Nonlinear Perturbation Theory of the Incompressible Richtmyer-Meshkov Instability

A single-mode nonlinear high-order perturbation theory is developed to describe the Richtmyer-Meshkov instability of an impulsively accelerated interface between an incompressible fluid and a constant supporting pressure. The nonlinear modification of Richtmyer's formula is presented and compared to experimental data with strong radiatively driven shocks. The theory allows a straightforward extension to more general cases of Richtmyer-Meshkov and Rayleigh-Taylor instabilities (multimode, more interfaces, three-dimensional flow, etc.).