Nonlinear growth of Kelvin–Helmholtz instability: Effect of surface tension and density ratio

Abstract

The nonlinear evolution of initially small disturbances at an interface separating two fluids of different density and velocity, including surface tension effects, is investigated with the use of the vortex-sheet discretization approach. The location of the interface is tracked in time by following the motion of each vortex under the combined influence of all other vortices. The influence of surface tension and density discontinuity is incorporated in an equation governing the evolution of the circulation of each vortex. Increasing the surface tension or the density ratio is shown to reduce the growth of the disturbance. For density ratios larger than 0.2 a critical wavenumber exists that divides the unstable part of the spectrum into a region where a vorticity singularity can develop (with interface rollup) and a region where two finite vortical centers are formed (with partial or no rollup). For lower density ratios this bifurcation phenomenon is not observed.