## Rossby wave

(

*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 where is the mean westerly flow, β is the Rossby parameter, and

*K*^{2}=*k*^{2}+*l*^{2}, 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.

Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact permissions@ametsoc.org. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.