Equatorial Waves - Equatorial Rossby and Rossby-gravity Waves

Equatorial Rossby and Rossby-gravity Waves

Rossby-gravity waves, first observed in the stratosphere by M. Yanai, always carry energy eastward. But, oddly, their 'crests' and 'troughs' may propagate westward if their periods are long enough. The eastward speed of propagation of these waves can be derived for an inviscid slowly moving layer of fluid of uniform depth H. Because the Coriolis parameter (ƒ = 2Ω sin(θ) where Ω is the angular velocity of the earth, 7.2921 10−5 rad/s, and θ is latitude) vanishes at 0 degrees latitude (equator), the “equatorial beta plane” approximation must be made. This approximation states that “f” is approximately equal to βy, where “y” is the distance from the equator and "β" is the variation of the coriolis parameter with latitude, . With the inclusion of this approximation, the governing equations become (neglecting friction):

• the continuity equation (accounting for the effects of horizontal convergence and divergence and written with geopotential height):

• the U-momentum equation (zonal wind component):

• the V-momentum equation (meridional wind component):

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These three equations can be separated and solved using solutions in the form of zonally-propagating waves, which are analogous to exponential solutions with a dependence on x and t and the inclusion of structure functions that vary in the y-direction:

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Once the frequency relation is formulated in terms of ω, the angular frequency, the problem can be solved with 3 distinct solutions. These three solutions correspond to the equatorial gravity waves, the equatorially trapped Rossby waves and the mixed Rossby-gravity wave (which has some of the characteristics of the former two). Equatorial gravity waves can be either westward- or eastward-propagating.