MULTIPLE EQUILIBRIA, PERIODIC, AND APERIODIC SOLUTIONS IN A WIND-DRIVEN, DOUBLE-GYRE, SHALLOW-WATER MODEL

A reduced-gravity shallow-water (SW) model is used to study the nonlin ear behavior of western boundary currents (WBCs), with particular emph asis on multiple equilibria and low-frequency variations. When the mer idionally symmetric wind stress is sufficiently strong, two steady sol utions-nearly antisymmetric about the x axis-are achieved from differe nt initial states. These results imply that 1) the inertial WBCs could overshoot either southward or northward along the western boundary, d epending on their initial states; and thus, 2) the WBC separation and eastward jet could occur either north or south of the maximum wind str ess line. The two equilibria arise via a perturbed pitchfork bifurcati on, as the wind stress increases. A low-order, double-gyre, quasigeost rophic (QG) model is studied analytically to provide further insight i nto the physical nature of this bifurcation. In this model, the basic state is exactly antisymmetric when the wind stress is symmetric. The perturbations destroying the symmetry of the pitchfork bifurcation can arise, therefore, in the QG model only from the asymmetric components of the wind stress. In the SW model, the antisymmetry of the system's basic response to the symmetric forcing is destroyed already at arbit rarily low wind stress. The pitchfork bifurcation from this basic stat e to more complex states at high wind stress is accordingly perturbed in the absence of any forcing asymmetry. Periodic solutions arise by H opf bifurcation from either steady-state branch of the SW model. A pur ely periodic solution is studied in detail. The subtropical and subpol ar recirculations, separation, and eastward jet exhibit a perfectly pe riodic oscillation with a period of about 2.8 years. Outside the recir culation zones, the solutions are nearly steady. The alternating anoma lies of the upper-layer thickness are periodically generated adjacent to the ridge of the first and strongest downstream meander and are the n propagated and advected into the two WBC zones, by Rossby waves and the recirculating currents, respectively. These anomalies periodically change the pressure gradient field near the WBCs and maintain the per iodic oscillation. Aperiodic solutions are also studied by either incr easing wind forcing or decreasing the viscosity.