A discrete vortex simulation of finite amplitude KelvinHelmholtz instability
Abstract
The discrete vortex method previously used by Rosenhead and others to compute the rollup 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.
 Publication:

2nd Computational Fluid Dynamics Conference
 Pub Date:
 1975
 Bibcode:
 1975cfd..conf..205Z
 Keywords:

 Computerized Simulation;
 Finite Difference Theory;
 Inviscid Flow;
 KelvinHelmholtz Instability;
 Vortex Sheets;
 Buoyancy;
 Flow Stability;
 Gravitational Effects;
 Interfacial Tension;
 Perturbation Theory;
 Vortices;
 Fluid Mechanics and Heat Transfer