Wind-driven Circulation and Eddies

Wind-driven gyre and Ekman dynamics

A wind-driven gyre is the large, nearly closed circulation of an ocean basin that the surface wind stress sets up. Wind stress is the frictional drag of the wind on the sea surface, and it enters the upper ocean as momentum. In the Ekman layer this momentum is balanced by the Coriolis force and by vertical friction, which is represented by the eddy (turbulent) viscosity A_z, so the vertical shear of the horizontal velocity carries momentum downward. The depth scale of this layer is \delta = \sqrt{A_z/|f|}, where f = 2\Omega\sin\phi is the Coriolis parameter. For example, with A_z = 0.004 m^2 s^{-1} and |f| = 10^{-4} s^{-1}, the depth is about 6.3 m, which shows that the wind-driven layer is shallow.

The net transport in the Ekman layer, integrated over depth, is M = \tau/(\rho f) per unit width. It points 90° to the right of the wind in the Northern Hemisphere and 90° to the left in the Southern Hemisphere. A westerly wind in the Northern Hemisphere therefore produces net transport directed toward the south. For instance, a wind stress of 0.2 N m^{-2} at 45°N with \rho = 1025 kg m^{-3} gives f \approx 1.03\times10^{-4} s^{-1} and M \approx 1.9 m^2 s^{-1}.

With increasing depth, the current in the Ekman spiral turns progressively to the right in the Northern Hemisphere and its speed decreases. The surface current is deflected about 45° to the right of the wind. The spiral is maintained by a balance of Coriolis force, the vertical shear of the horizontal velocity, and frictional force. The balance of Coriolis force and pressure gradient describes geostrophic flow above the Ekman layer, not the spiral itself.

Western boundary currents such as the Gulf Stream and the Kuroshio are narrow and intense. Their westward intensification arises from the latitudinal variation of the Coriolis parameter, the beta effect, which is a consequence of the rotation of the earth. Wind forcing drives the gyre as a whole, but the east–west asymmetry is set by rotation. Ekman pumping controls the large-scale vertical motion but does not by itself produce the intensified western flow, while river discharge and bottom topography do not control basin-scale western intensification. The Stommel and Munk theories explain this behaviour.

The Sverdrup relation \beta V = \frac{1}{\rho_0}(\nabla\times\boldsymbol{\tau})_z links the vertically integrated meridional transport V in the ocean interior to the curl of the wind stress, where \beta = df/dy is the meridional gradient of the Coriolis parameter. The relation is obtained by taking the curl of the depth-integrated momentum balance, which eliminates the pressure-gradient term. Its three ingredients are therefore the curl of the wind stress, the variation of the Coriolis force with latitude, and the meridional transport. The transport is meridional, its magnitude depends on \beta, and it is not always perpendicular to the wind direction, because it follows the wind-stress curl rather than the wind direction itself. The interior flow is geostrophic and is balanced by vertical stretching driven by Ekman pumping, not by ageostrophic currents.

Subtropical gyres are anticyclonic. In the Northern Hemisphere they circulate clockwise, and in the Southern Hemisphere counter-clockwise. The North Atlantic subtropical gyre therefore circulates clockwise, while the South Pacific subtropical gyre circulates counter-clockwise.