# Shear-gravity wave

From Glossary of Meteorology

## shear–gravity wave

A combination of gravity waves and a Helmholtz wave on a surface of discontinuity of density and velocity.

If the densities of the lower and upper layers respectively are ρ and ρ′ and the velocities where

*U*and*U*′, the phase speed*c*of the shear–gravity wave is*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.