Nonlinear Tropical Air–Sea Interaction in the Fast-Wave Limit

Abstract

The fast-wave limit is an approximation useful for understanding many aspects of tropical air?sea interaction. It is obtained when the time scale of dynamical adjustment of the ocean by equatorial waves occurs fast compared to the time scale on which the system is evolving through coupled processes. The linear and nonlinear behavior of a simple coupled model is examined for the Pacific basin. It consists of an SST equation for an equatorial band, shallow-water ocean dynamics in the fast-wave limit governing the thermocline, and an embedded surface layer for equatorial Ekman pumping; it may be characterized as a simple fast-wave limit version of the Neelin model, which is in turn a stripped-down version of the Zebiak and Cane model. It offers a converse approximation to simple models that retain wave dynamics while eliminating SST time scales. This simple model produces a rich variety of flow regimes. The first bifurcation can give westward-propagating, stationary, or eastward-propagating variability according to the relative strength of the surface-layer and thermocline processes and the atmospheric damping length. These parameter dependences can be largely explained by reference to the simpler zonally periodic case, but the finite basin and zonally varying basic state introduce east basin trapping. These weakly nonlinear regimes offer a simple analog of oscillations in a number of other models. Some of the oscillations show thermocline evolution that could be easily mistaken for wave-dependent behavior in other models. Over a substantial region of parameter space, two SST modes?one stationary and one westward-propagating?have comparable growth rate in the linear problem. This introduces mode interaction in the nonlinear problem. Relaxation oscillations at strong nonlinearity prove to be a very robust feature of the model, showing strong parallels to behavior noted in a hybrid coupled general circulation model.