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

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 current 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 produces the barotropic response which, via nonlinear interaction with the mean equatorial current and with the trapped waves, leads to the saturation of the growing modes. The excited baroclinic waves can reach significant amplitudes depending on the magnitude of the mean current. In the absence 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 latter 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 equation, 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 nonlinear Schrodinger equation well studied in the literature.