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Pref P

eastern bdy

This simple formula is remarkably successful—it predicts the sense of circulation and volume transport of all the major ocean gyres, rationalizing the patterns of ocean currents shown in Figs. 9.14, 9.15 and 9.16 in terms of the pattern of imposed winds. Note, in particular, that Eq. 10-17 tells us that y = 0 along the lines of zero wind stress curl, the thick black lines in Fig. 10.11. Where z.V x rwind < 0, y < 0 and visa-versa, allowing us to define subpolar and subtropical gyres, etc., and rationalizing the pattern of zonal jets observed in the tropical oceans, as sketched in the schematic diagram in Fig. 10.20.

7Since U = 0 at the eastern boundary, Eq. 10-19 tells us that Y is a constant there. Equation 10-19 allows us to add any arbitrary constant to Y, so we are free to set Y = 0 at the boundary. Note, however, that we cannot simultaneously satisfy a vanishing normal flow condition through the western and eastern boundary using Eq. 10-17, because it involves only one derivative in x. As discussed in Section 11.3.3, dissipative processes must be invoked at the western boundary to obtain a complete solution. In Fig. 10.21, the western boundary is sketched in as a feature required by mass continuity.

"x Nrni5 Long tu do u era's

FIGURE 10.21. (left) The zonal-average of the zonal wind stress over the Pacific Ocean. (middle) The Sverdrup transport stream function (in Sv = 106m3s-1) obtained by evaluation of Eq. 10-20 using climatological wind stresses, Fig. 10.2. Note that no account has been made of islands; we have just integrated right through them. The transport of the western boundary currents (marked by the N « S arrows) can be read off from xVwes^bdy. (right) The zonal-average zonal current over the Pacific obtained from surface drifter data shown in Fig. 9.14. Key features corresponding to Fig. 9.13 are indicated.

"x Nrni5 Long tu do u era's

FIGURE 10.21. (left) The zonal-average of the zonal wind stress over the Pacific Ocean. (middle) The Sverdrup transport stream function (in Sv = 106m3s-1) obtained by evaluation of Eq. 10-20 using climatological wind stresses, Fig. 10.2. Note that no account has been made of islands; we have just integrated right through them. The transport of the western boundary currents (marked by the N « S arrows) can be read off from xVwes^bdy. (right) The zonal-average zonal current over the Pacific obtained from surface drifter data shown in Fig. 9.14. Key features corresponding to Fig. 9.13 are indicated.

Figure 10.21 shows Y in the Pacific sector and should be compared with Fig. 10.20. The curl of the annual-mean surface stress shown in Fig. 10.2 was computed and integrated westward from the eastern boundary to yield Y from Eq. 10-20 as a function of horizontal position. The units are in 106 m3 s-1. It is convenient to use 1 million cubic meters per second as a unit of volume transport, which is known as the "Sverdrup" (or Sv, after Harald Sverdrup). To put things in perspective, the flow of the Amazon river as it runs into the sea is about 0.2 Sv. Thus transport of the subtropical gyre of the North Pacific is about 50 Sv, or 250 times that of the Amazon, the biggest river on Earth!

One interesting rationalization provided by Sverdrup theory is that it accounts for the countercurrents observed in the tropical oceans discussed in Chapter 9, which are currents that flow in a direction opposite to the prevailing winds. As can be seen in Figs. 10.20 and 10.21, Sver-drup balance implies meridional flow away from the Doldrums in the interior with a return flow in a western boundary current.

Convergence of these boundary currents drives an eastward flow just north of the equator, even though the winds are blowing toward the west here. This is just as observed in surface drifter data (see Fig. 9.14 and the zonal-average surface currents across the Pacific plotted in the right-most panel in Fig. 10.21).

The transport of the western boundary current must be equal and opposite to that in the interior. The total interior transport is western bdy

Vdx eastern bdy western bdy

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