Responses of the equatorial ocean to a Rossby wave packet, which assumes the form of either a cyclonic or an anticyclonic vortex pair, are simulated with the spectral element shallow water equation model (reduced gravity). We found that during the course of the western boundary reflection of an incoming equatorial Rossby wave packet, strong wave-wave interaction has significant influence on local dynamic and kinetic structures in the western tropical ocean. In the case of the western boundary reflection of a cyclonic Rossby wave vortex pair, the nonlinear effect tends to induce a strong, long-lasting eastward equatorial current; while in the case of the western boundary reflection of an anticyclonic Rossby wave vortex pair, the nonlinear effect significantly weakens movements in the western equatorial region, but greatly enhances the extra-equatorial western boundary currents. Moreover, an extra amount of the energy carried by long waves is permanently lost to short waves due to the strong wave-wave interaction in the western boundary region; therefore, strong nonlinearity has further reduced the effectiveness of the western boundary in reflecting the long Rossby wave signals. The total energy loss through the horizontal eddy viscosity can also be reduced by the strong nonlinear effect. The numerical results show that the phase speeds of the nonlinear equatorial Rossby wave and the nonlinear equatorial Kelvin wave are different from those of the linear waves: the nonlinear waves are faster if the initial Rossby wave packet is an anticyclonic vortex pair which is related to the thermocline deepening, and slower if it is a cyclonic vortex pair which is related to the thermocline shoaling. The simulation with a low Reynolds number shows that high horizontal eddy viscosity can severely suppress the nonlinear activities. The simulation results in the western boundary region with Re = 200 are largely explainable by the linear equatorial wave theory.
Ma, Hong. 1992. "The equatorial basin response to a Rossby wave packet: The effects of nonlinear mechanism." Journal of Marine Research 50, (4). https://elischolar.library.yale.edu/journal_of_marine_research/2047