Nonlinearly coupled KdV equations describing the interaction of equatorial and midlatitude Rossby waves

Abstract

Amplitude equations governing the nonlinear resonant interaction of equatorial baroclinic and barotropic Rossby waves were derived by Majda and Biello and used as a model for long range interactions (teleconnections) between the tropical and midlatitude troposphere. An overview of that derivation is presented and geared to readers versed in nonlinear wave theory, but not in atmospheric sciences. In the course of the derivation, two other sets of asymptotic equations are presented: the long equatorial wave equations and the weakly nonlinear, long equatorial wave equations. A linear transformation recasts the amplitude equations as nonlinear and linearly coupled KdV equations governing the amplitude of two types of modes, each of which consists of a coupled tropical/midlatitude flow. In the limit of Rossby waves with equal dispersion, the transformed amplitude equations become two KdV equations coupled only through nonlinear fluxes. Four numerical integrations are presented which show (i) the interaction of two solitons, one from either mode, (ii) and (iii) the interaction of a soliton in the presence of different mean wind shears, and (iv) the interaction of two solitons mediated by the presence of a mean wind shear.

Keywords

Coupled KdV equations / Equatorial Rossby waves / Solitary waves / Atmospheric teleconnections

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