A discrete vortex simulation of finite amplitude Kelvin-Helmholtz instability

The discrete vortex method previously used by Rosenhead and others to compute the roll-up of a vortex sheet in a single fluid is extended to the situation in which the vortex sheet is a horizontal interface separating a lighter inviscid fluid above from a heavier fluid below. The stabilizing effects of gravity and surface tension are included in a discretized circulation equation used to calculate the circulations of individual vortices during the course of the computation. Calculations show the evolution of the interface under stable, unstable and marginally unstable conditions as given by Kelvin's classical theory. Under stable conditions, finite amplitude disturbances oscillate with a period slightly larger than predicted by classical theory for infinitesimal perturbations. For unstable conditions, the finite amplitude growth rate is much smaller than the corresponding linearized growth rate for infinitesimal disturbances. Under marginally unstable conditions, the generation of drops from small irregularities along the interface is suggested by the computations.