We study numerically the simplest model of two incompressible, immiscible fluids shearing
past one another. The fluids are two-dimensional, inviscid, irrotational, density matched, and
separated by a sharp interface under a surface tension. The nonlinear growth and evolution
of this interface is governed by only the competing effects of the Kelvin–Helmholtz instability
and the dispersion due to surface tension. We have developed new and highly accurate
numerical methods designed to treat the difficulties associated with the presence of surface …