Interaction of free rossby wave with semi-transparent equatorial waveguide

Abstract

We study non-linear interactions between the waves trapped in equatorial waveguide and the barotropic Rossby waves freely propagating across the waveguide. The model of two-layer shallow water on the equatorial beta-plane is used. We consider the interaction of one barotropic Rossby wave with two equatorial modes, and with one equatorial mode in the presence of zonal equatorial current. It is found in both cases that the free barotropic Rossby wave resonantly excites the baroclinic equatorial Rossby or Yanai waves with amplitudes much exceeding its own amplitude. The baroclinic wave envelopes obey Ginzburg-Landau type equations and exhibit non-linear saturation and formation of characteristic “domain wall” and “dark soliton” defects. In turn, self-interaction of the “trapped” part of flow results in a non-linear scattering of the free wave on the waveguide. Thus, this mechanism provides both generation of large-amplitude equatorial waves and back reaction of the equatorial region on the mid-latitudes.