D

is the depth-integrated meridional transport. Equation 10-17 is the result we seek. It is known as the Sverdrup relation6 and relates the vertically-integrated meridional flow to the curl of the wind stress. The key assumption that must be satisfied for its validity—in addition to Ro << 1—is that mean flow in the deep ocean must be sufficiently weak (well supported by observation), so that both frictional stress on the ocean bottom and vertical motion are negligibly small.

Note the close connection between Eq. 10-17 and Eq. 10-15, (see Problem 3 at the end of the chapter, for a detailed look), when we realize that hv = V is the transport and f wEK is (if f were constant) the wind-curl divided by pref (cf. Eq. 10-8). Thus, despite the apparent restrictions in the assumptions made in deriving Eq. 10-15, it turns out to have wide applicability. Moreover, when combined with the preference

Harald Ulrik Sverdrup (1888—1957), a Norwegian who began his career studying meteorology with Vilhelm Bjerknes in Oslo, was appointed director of Scripps Oceanographic Institution in 1936. His 1947 paper ''Wind-driven currents in a baroclinic ocean,'' which showed the link between meridional currents and the curl of the wind stress, began the modern era of dynamical oceanography and initiated large-scale modeling of ocean circulation.

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