Multiple-scale analysis on the radiation within the coupled KdV equations

TL;DR

This paper develops a multiple scale model for coupled KdV equations to analyze equatorial wave interactions, accurately predicting radiation phenomena and elucidating underlying mechanisms, with strong agreement between theory and numerical simulations.

Contribution

It introduces a novel multiple scale analytical framework for coupled KdV equations that quantitatively explains radiation and wave interactions beyond previous qualitative models.

Findings

Predicted precursor radiation is centrosymmetric.

Excellent quantitative agreement with numerical simulations.

Elucidates mechanisms of solitary wave interaction and radiation formation.

Abstract

A multiple scale model of the nonlinearly coupled KdV equations is established to predict mechanism of interaction of equatorial Rossby waves and barotropic waves in certain case. Analytically, predicted precursor radiation is a centrosymmetric object and is shown in excellent quantitative agreement with numerical simulations; furthermore, the multiple scale model elucidates the salient mechanisms of the interaction of solitary waves and the mechanism for radiation. While the atmosphere-ocean science community is very interested in theoretical studies of tropical wave interactions and in developing reduced dynamical models that can explain some key features of equatorial phenomena, our analytic predictions quantitively explain formation of radiation during interaction in Biello's model beyond qualitative level.