Kelvin–Helmholtz Vortex Roll-up

Shear layer instability via point vortex sheet discretization

A shear layer between fluids of different velocities is unstable to Kelvin–Helmholtz modes. Discretizing the vortex sheet as N point vortices, each with circulation Γ = U·L/N, and integrating the Biot–Savart law gives the non-linear roll-up. Small perturbations grow exponentially at rate σ = k·U/2 (linear theory), then saturate into characteristic cat's-eye vortex structures.