Kelvin-helmholtz instability

From Glossary of Meteorology

Kelvin–Helmholtz instability

An instability of the basic flow of an incompressible inviscid fluid in two parallel infinite streams of different velocities and densities.

If the overlying fluid has velocity U2 and density ρ2, and the underlying fluid has velocity U1 and density ρ1, disturbances of the form eikx (where k is the wavenumber) are unstable if
where g is the acceleration of gravity. Thus, the flow is always unstable to short waves (high wavenumber) if U1U2.

Drazin, P. G., and W. H. Reid 1981. Hydrodynamic Stability. Cambridge University Press, . 14–22.