Global Bifurcation of Shilnikov Type in a Double-Gyre Ocean Model

Abstract

The dynamics of an idealized wind-driven double-gyre circulation in an ocean basin are studied from a dynamical systems point of view in an effort to better understand its variability. While previous analyses of this circulation have mostly dealt with local bifurcations of steady states and limit cycles, this study demonstrates the importance of considering global bifurcations as well. In one case, a coherent picture of the global dynamics spanning a range of parameters from where there are only stable steady-state solutions to where there is chaotic eddy shedding is presented. A simple but novel use of power spectra along with dynamical projections of the dynamics suggests that just beyond the regime in which there are only stable steady states, the system exhibits a complicated global bifurcation known as the ?Shilnikov phenomenon.?