Kelvin-Helmholtz Instability

Vortex sheet rollup at a shear interface. Perturbations grow exponentially with rate σ = k|ΔU|/2, then roll into billows.

σ = k|ΔU|/2 · √(1-(kδ)²)

KH instability occurs wherever two fluid layers move at different speeds. Seen in clouds, ocean stratification, Jupiter's bands, and solar wind–magnetosphere boundary. At high density contrast, stabilized by gravity (Richardson number Ri > 1/4).