Nonlinear Interactions Among Equatorial Waves

Abstract

The asymptotic method multiple scales is used to investigate nonlinear interactions among equatorial waves (Kelvin, mixed Rossby-gravity, Rossby, eastward and westward propagating inertial-gravity) using a divergent equatorial beta-plane model. The Hermite polynomial meridional structure of equatorial waves results in a relaxation of the kinematic resonance conditions in the present model as compared to similar investigations in a mid-latitude context. Numerical solutions of the resonance conditions establish that triads composed of the same as well as different wave types exist. Energy solutions obtained in the absence of spatial and phase modulations show that the triad members having maximum absolute frequency always grows (decays) at the expense of the remaining triad members. It is suggested that a single finite-amplitude equatorial wave may be unstable with respect to lower frequency ?parasitic? resonant wave perturbations. In the tropical atmosphere, nonlinear wave instability may he an important energy redistribution mechanism where naturally occurring forcing mechanisms excite selected wave types over a restricted range of wavenumbers.