This equation can be used to estimate the depth of the wind-driven gyre in the subpolar basin. Using the definition H = —Apfp^, we obtain the following estimate

Assumingthat g = 9.8 m/s2, paz = -0.333 x 10-3 kg/m4, p = 10—10/s/m,f = 1.5x10-4/s, f0 = 1.3 x 10-4/s, we = 10-6 m/s, and Ax = 5,000 km, then the depth of the wind-driven gyre is about 3 km; thus, the wind-driven gyre in the subpolar basin is quite deep. In comparison, owing to the relative strong stratification in the subtropics, most wind-driven gyres in the subtropical basin are on the order of 2 km in depth.

The case with a non-constant potential vorticityfor the unventilated thermocline

As an example, we discussed the structure of the subpolar gyre circulation for a case where the potential vorticity in the unventilated thermocline is a function of density. The solution is calculated from a simple numerical model based on a shooting method for solving the nonlinear equation. The subpolar basin interior, excluding the western boundary region, is divided into m x n stations. The solution is calculated by solving the above free boundary value problem, Eqns. (4.327,4.328, 4.329), station by station.

The model ocean is a rectangular basin of 60° x 20° (0° — 60° E, 45° — 65° N), mimicking the northern North Atlantic. Input data required for the calculation include the Ekman pumping rate and the background stratification (or the potential vorticity for all the moving water). The Ekman pumping forcing has a simple form where Os is the southern boundary of the model basin, and AO = 20° is the meridional range of the model basin (Fig. 4.55b).

As discussed above, the major difference between subtropical and subpolar gyres is that isopycnals in the subpolar gyre are all unventilated, because these isopycnals come from the deeper part of the ocean and move upward in the cyclonic gyre. As a result, the formulation of the ideal-fluid thermocline model is different for the subtropical and subpolar gyres. In the subpolar gyre, we cannot specify the density and depth of the mixed layer, but the potential vorticity for all isopycnals is specified.

Winter cooling at the sea surface is one of the most essential aspects of the circulation in a subpolar basin. In order to account for the cooling effect, Huang (1988b) proposed a model in which cooling is treated in terms of a weakly convective adjustment to the thermal structure set up by the model without considering the cooling. While the approach provides useful information about the dynamical structure of the circulation in the subpolar basin, the cooling pattern is subject to certain dynamical constraints. As a result, there may not be any solution for a given cooling pattern.

In this section, we adopt a different approach. First, we will find a steady solution with a mixed layer with zero depth for the wind-driven circulation in a subpolar basin, without

Background stratification

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