Vortex simulations of the Kelvin-Helmholtz instability with surface tension in density-stratified flows

In this paper, we study long-time evolutions of the Kelvin-Helmholtz instability with surface tension and density jump by using the vortex sheet model. Applying a spectrally accurate numerical method, we investigate effects of surface tension and density jump on the instability in various regimes of parameters. The numerical results show that by varying the density ratio, the large-scale feature of the roll-up of the interface is basically similar, but the structure of the inner roll-up is significantly different. At high Weber numbers, the interface collides with itself at the finger tip for low Atwood numbers, but for high Atwood numbers, the finger is pinched off. The dispersive waves and corrugations on the interface are more prominent for low Atwood numbers. For a very high Weber number, the finger of the interface becomes small, while for a low Weber number, the interface has a structure of long filament. Results for initial multi-mode perturbations show the competition and merging of fingers as well as pinching and elongation.