Linear and nonlinear interactions between an interface and bulk vortices in Richtmyer–Meshkov instability

Abstract

When a planar shock hits a corrugated interface between two fluids, the Richtmyer–Meshkov instability (RMI) occurs. Vortices are generated in bulk behind the transmitted and reflected shocks in RMI. As the shock intensity becomes larger, the stronger bulk vortices are created. The nonlinear evolution of RMI is investigated within the vortex sheet model (VSM), taking the nonlinear interaction between the interface and the vortices into account. The fluid becomes incompressible as the shocks move away from the interface, and VSM can then be applied. The vorticity and position of the bulk vortices obtained from the compressible linear theory [F. Cobos-Campos and J. G. Wouchuk, Phys. Rev. E93, 053111 (2016)] are applied as initial conditions of the bulk point vortices in VSM. The suppression of RMI due to the bulk vortices is observed in the region such that the corrugation amplitude is less than one-tenth of the wavelength, and the reduction of the growth is quantitatively evaluated and compared with the compressible linear theory. In the nonlinear stage, the interaction between the interface and the bulk vortices strongly affects the interfacial shape and the dynamics of bulk vortices, e.g., the creation of a vortex pair is observed. Strong bulk vortices behind the transmitted shock enhance the growth of spike, supplying flow from spike root to its top and mushroom umbrella in the fully nonlinear stage.