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

Successive bifurcations — from steady states through periodic to aperiodic solutions — are studied in a shallow-water, reduced-gravity, 2.5-layer model of the mid-latitude 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 quasi-geostrophic and 1.5layer shallow-water models. As the intensity of the North-South symmetric wind stress is increased, the nearly symmetric double-gyre circulation is destabilized through a perturbed pitchfork bifurcation. The near-antisymmetry of the low-stress steady solution, with its nearly equal subtropical and subpolar gyres, is replaced by an approximately mirror-symmetric pair of stable equilibria. On the upper branch, the subtropical gyre is stronger while on the lower one the subpolar gyre dominates. This perturbed pitchfork bifurcation is robust to changes in the interface friction between the two active layers and the thickness H2 of the lower active layer. It persists in the presence of asymmetries in the wind stress and of changes in the model’s spatial resolution and finite-difference 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.