ON THE ATTRACTORS OF AN INTERMEDIATE COUPLED OCEAN-ATMOSPHERE MODEL

Techniques of numerical bifurcation theory are used to study stationar y and periodic solutions of an intermediate coupled model for tropical ocean-atmosphere interaction. The qualitative dynamical behavior is d etermined for a volume in parameter space spanned by the atmospheric d amping length, the coupling parameter, the surface layer feedback stre ngth and the relative adjustment time coefficient. Time integration me thods have previously shown much interesting dynamics, including multi ple steady states, eastward- or westward-propagating orbits and relaxa tion oscillations. The present study shows how this dynamics arises in parameter space through the interaction of the different branches of equilibrium solutions and the singularities on these branches. For exa mple, we show that westward-propagating periodic orbits arise through an interaction of two unstable stationary modes and that relaxation os cillations occur through a limit cycle-saddle node interaction. There are several dynamical regimes in the coupled model which are determine d by the primary bifurcation structure; this structure depends strongl y on the parameters in the model. Although much of the dynamics may be studied in the fast-wave limit, it is shown that ocean wave dynamics introduces additional oscillatory instabilities and how these relate t o propagating oscillations.