The dynamics of an equivalent-barotropic model of the wind-driven circulation

Abstract

Various steady and time-dependent regimes of a quasi-geostrophic 1.5 layer model of an oceanic circulation driven by a steady wind stress are studied. After being discretized as a numerical model, the quasi-geostrophic equations of motion become a dynamical system with a large dimensional phase space. We find that, for a wide range of parameters, the large-time asymptotic regimes of the model correspond to low-dimensional attractors in this phase space. Motion on these attractors is significant in determining the intrinsic time scales of the system. In two sets of experiments, we explore the dependence of solutions on the viscosity coefficient and the deformation radius. Both experiments yielded a succession of solutions with different forms of time dependence including chaotic solutions. The transition to chaos in this model occurs through a modified classical Ruelle-Takens scenario. We computed some unstable steady regimes of the circulation and the associated fastest growing linear eigenmodes. The structure of the eigenmodes and the details of the energy conversion terms allow us to characterize the primary instability of the steady circulation. It is a complex instability of the western boundary intensification, the western gyre and the meander between the western and central gyres. The model exhibits ranges of parameters in which multiple, stable, time-dependent solutions exist. Further, we note that some bifurcations involve the appearance of variability at climatological time scales, purely as a result of the intrinsic dynamics of the wind-driven circulation.