F

Thus the ageostrophic component is always directed "to the right'' of F (in the northern hemisphere).

We can readily demonstrate the role of Ekman layers in the laboratory as follows.

7.4.1. GFD Lab X: Ekman layers: frictionally-induced cross-isobaric flow

We bring a cylindrical tank filled with water up to solid-body rotation at a speed of 5 rpm. A few crystals of potassium permanganate are dropped into the tank—they leave streaks through the water column as they fall and settle on the base of the tank—and float paper dots on the surface to act as tracers of upper level flow. The rotation rate of the tank is then reduced by 10% or so. The fluid continues in solid rotation, creating a cyclonic vortex (same sense of rotation as the table) implying, through the geostrophic relation, lower pressure in the center and higher pressure near the rim of the tank. The dots on the surface describe concentric circles and show little tendency toward radial flow. However at the bottom of the tank we see plumes of dye spiral inward to the center of the tank at about 45° relative to the geostrophic current (see Fig. 7.23, top panel). Now we increase the rotation rate. The relative flow is now anticyclonic with, via geostrophy, high pressure in the center and low pressure on the rim. Note how the plumes of dye sweep around to point outward (see Fig. 7.23, bottom panel).

In each case we see that the rough bottom of the tank slows the currents down there, and induces cross-isobaric, ageostrophic flow from high to low pressure, as schematized in Fig. 7.24. Above the frictional layer, the flow remains close to geostrophic.

7.4.2. Ageostrophic flow in atmospheric highs and lows

Ageostrophic flow is clearly evident in the bottom kilometer or so of the atmosphere, where the frictional drag of the rough underlying surface is directly felt by the flow. For example, Fig. 7.25 shows the surface pressure field and wind at the

FIGURE 7.23. Ekman flow in a low-pressure system (top) and a high-pressure system (bottom), revealed by permanganate crystals on the bottom of a rotating tank. The black dots are floating on the free surface and mark out circular trajectories around the center of the tank directed anticlockwise (top) and clockwise (bottom).

FIGURE 7.23. Ekman flow in a low-pressure system (top) and a high-pressure system (bottom), revealed by permanganate crystals on the bottom of a rotating tank. The black dots are floating on the free surface and mark out circular trajectories around the center of the tank directed anticlockwise (top) and clockwise (bottom).

surface at 12 GMT on June 21, 2003, at the same time as the upper level flow shown in Fig. 7.4. We see that the wind broadly circulates in the sense expected from geostrophy, anticylonically around highs and cycloni-cally around the lows. But the surface flow also has a marked component directed down the pressure gradient, into the lows and out of the highs, due to frictional drag at the ground. The sense of the ageostrophic flow is exactly the same as that seen in GFD Lab X (cf. Fig. 7.23 and Fig. 7.24).

A simple model of winds in the Ekman layer

Equation 7-25 can be solved to give a simple expression for the wind in the Ekman layer. Let us suppose that the x-axis is directed along the isobars and that the surface stress decreases uniformly throughout the depth of the Ekman layer from its surface value to become small at

FIGURE 7.24. Flow spiraling in to a low-pressure region (left) and out of a high-pressure region (right) in a bottom Ekman layer. In both cases the ageostrophic flow is directed from high pressure to low pressure, or down the pressure gradient.

z = 5, where 5 is the depth of the Ekman layer such that

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