Birkhoff–Rott equation discretizes a vortex sheet into N point vortices. The tangential velocity discontinuity drives the Kelvin-Helmholtz instability, rolling the sheet into spiral vortices.
The Birkhoff–Rott equation: dz̄/dt = (Γ/4πi)∮ cot(π(z−ζ)/L) dΓ(ζ). Regularized with δ-smoothing (δ≈0.2) to avoid Moore's curvature singularity. The roll-up time scales as t ~ (L/Γ)^(1/2).