# Difference between revisions of "Rossby wave"

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− | <div class="definition"><div class="short_definition">( | + | <div class="definition"><div class="short_definition">(''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]]).</div><br/> <div class="paragraph">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 <div class="display-formula"><blockquote>[[File:ams2001glos-Re49.gif|link=|center|ams2001glos-Re49]]</blockquote></div> where <div class="inline-formula">[[File:ams2001glos-Rex15.gif|link=|ams2001glos-Rex15]]</div> is the mean westerly flow, β is the [[Rossby parameter]], and ''K''<sup>2</sup> = ''k''<sup>2</sup> + ''l''<sup>2</sup>, 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. <br/>''See'' [[long wave]].</div><br/> </div><div class="reference">Holton, J. R. 1992. An Introduction to Dynamic Meteorology. 3d edition, Academic Press, . 216–222. </div><br/> |

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## Revision as of 15:02, 20 February 2012

## 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.