Kelvin-helmholtz instability

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 e^ikx (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 U₁ ≠ U₂.

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

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