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

Abstract

We study the behavior of an iterative map as a model for El Niño and the Southern Oscillation (ENSO). This map is derived from a model that combines linear equatorial beta-plane ocean dynamics with a version of the Bjerknes hypothesis for ENSO. It differs from the linear model of Cane et al. only in that the coupling from ocean to atmosphere is idealized as a nonlinear relation τ(he) between a wind stress τ of fixed spatial form and he, the thermocline displacement at the eastern end of the equator. The model sustains finite amplitude periodic and aperiodic oscillations. A period doubling bifurcation leads from a period of less than 2 years to the 3–4 year one observed in nature. Other principal results are: the resulting period depends on the curvature of the function away from the unstable equilibrium at he = 0, and not solely on its linear instability; at least two Rossby modes must be included in the model for aperiodic oscillations to appear; no stochastic term is needed for this aperiodicit... Abstract We study the behavior of an iterative map as a model for El Niño and the Southern Oscillation (ENSO). This map is derived from a model that combines linear equatorial beta-plane ocean dynamics with a version of the Bjerknes hypothesis for ENSO. It differs from the linear model of Cane et al. only in that the coupling from ocean to atmosphere is idealized as a nonlinear relation τ(he) between a wind stress τ of fixed spatial form and he, the thermocline displacement at the eastern end of the equator. The model sustains finite amplitude periodic and aperiodic oscillations. A period doubling bifurcation leads from a period of less than 2 years to the 3–4 year one observed in nature. Other principal results are: the resulting period depends on the curvature of the function away from the unstable equilibrium at he = 0, and not solely on its linear instability; at least two Rossby modes must be included in the model for aperiodic oscillations to appear; no stochastic term is needed for this aperiodicit...