The western edge of this region is defined by the outcrop line of the upper layer h1 = 0 (4.318)

Region III, where the first layer vanishes and the second layer is the only active layer, so the solution is

2a f ^e hi = 2h\e + 2hieh2e + h22e + — Prd X (4.319)

g Jx

The shape of these dynamical regimes will be shown clearly in the following discussion about the subpolar gyre obtained from a model with continuous stratification. In particular, we will show the horseshoe shape of the shadow zone or the stagnant water below the wind-driven gyre.

4.3.3 A continuously stratified model

The three-dimensional structure of the wind-driven gyre in the subpolar basin for a model with continuous stratification can be described in terms of the Bernoulli function

The derivation of the basic equations discussed below parallels that for the subtropical basin. For large-scale circulation, geostrophy is a good approximation, so the horizontal momentum equations are reduced to f pov = Bx, f pou = -By

and the vertical momentum equation degenerates to the hydrostatic relation

where the subscript p indicates a partial derivative. The linear vorticity equation is

Using Eqns. (4.321,4.322, 4.323) to eliminate v and z leads to

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