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Nonlinear interactions of the barotropic Rossby waves propagating across the equator with trapped baroclinic Rossby or Yanai modes and mean zonal flow are studied within the two-layer model of the atmosphere, or the ocean. It is shown that the equatorial waveguide with a mean cur- rent acts as a resonator and responds to barotropic waves with certain wavenumbers by making the trapped baroclinic modes grow. At the same time the equatorial waveguide pro- duces the barotropic response which, via nonlinear interac- tion with the mean equatorial current and with the trapped waves, leads to the saturation of the growing modes. The ex- cited baroclinic waves can reach significant amplitudes de- pending on the magnitude of the mean current. In the ab- sence of spatial modulation the nonlinear saturation of thus excited waves is described by forced Landau-type equation with one or two attracting equilibrium solutions. In the lat- ter case the spatial modulation of the baroclinic waves is expected to lead to the formation of characteristic domain- wall defects. The evolution of the envelopes of the trapped Rossby waves is governed by driven Ginzburg-Landau equa- tion, while the envelopes of the Yanai waves obey the "first- order" forced Ginzburg-Landau equation. The envelopes of short baroclinic Rossby waves obey the damped-driven non- linear Schrodinger equation well studied in the literature. and a pair of trapped modes in the framework of the simplest two-layer equatorial beta-plane model with a rigid lid. Let us remind that free modes in the model are barotropic Rossby waves, while all baroclinic modes (Kelvin, Inertia-Gravity, Rossby and Yanai ones) are trapped. We showed in Part 1 that although in the linear approximation the barotropic Rossby wave does not "feel" the equator and propagates freely across the equatorial waveguide, this wave resonantly excites the waveguide Rossby or Yanai modes if nonlinear effects are taken into account. The amplitudes of the excited modes first grow exponentially in time, and then stabilize at the level greatly exceeding the amplitude of the incoming free wave. The envelope of the trapped waves obeys the so- called resonantly excited Ginzburg-Landau (GL) equation, or a pair of coupled GL-equations, which describes the forma- tion of specific spatio-temporal patterns. In turn, nonlinear interactions of the waveguide modes engender a secondary barotropic wave which propagates out of equator toward the poles, grows in time and becomes comparable with the pri- mary free wave.

The interaction of free Rossby waves with semi-transparent equatorial waveguide – wave-mean flow interaction