## The Ekman and windinduced geostrophic flows

We show first that the wind does indeed induce a geo-strophic flow that has the same sense as the wind itself. The mean winds are to the east in midlatitudes and to the west in the tropics and, as we showed in the section in chapter 3 on Ekman layers, there is a flow in the upper winds

\Ekman transport //

winds

Figure 4.2. Production of gyres by winds. The winds blowing as shown induce a converging Ekman flow, causing the sea level to increase in the center, thus giving rise to a pressure gradient. This gradient in turn induces a geostrophic flow around the gyre, in the same sense as the winds themselves.

winds

Figure 4.2. Production of gyres by winds. The winds blowing as shown induce a converging Ekman flow, causing the sea level to increase in the center, thus giving rise to a pressure gradient. This gradient in turn induces a geostrophic flow around the gyre, in the same sense as the winds themselves.

ocean at right angles to the wind. As illustrated in figure 4.2, this combination causes the flow to converge in the center of the gyre. This convergence pushes up the surface of the ocean, causing the sea surface to form a gentle dome, with the ocean surface at the center of the gyre a few tens of centimeters higher than at the edges. The converging fluid must go somewhere, and the only place for it to go is downward. A complementary situation arises in the subpolar gyre, where the westerly (eastward) winds are strongest on the equatorial side. Now the Ekman transport is directed away from the center of the gyre, and the sea level is depressed and upwelling occurs.

The doming of the sea surface produces a pressure gradient in the ocean, as illustrated in figure 4.2. Consider a horizontal plane at a level a little below the sea surface. The pressure at that level is produced by the weight of the fluid above it, as we discovered in the section in chapter 3 on hydrostatic balance, and so is higher where the sea surface is higher. This pressure gradient produces a geostrophic flow perpendicular to the pressure gradient, and so in the same direction as the wind that originally produced the doming. Thus, when all is said and done, on a rotating planet the wind leads to the production of an ocean current that is aligned with the wind, rather as we would expect in the nonrotating case. However, the pressure gradients in the two cases are quite different because of the presence of the Coriolis force in the rotating case; note in particular that the horizontal pressure gradient produced by the doming extends all the way to the bottom of the ocean. Thus, even though the direct effects of the wind stress are confined to the upper few tens of meters, the wind produces geostrophic currents that can extend to great depths.

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