# Baroclinic and barotropic aspects of the wind-driven ocean circulation

### Citation:

Ghil, M, Y Feliks, and L. U. Sushama. “Baroclinic and barotropic aspects of the wind-driven ocean circulation.” Physica D: Nonlinear Phenomena 167, no. 1 (2002): 1–35.
 PDF 569 KB

### Abstract:

The double-gyre circulation induced by a symmetric wind-stress pattern in a quasi-geostrophic model of the mid-latitude ocean is studied analytically and numerically. The model is discretized vertically by projection onto normal modes of the mean stratification. Within its horizontally rectangular domain, the numerical model captures the wind-driven circulation’s three dynamic regimes: (1) a basin-scale double-gyre circulation, cyclonic in the basin’s northern part and anticyclonic in the south, which is dominated by Sverdrup balance; (2) a swift western boundary current in either gyre, with dissipation most important near the coast and inertial balance further out; and (3) a strong recirculating dipole near the intersection of the western boundary with the symmetry line of zero wind-stress curl. The flow inside this stationary dipole is highly nonlinear, and equivalent-barotropic. An analytical solution to the potential vorticity equation with variable stratification describes the dipole, and fits well the full numerical model’s steady-state solutions. Changes in the numerical model’s solutions are investigated systematically as a function of changes in the strength of the wind stress $\tau$ and the Rossby radius of deformation LR. The main changes occur in the recirculation region, while the basin-scale gyres and the western boundary currents are affected but little. A unique symmetric dipole is observed for small $\tau$, and agrees in its properties with the analytical solution. As $\tau$ increases, multiple asymmetric equilibria arise due to pitchfork bifurcation and are stable for large enough LR. The numerically obtained asymmetric equilibria also agree in their main properties with the analytical ones, as well as with the corresponding solutions of a shallow-water model. Increasing $\tau$ further results in two successive Hopf bifurcations, that lead to limit cycles with periods near 10 and 1 years, respectively. Both oscillatory instabilities have a strong baroclinic component. Above a certain threshold in $\tau$ the solutions become chaotic. Flow pattern evolution in this chaotic regime resembles qualitatively the circulation found in the Gulf Stream and Kuroshio current systems after their separation from the continent.

Last updated on 07/26/2016