Shear flow instability at a fluid interface — vortex roll-up from velocity discontinuity
The Kelvin-Helmholtz instability occurs at the interface between two fluids with different velocities. A small perturbation at the interface grows exponentially at rate σ = k·ΔU/2 (for equal densities), rolling up into characteristic vortex billows. The instability is suppressed by gravity (Richardson number Ri = N²/S²) and surface tension. KH billows are visible at cloud boundaries, in Jupiter's atmosphere, and at the Earth's magnetopause.