An analysis is presented of the potential vorticity dynamics responsible for western boundary current (WBC) separation in a single barotropic wind-driven gyre on a beta-plane with a circular boundary.
It is often difficult to obtain realistic WBC separation in ocean circulation models, and better understanding of the underlying physics of this process is needed. A variety of features have been shown to influence or induce separation (e.g. a collision with another western boundary current, a change in sign of the wind stress curl, outcropping of isopycnals or an abrupt change in bottom topography or boundary shape). However separation also occurs in the simple model presented here, despite the absence of these features. Identifying the cause of this apparently unprovoked separation is of interest because the mechanism which operates in this ″lowest common denominator″ model may also apply in more complex and realistic models.
Potential vorticity (PV) considerations provide an explanation for WBC separation in this model. Fluid parcels have their PV reduced by anticyclonic wind stress in the ocean interior, and this PV is then recovered in the WBC via lateral and bottom friction. The bulk of the WBC is anticyclonic, but under no-slip boundary conditions there is also a strongly cyclonic region against the western boundary. This relative vorticity distorts the PV contours in the WBC, delaying PV recovery in the anticyclonic region and producing early recovery in the cyclonic sublayer. When the relative vorticity is large, flow in the cyclonic sublayer acquires more PV than was lost in the interior, forcing a change in the WBC outflow structure to allow this excess PV to be dissipated. It is demonstrated that this dissipation must involve a change in sign of the Laplacian viscous term (even when bottom friction is also present), and that this in turn creates a PV structure which guides the outer WBC offshore as a separated jet. An adverse streamwise pressure gradient is also produced in the separation region. Under free-slip boundary conditions the cyclonic sublayer is absent and this mechanism does not operate, resulting in a very different WBC outflow structure.
This WBC separation mechanism depends on the PV dynamics of the thin cyclonic sublayer against the western boundary, and this must be adequately resolved for a numerical model to correctly predict the separation behaviour. |
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