a twice-accelerated interface in an incompressible ideal fluid

We report on a direct numerical simulation (DNS) of the evolution of a two-dimensional sinusoidal density-stratified interface subjected to two sequential impulsive accelerations. The concepts and phenomena are immediately applicable to the "reshock" problem of the Richtmyer-Meshkov (RM) environment. The computational parameters and geometry are chosen such as to model the experimental results of the incompressible RM instability of Jacobs and Niederhaus performed with an impulsively reaccelerated free-falling tank. Our DNS results are in very good agreement with the experiment after the first impulse and in qualitative agreement with the short time evolution after the second impulse. We explain the phenomena, including the rate of growth of the interface, in terms of the evolving vortex layers and projected rate-of-strain tensor onto the interfacial vortex layer. In particular, the presence of nearby oppositely signed layers of vorticity after the second impulse contributes to the rapid turbulization of the region. The numerical method applied is based on the Contour Advection Semi-Lagrangian algorithm modified with the vortex-in-cell method for density interfaces in incompressible ideal fluids.