KelvinHelmholtz

Kelvin-Helmholtz instability (KHI) is a fluid dynamical instability that arises at the interface between two fluids or two stratified layers that move with different velocities. Small perturbations at the shear layer can grow and roll up into vortex structures, producing characteristic billow-like waves along the interface.

In the simplest two-fluid, incompressible model, the instability develops when shear across the interface overcomes stabilizing influences such as gravity and surface tension. The growth rate depends on factors including the wavenumber of the perturbation, the density contrast between the fluids, and the velocity difference. Gravity tends to stabilize configurations where a heavier fluid sits below a lighter one, while surface tension damps short-wavelength perturbations; different regimes determine which wavelengths grow fastest.

KHI is observed in a variety of contexts. In the Earth's atmosphere, it creates billow clouds along strong jet streams. In the oceans, it appears at density interfaces to generate internal waves and mixing. In astrophysics, KH-like vortices arise at the boundaries of relativistic jets, accretion disks, and the interfaces of galaxy clusters, where magnetic fields can modify or suppress the instability through magnetic tension.

History and naming reflect its founders: the instability is named for Lord Kelvin (William Thomson) and Hermann von Helmholtz, who studied shear layers and vortex dynamics in the 19th century. Kelvin-Helmholtz instability remains a fundamental mechanism for mixing and momentum transport across interfaces, explored through linear stability analysis, nonlinear simulations, and laboratory experiments.