Numerical Simulations of Vortex Sheet Evolution in Stratified Shear Flow

Abstract

The nonlinear evolution of an interface subject to a parallel shear flow is studied on the basis of the vortex sheet model. We perform numerical simulations of the vortex sheet in density stratified fluids by using the point vortex method. The numerical algorithm based on two types of regularization method improves the stability of the vortex method and provides solutions with much higher resolutions than previous results. The numerical results show that, for a smaller density ratio, the interface has a larger growth rate and a more singular vortex sheet strength and curvature at late times. It is also found that, for an infinite density ratio, the interface has a solution of a travelling wave with no deformations.