Can the Western Boundary Layer Affect the Potential Vorticity Distribution in the Sverdrup interior of a Wind Gyre?

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  • 1 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139
  • | 2 Department of Physical Oceanography, Woods Hole Oceanographic institution, Woods Hole, MA 02543
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Abstract

The question posed in the title of this paper is answered in the affirmative by investigating a two-layer, quasi-geostrophic model of the wind-driven circulation. The two layers model the thermocline rather than the whole depth of the ocean. The wind stress is balanced by interfacial and bottom drag. This is perhaps the simplest baroclinic extension of Stommel's (1948) barotropic circulation model. It differs from an earlier model of Welander (1966) in that the vortex stretching nonlinearity is of primary importance.

In this model the dynamics of the frictional western boundary layer determine the vertical structure of the wind-driven flow in the Sverdrup interior. Thus, in a sense, the boundary layer is “active” and cannot be appended to an arbitrary interior flow; rather it partially determines the interior circulation by setting the functional relationship between the streamfunction and the potential vorticity in the lower layer.

In previous studies (Rhines and Young 1982b) this functional relationship has been calculated using a generalized Prandtl-Batchelor theorem. This result does not apply to the present calculation because every lower layer streamline passes through a frictional boundary layer.

Abstract

The question posed in the title of this paper is answered in the affirmative by investigating a two-layer, quasi-geostrophic model of the wind-driven circulation. The two layers model the thermocline rather than the whole depth of the ocean. The wind stress is balanced by interfacial and bottom drag. This is perhaps the simplest baroclinic extension of Stommel's (1948) barotropic circulation model. It differs from an earlier model of Welander (1966) in that the vortex stretching nonlinearity is of primary importance.

In this model the dynamics of the frictional western boundary layer determine the vertical structure of the wind-driven flow in the Sverdrup interior. Thus, in a sense, the boundary layer is “active” and cannot be appended to an arbitrary interior flow; rather it partially determines the interior circulation by setting the functional relationship between the streamfunction and the potential vorticity in the lower layer.

In previous studies (Rhines and Young 1982b) this functional relationship has been calculated using a generalized Prandtl-Batchelor theorem. This result does not apply to the present calculation because every lower layer streamline passes through a frictional boundary layer.

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