Chapter 11 - Wind Driven Ocean Circulation

Chapter 11 Contents

11.2 Stommel's Theory of Western Boundary Currents

At the same time Sverdrup was beginning to understand circulation in the eastern Pacific, Stommel was beginning to understand why western boundary currents occur in ocean basins. To study the circulation in the North Atlantic, Stommel (1948) used essentially the same equations used by Sverdrup (11.1, 11.2, and 11.3) but he added a simple bottom stress proportional to velocity to (11.3):

(11.16a)
(11.16b)

where F and R are constants.

Stommel calculated steady-state solutions for flow in a rectangular basin 0 y b, 0 x λ of constant depth D filled with water of constant density. His first solution was for a non-rotating Earth. This solution had a symmetric flow pattern with no western boundary current (Figure 11.5, left). Next, Stommel assumed a constant rotation, which again led to a symmetric solution with no western boundary current. Finally, he assumed that the Coriolis force varies with latitude. This led to a solution with western intensification (Figure 11.5, right). Stommel suggested that the crowding of stream lines in the west indicated that the variation of Coriolis force with latitude may explain why the Gulf Stream is found in the ocean. We now know that the variation of Coriolis force with latitude is required for the existence of the western boundary current, and that other models for the flow which use different formulations for friction, lead to western boundary currents with different structure. Pedlosky (1987, Chapter 5) gives a very useful, succinct, and mathematically clear description of the various theories for western boundary currents.

Figure 11.5 Stream function for flow in a basin as calculated by Stommel (1948). Left: Flow for non-rotating basin or flow for a basin with constant rotation. Right: Flow when rotation varies linearly with y.

In the next chapter, we will see that Stommel's results can also be explained in terms of vorticity - wind produces clockwise torque (vorticity), which must be balanced by a counterclockwise torque produced at the western boundary.

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