Long-time simulations of the Kelvin-Helmholtz instability using an adaptive vortex method

Abstract

The nonlinear evolution of an interface subject to a parallel shear flow is studied by the vortex sheet model. We perform long-time computations for the vortex sheet in density-stratified fluids by using the point vortex method and investigate late-time dynamics of the Kelvin-Helmholtz instability. We apply an adaptive point insertion procedure and a high-order shock-capturing scheme to the vortex method to handle the nonuniform distribution of point vortices and enhance the resolution. Our adaptive vortex method successfully simulates chaotically distorted interfaces of the Kelvin-Helmholtz instability with fine resolutions. The numerical results show that the Kelvin-Helmholtz instability evolves a secondary instability at a late time, distorting the internal rollup, and eventually develops to a disordered structure.