Shear-gravity wave

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shear–gravity wave

If the densities of the lower and upper layers respectively are ρ and ρ′ and the velocities U and U′, the phase speed c of the shear–gravity wave is
where g is the acceleration of gravity and L the wavelength. The motion is unstable if and only if the bracketed quantity is negative; the density difference thus contributes to stability and the velocity difference to instability. Applications have been made to atmospheric frontal surfaces and inversions; perhaps the most successful of these is to the phenomenon of billow clouds. Reasonable atmospheric values for the parameters yield stationary wavelengths of the order of 1 km.

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