From Glossary of Meteorology
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(Also called planetary wave.) A wave on a uniform current in a two-dimensional nondivergent fluid system, rotating with varying angular speed about the local vertical (beta plane).
This is a special case of a barotropic disturbance, conserving absolute vorticity. Applied to atmospheric flow, it takes into account the variability of the Coriolis parameter while assuming the motion to be two-dimensional. The wave speed c is given by
See long wave.
is the mean westerly flow, β is the Rossby parameter, and K2 = k2 + l2, the total wavenumber squared. (This formula is known as the Rossby formula, long-wave formula, or planetary-wave formula.) A stationary Rossby wave is thus of the order of the distance between the large-scale semipermanent troughs and ridges in the middle troposphere. The Rossby wave moves westward relative to the current, in effect slowing the eastward movement of long-wave components relative to the short-wave components in a barotropic flow. This effect is important in a numerical forecast with a barotropic model, but attempts to apply the formula to actual contour patterns considered as waves have less dynamic justification and correspondingly less success.
See long wave.
Holton, J. R. 1992. An Introduction to Dynamic Meteorology. 3d edition, Academic Press, . 216–222.
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