9.4 Application of Ekman Theory
Because winds blowing on the sea surface produce an Ekman layer that trans-ports water at right angles to the wind direction, any spatial variability of the wind, or winds blowing along some coasts, can lead to upwelling. And upwelling is important:
Upwelled water is colder than water normally found on the surface, and it is richer in nutrients. The nutrients fertilize phytoplankton in the mixed layer, which are eaten by zooplankton, which are eaten by small fish, which are eaten by larger fish and so on to infinity. As a result, upwelling regions are productive waters supporting the world's major fisheries. The important regions are offshore of Peru, California, Somalia, Morocco, and Namibia.
Now we can answer the question we asked at the beginning of the chapter: Why is the climate of San Francisco so different from that of Norfolk, Virginia? Figures 4.2 or 9.7 show that wind along the California and Oregon coasts has a strong southward component. The wind causes upwelling along the coast; which leads to cold water close to shore. The shoreward component of the wind brings warmer air from far o shore over the colder water, which cools the incoming air close to the sea, leading to a thin, cool atmospheric boundary layer. As the air cools, fog forms along the coast. Finally, the cool layer of air is blown over San Francisco, cooling the city. The warmer air above the boundary layer, due to downward velocity of the Hadley circulation in the atmosphere (see Figure 4.3), inhibits vertical convection, and rain is rare. Rain forms only when winter storms coming ashore bring strong convection higher up in the atmosphere.
In addition to upwelling, other processes influence weather in California and Virginia.
All these processes are reversed o shore of east coasts, leading to warm water close to shore, thick atmospheric boundary layers, and frequent convective rain. Thus Norfolk is much different that San Francisco due to upwelling and the direction of the coastal currents.
By definition, the Ekman velocities approach zero at the base of the Ekman layer, and the vertical velocity at the base of the layer wE (-d) due to divergence of the Ekman flow must be zero. Therefore:
Where ME is the vector mass transport due to Ekman flow in the upper boundary layer of the ocean, and ∇H is the horizontal divergence operator. (9.29) states that the horizontal divergence of the Ekman transports leads to a vertical velocity in the upper boundary layer of the ocean, a process called Ekman Pumping.
If we use the Ekman mass transports (9.26) in (9.29) we can relate Ekman pumping to the wind stress.
where T is the vector wind stress.
The vertical velocity at the sea surface w(0) must be zero because the surface cannot rise into the air, so wE(0) must be balanced by another vertical velocity. We will see in Chapter 12 that it is balanced by a geostrophic velocity wG(0) at the top of the interior flow in the ocean.
Note that the derivation above follows Pedlosky (1996: 13), and it differs from the traditional approach that leads to a vertical velocity at the base of the Ekman layer. Pedlosky points out that if the Ekman layer is very thin compared with the depth of the ocean, it makes no difference whether the velocity is calculated at the top or bottom of the Ekman layer, but this is usually not true for the ocean. Hence, we must compute vertical velocity at the top of the layer.
|Department of Oceanography, Texas A&M University
Robert H. Stewart, firstname.lastname@example.org
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Updated on October 5, 2007