The effect of varying stratification on low frequency equatorial motions.

A formalism is developed to examine the effect of zonally varying stratification on equatorial wave phenomena; an effect present in the real ocean but neglected from standard linear theory. The approach utilized involves the application of a matching condition to equatorial waves incident on a single zonal discontinuity in the density field of a shallow water system. Transmission and reflection coefficients are sought for the projection of an incoming wave on to the entire set of resultant vertical and horizontal wave modes of a general continuously stratified fluid. The limiting case of a meridional density front is extended, in a manner analogous to radiative transfer problems, to a series of discrete density intervals. These techniques are applied to specific choices of stratification ranging from a zonal jump discontinuity in the density field to density changes with zonal scales large with respect to the waves in question, i.e., a WKB limit. The results demonstrate that zonally varying stratification does not produce substantial changes in the energy flux of propagating equatorial waves. However, as a result of changes to the equatorial radius of deformation, the amplification of equatorial zonal velocity can be appreciable. A corresponding decrease in pressure, albeit smaller, may also be non negligible.