# Kelvin-helmholtz instability

From AMS Glossary

## 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 where

*U*_{2}and density ρ_{2}, and the underlying fluid has velocity*U*_{1}and density ρ_{1}, disturbances of the form*e*^{ikx}(where*k*is the wavenumber) are unstable if*g*is the acceleration of gravity. Thus, the flow is always unstable to short waves (high wavenumber) if*U*_{1}≠*U*_{2}.Drazin, P. G., and W. H. Reid 1981. Hydrodynamic Stability. Cambridge University Press, . 14–22.