The impact of compressibility in Richtmyer–Meshkov instability

The Richtmyer–Meshkov (RM) instability occurs in various natural and laboratory scenarios, with extensive studies conducted on this phenomenon. This work focuses on exploring the impact of compressibility on RM instability beyond the linear theory. We employ a perturbative expansion method with respect to the initial perturbative degree of the interface, to solve the evolution of compressible RM instability up to the second order. The second-order compressible solutions are applicable during the early stages of the instability, and then they are integrated with incompressible nonlinear results using two types of Padé approximations to extend the valid range of computational results. The translation velocities of the interface, along with the growth rates of the spike and bubble, are derived from multiple approaches: the perturbative compressible solutions, the nonlinear theory combined with linear results, two forms of Padé approximations, and numerical simulations. These results are plotted and compared. The comparison reveals that compressibility beyond the linear regime has a significant influence on the translation velocity and introduces certain corrections to the growth rates of the spike and bubble.