Successive bifurcations in a shallow-water model applied to the wind-driven ocean circulation

Abstract

Climate-the “coarse-gridded” state of the coupled ocean-atmosphere system - varies on many time and space scales. The challenge is to relate such variations to specific mechanisms and to produce verifiable quantitative explanations. In this paper, we study the oceanic component of the climate system and, in particular, the different circulation regimes of the mid-latitude wind- driven ocean on the interannual time scale. These circulations are dominated by two counterrotating, basin- scale gyres: subtropical and subpolar. Numerical techniques of bifurcation theory are used to study the multiplicity and stability of the steady-state solutions of a wind-driven, double-gyre, reduced-gravity, shallow- water model. Branches of stationary solutions and their linear stability are calculated systematically as parameters are varied. This is one of the first geophysical studies in which such techniques are applied to a dynamical system with tens of thousands of degrees of freedom. Multiple stationary solutions obtain as a result of nonlinear interactions between the two main recirculating cells (cyclonic and anticyclonic) of the large-scale double-gyre flow. These equilibria appear for realistic values of the forcing and dissipation parameters. They undergo Hopf bifurcation and transition to aperiodic solutions eventually occurs. The periodic and chaotic behavior is probably related to an increased number of vorticity cells interacting with each other. A preliminary comparison with observations of the Gulf Stream and Kuroshio Extensions suggests that the internal variability of our simulated mid-latitude ocean is an important factor in the observed interannual variability of these two current systems. © European Geophysical Society 1995.