Alternative analytical solution of linear Richtmyer-Meshkov-like flows for corrugated shocks driven by a rigid piston.

Abstract

An analytical model to study the perturbation flow that evolves between a rippled piston and a shock is presented, based on previous published work. Only the rigid piston boundary condition is considered at the piston surface driving the shock. 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 finite and closed form analytical formulas to calculate the different perturbed quantities in the compressed fluid, namely, shock pressure perturbations and compressed fluid velocity perturbations for very large times, in contrast to previous work in which only an iterated solution was presented. Comparison to published experiments is shown.