equatorial Poincare wave

By analogy with a Poincare wave in a channel, an inertio-gravity wave confined to a region about the equator. The meridional velocity of the nth mode of these waves has meridional structure of the form

in which y is the meridional distance from the equator, R is the equatorial Rossby radius of deformation, and H_n is the nth Hermite polynomial. In the shallow water approximation

in which β is the meridional gradient of the Coriolis parameter at the equator, g is the acceleration of gravity, and H is the mean fluid depth.