Analytical asymptotic velocities in linear Richtmyer-Meshkov-like flows.

An analytical model to study the perturbation flow that evolves between a rippled piston and a shock is presented. Two boundary conditions are considered: rigid and free surface. Any time a corrugated shock is launched inside a fluid, pressure, velocity, density, and vorticity perturbations are generated downstream. As the shock separates, the pressure field decays in time and a quiescent velocity field emerges in the space in front of the piston. Depending on the boundary conditions imposed at the driving piston, either tangential or normal velocity perturbations evolve asymptotically on its surface. The goal of this work is to present explicit analytical formulas to calculate the asymptotic velocities at the piston. This is done in the important physical limits of weak and strong shocks. An approximate formula for any shock strength is also discussed for both boundary conditions.