A Study of Self-excited Oscillations of the Tropical Ocean–Atmosphere System. Part II: Nonlinear Cases

We analyze the linearized version of an analytical model, which combines linear ocean dynamics with a simple version of the Bjerknes hypothesis for El Nino. The ocean is represented by linear shallow water equations on an equatorial beta-plane. It is driven by zonal wind stress, which is assumed to have a fixed spatial form. Stress amplitude is set to be proportional to the thermocline displacement at the eastern boundary. It is shown that, for physically plausible parameter values, the model system can sustain growing Oscillations. Both growth rate and period scale directly with the time that an oceanic Kelvin wave needs to crow the basin. They are quite sensitive to the coupling parameter between thermocline displacement and wind stress, and the zonal location and meridional width of the wind. The most important parameter determining this behavior of the system is the coupling constant. For strong coupling the system exhibits exponential growth without oscillation. As the coupling is decreased ...