From Eqns. (4.40, 4.49), the streamfunction within the boundary layer is (Fig. 4.5a):
The global structure of the boundary layer solution depends on the choice of parameters used in the model, in particular the choice of R. From observations, the width of the Gulf Stream is about 50 km, thus we choose Ss ~ 25 km. Assuming P ~ 2 x 10-11 /m/s, hi — 400 m, then the suitable choice is R — Phi Ss = 2 x 10-4 m/s2.
As an example, we choose a model mimicking the North Atlantic Ocean, with parameters: he = 300, g' = 0.015 m/s2, and subject to the following wind stress rx = -0.15 cos ( —^^^ (inN/m2) (4.53)
Although similar maps of the Sverdrup function can be obtained from a quasi-geostrophic model, the map of thermocline depth can be obtained from a reduced-gravity model only. This is one of the most important advantages of the reduced-gravity model.
The dynamic balance of the circulation is best illustrated in terms of the potential vorticity change along closed streamlines. Since the relative vorticity is very small, the potential vorticity can be approximated by (Ap/p0) (f /h). In the basin interior the wind-stress curl is a sink of potential vorticity; thus, potential vorticity declines downstream (Fig. 4.6b).
a Western boundary b Basin interior a Western boundary b Basin interior
In the western boundary, the interfacial friction torque is a source of positive potential vorticity; thus, potential vorticity of a water parcel increases along the pathway (Fig. 4.6a).
Potential vorticity and its meridional gradient are very high within the northern part of the basin, but they are rather small elsewhere. If an active second layer is added below this top layer, the corresponding meridional gradient of potential vorticity in the second layer is
Basin interior a Western boundary b 50N
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