E 10e 15e 0 10e 20e 30e 40e 50e 60e

Fig. 4.4 Thermocline depth (in 100 m) and a streamline (heavy dashed line) in a model with aStommel boundary layer.

over the whole basin, such a large-scale pressure field should change over decadal time scales, bringing changes to the coastal circulation.

Stommel boundary layer Stommel (1948) made the assumption that interfacial friction is in the form of a linear drag law. Thus, within the western boundary layer the downstream momentum equation is in an ageostrophic balance fhu = -g'hhy - Rv (4.45)

For the model with zonal wind only, the potential vorticity equation is reduced to

Within the western boundary layer, the contribution due to wind-stress curl is negligible compared with the contributions from the interfacial frictional torque and planetary vorticity gradient, so the potential vorticity equation is further reduced to

Integrating this equation across the western boundary current leads to

Using Eqn. (4.40), we obtain hx + 2R (h2 - h2) = 0 (4.47)

subject to the following boundary condition h(0) = hw (4.48)

The corresponding solution is

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