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equatorial rossby wave

An equatorially trapped westward propagating wave that moves due to isentropic gradients of potential vorticity. The meridional velocity of the n'th mode of these waves has the form exp(-y2/2R2) H_n(y/R), in which y is the meridional distance from the equator, R is the equatorial rossby deformation radius, and H_n is the n'th Hermite polynomial. In the shallow water approximation R2=(gH)(1/2)/eta in which, eta is the meridional gradient of the Coriolis parameter at the equator, g is the acceleration of gravity, and H is the mean fluid depth. The dispersion relation for the n'th mode (n>0) with zonal wavenumber k is given by those roots of the equation, cubic in the frequency omega, ((gH)(1/2)/eta) - k2 + omega2/(gH) =2n+1 for which the frequency is less than Reta.

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