Interaction of free Rossby waves with semi-transparent equatorial waveguide. Part 1. Wave triads

We study nonlinear interactions between the baroclinic Rossby and/or Yanai waves trapped in the equatorial waveguide and the barotropic Rossby waves freely propagating across the equator. We demonstrate that, depending on its parameters, a barotropic wave can resonantly excite a single, or a pair of exponentially growing baroclinic waves with frequencies lower than its proper one. It is shown that nonlinear saturation of the amplitudes of the baroclinic waves takes place at a level much greater than the amplitude of the barotropic wave. The envelopes of the baroclinic waves obey modulation equations of Ginzburg–Landau type. Formation of characteristic “domain wall” and “dark soliton” patterns in the envelopes of the baroclinic waves is displayed. The growing trapped waves also generate a barotropic response modifying the primary barotropic wave.