11 - Wave interactions in the equatorial atmosphere – an analytical Study

Summary

The effect of zonal motion on wave interactions is considered in an equatorial atmosphere. Extending the formulation of Matsuno (1966), Duffy (1974), and Domaracki and Loesch (1977), perturbations are imposed on a zonal current which varies slowly with time. Considering the conditions for resonance between wave triads, coupling coefficients are computed between the zonal motion and the equatorial waves. It is shown that these coupling coefficients do not involve an energy exchange between the zonal current and the perturbed motion, but that the zonal current does lead to phase changes in the complex amplitude of resonant waves. A stability analysis is made to indicate how the zonal current could alter the growth of interacting waves.

Introduction

When the governing equations of a system are nonlinear, one of the analytical methods for obtaining the solution is the perturbation technique. In such a situation the system is reduced to a non-dimensional form by referring different physical variables to characteristic scales. The dependent variables are expanded asymptotically in terms of small parameters which occur in a natural way depending on the physics of the problem. It is assumed that each term of the perturbation series is smaller in magnitude than its preceding term throughout the region of interest. If this condition breaks down in any part of the region, the asymptotic expansion is no longer valid. An important reason why perturbation solutions are often not uniformly valid is concerned with the ‘large integrated effect’.