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6.8 The Wind-Driven Circulation of the Ocean 1416.8.7 The Sverdrup BalanceOn the β plane, the divergence of lateral volume transport inherent with geostrophicfl w is given by:∂ Q geox∂x+ ∂ Qgeo y∂y=− β f Qgeo y (6.46)On the large scale, this divergence (or convergence) of the geostrophic f ow balancesthe convergence (or divergence) of the drift in the surface Ekman layer. Effectsassociated with bottom friction are irrelevant here. Under the assumption of purelyzonal wind (τywind = 0), the steady-state balance leading to an equilibrium sea-leveldistribution is given by:β Q geoy≈− 1 ∂τxwindρ o ∂y(6.47)This balance is called the Sverdrup relation (Sverdrup, 1947) and allows forcalculation of the meridional geostrophic volume transport (also called Sverdruptransport) from knowledge of the average zonal wind-stress distribution. The correspondingzonal volume transport can be estimated from:∂ Q geox∂x+ ∂ Qgeo y∂y≈ 0 (6.48)where the β effect can be ignored since this equation is used for diagnostic purposesonly. It is important to note that the Sverdrup balance can only establish withexistence of a meridional boundary. The dynamics of unbounded fl ws, such as theAntarctic Circumpolar Current, is more complex.6.8.8 Interpretation of the Sverdrup RelationFirst and foremost, the Sverdrup relation implies that latitudes of vanishing windstresscurl (∂τxwind /∂y = 0) coincide with regions of vanishing meridional geostrophicf ow. Hence, these regions form natural boundaries that, for instance,separate subtropical from subpolar gyres in the ocean.In the midlatitude ocean of the northern hemisphere, the main wind pattern consistsof trades to the south and westerlies to the north. This wind pattern provides∂τxwind /∂y > 0 and produces a convergence of volume transport in the surfaceEkman layer. Hence, equatorward Sverdrup transport is required to balance thisconvergence.Since no geostrophic f ow is possible across the natural boundaries marked bythe maximum trade winds and the maximum westerlies, this equatorward fl w must