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Alan Domaracki and Arthur Z. Lossch

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.

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Arthur Z. Loesch and Alan Domaracki

Abstract

Dynamics of N ≥ 5 resonantly interacting baroclinic waves, one of which is marginally unstable and the remaining N − 1 are neutral, are investigated in a quasi-geostrophic inviscid two-layer model. Numerical solutions of equations governing the long time evolution of the wave amplitudes predominantly yield a separation between instability and interactions in period and characteristics of amplitude oscillations. The instability is felt on a longer time scale and via the marginal wave. For certain choices of initial conditions and/or neutral waves the separation breaks down in favor of one of the following. (i) resonant-like behavior of all amplitudes, (ii) a multi-time scale evolution of the amplitudes, or (iii) a very long-period, complex finestructure evolution of the individual amplitudes. The strongest energy exchange between the wave field and the mean field occurs whenever the separation takes place.

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