Estimation of shock induced vorticity on irregular gaseous interfaces: a wavelet-based approach

We study the interaction of a shock with a density-stratified gaseous interface (Richtmyer–Meshkov instability) with localized jagged and irregular perturbations, with the aim of developing an analytical model of the vorticity deposition on the interface immediately after the passage of the shock. The jagged perturbations, meant to simulate machining errors on the surface of a laser fusion target, are characterized using Haar wavelets. Numerical solutions of the Euler equations show that the vortex sheet deposited on the jagged interface rolls into multiple mushroom-shaped dipolar structures which begin to merge before the interface evolves into a bubble-spike structure. The peaks in the distribution of x-integrated vorticity (vorticity integrated in the direction of the shock motion) decay in time as their bases widen, corresponding to the growth and merger of the mushrooms. However, these peaks were not seen to move significantly along the interface at early times i.e. t < 10 τ, where τ is the interface traversal time of the shock. We tested our analytical model against inviscid simulations for two test cases – a Mach 1.5 shock interacting with an interface with a density ratio of 3 and a Mach 10 shock interacting with a density ratio of 10. We find that this model captures the early time (t/τ ∼ 1) vorticity deposition (as characterized by the first and second moments of vorticity distributions) to within 5% of the numerical results. PACS 47.40.Nm; 47.20.Ma