Nonlinear interaction of two non-uniform vortex sheets and large vorticity amplification in Richtmyer–Meshkov instability

Abstract

Vortex dynamics is an important research subject for geophysics, astrophysics, engineering, and plasma physics. Regarding vortex interactions, only limited problems, such as point vortex interactions, have been studied. Here, the nonlinear interaction of two non-uniform vortex sheets with density stratification is investigated using the vortex sheet model. These non-uniform vortex sheets appear, for example, in the Richtmyer–Meshkov instability that occurs when a shock wave crosses a layer with two corrugated interfaces. When a strong vortex sheet approaches a weaker vortex sheet with opposite-signed vorticity, a locally peaked secondary vorticity is induced on the latter sheet. This emerging secondary vorticity results in a remarkable vorticity amplification on the stronger sheet, and a strong vortex core is formed involving the weak vortex sheet. The amplified vortices with opposite signs on the two vortex sheets form pseudo-vortex pairs, which cause an intense rolling-up of the two sheets. We also investigated the dependence of distance and initial phase difference of vorticity perturbations between two vortex sheets on the vorticity amplification and vortex sheet dynamics.