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We analyze the linearized version of an analytical model, which combines linear ocean dynamics with a simple version of the Bjerknes hypothesis for El Niño. 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 the growth rate decreases until a transition value is reached. For smaller values of the coupling the growing modes of the system oscillate, with a period which is infinite at the transition value and decreases for decreasing coupling. The inviscid system has growing modes for any positive feedback, no mater how weak, though the growth rate rapidly becomes very small. For very weak coupling the period approaches the first resonance period of the free ocean. The model can also be expressed as a nondifferential delay equation, The components of dfis equation are easy to interpret physically and allow some insights into the nature of the oscillations. The relation of our results to other recent work and its implications for El Niño and the Southern Oscillation are discussed.
Cane et al. (Sun,) studied this question.