Ekman Layers

In the final topic of this chapter, we consider what happens to water in the upper few tens of meters when the wind blows over it. The water moves, and hence the Coriolis force acts, but because there is an additional force coming from the wind, geostrophic balance cannot exactly hold. So what does happen? The problem was first considered by Vagn Walfrid Ekman, a Swedish oceanog-rapher, at the beginning of the twentieth century, at the suggestion of Fridtjof Nansen, the Norwegian explorer and statesman. Nansen had noticed that icebergs did not move in the same direction as the wind, but at an angle of about 45° to the right of the wind. In explaining this, Ekman was led to discover the eponymous Ekman layer, which we now discuss.

The blowing wind supplies a stress to the ocean and causes the uppermost layer of fluid to accelerate in the direction of the wind. As the fluid moves, two things happen. First, the fluid feels the effect of the Coriolis force, which in the Northern Hemisphere causes the fluid to veer to the right, as we have seen. Second, the fluid layer imparts a stress to the fluid just below the surface, and this layer is then set in motion. At the same time, the deeper layer provides a retarding force on the surface layer, so that the surface layer comes into a mechanical equilibrium, moving in a direction somewhat to the right of the wind at the surface. While this is happening, the deeper layer of fluid veers more to the right and imparts a stress to the still deeper fluid, and so on. The upshot of all this is that the flow veers more and more to the right with depth, and also becomes weaker with depth, as the wind's influence wanes. The net result is that the wind-induced flow forms a spiral, as illustrated in figure 3.4, with the flow magnitude typically falling essentially to zero after about 100 m, at which depth the wind-induced stress is negligible. Below this level, the flows are geostrophic.

In reality, such an ideal spiral is rarely, if ever, observed because of the myriad other processes occurring in the upper ocean. However, one robust property of Ekman layers transcends the fragility of the spiral structure itself. And that is that the mean transport in the Ekman layer—Ekman transport—is at right angles to the direction of the wind. The reason for this is relatively straightforward; it stems from the fact that the Coriolis force acts at right angles to the direction of the fluid flow. When the wind blows, it imparts a stress to the ocean,

Figure 3.4. An idealized Ekman spiral in the Northern Hemisphere.

and the fluid begins to accelerate in the direction of the wind. The Coriolis force deflects the fluid (the deflection is to the right in the Northern Hemisphere), and the fluid comes into an equilibrium when the direction of the wind-induced flow is at right angles to the wind itself, for then the Coriolis force can exactly balance the wind stress. The situation is analogous to that giving rise to a geostrophically balanced flow, but now with the wind stress instead of a pressure gradient. Of course, in addition to the Ekman transport there is a geostrophic flow if there is a pressure gradient in the fluid. (Also, it turns out that just at the surface the flow is at 45° to the wind, as sketched in figure 3.4, thus explaining Nansen's observations of icebergs.) A more mathematical derivation of the Ekman transport is given in appendix B

of this chapter, but trusting readers may be tempted to skip it.

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