Low-Frequency Variability in Shallow-Water Models of the Wind-Driven Ocean Circulation. Part I: Steady-State Solution*

Abstract

Successive bifurcations—from steady states through periodic to aperiodic solutions—are studied in a shallowwater, reduced-gravity, 2‰-layer model of the midlatitude ocean circulation subject to time-independent wind stress. The bifurcation sequence is studied in detail for a rectangular basin with an idealized spatial pattern of wind stress. The aperiodic behavior is studied also in a North Atlantic‐shaped basin with realistic continental contours. The bifurcation sequence in the rectangular basin is studied in Part I, the present article. It follows essentially the one reported for single-layer quasigeostrophic and 1‰-layer shallow-water models. As the intensity of the north‐ south-symmetric, zonal wind stress is increased, the nearly symmetric double-gyre circulation is destabilized through a perturbed pitchfork bifurcation. The low-stress steady solution, with its nearly equal subtropical and subpolar gyres, is replaced by an approximately mirror-symmetric pair of stable equilibria. The two solution branches so obtained are named after the inertial recirculation cell that is stronger, subtropical or subpolar, respectively. This perturbed pitchfork bifurcation and the associated Hopf bifurcations are robust to changes in the interface friction between the two active layers and the thickness H2 of the lower active layer. They persist in the presence of asymmetries in the wind stress and of changes in the model’s spatial resolution and finitedifference scheme. Time-dependent model behavior in the rectangular basin, as well as in the more realistic, North Atlantic‐shaped one, is studied in Part II.