where f is the Coriolis parameter, Eq. 6-42, and h is the thickness of the layer in the direction of gravity measured in the vertical, as sketched in Fig. 10.23.

FIGURE 10.23. Miniature T-P columns in a layered fluid. The layers increase in density going downward with Pi > p2

fiTi on a fiTi on a

M «0t 'MT -MT IX* I«W W» t*C -WC ■•! tXV law HM

FIGURE 10.24. The quantity (-f /pref da/dz) where a is the potential density on a shallow density surface in the Pacific (left; a = 26.5 ; the depth of this surface is plotted in Fig. 9.8) and on a deeper density surface (right; a = 27.5). Note that da/dz < 0 because the ocean is stably stratified and so (-f /pref da/dz) is positive in the northern hemisphere and negative in the southern hemisphere.

M «0t 'MT -MT IX* I«W W» t*C -WC ■•! tXV law HM

FIGURE 10.24. The quantity (-f /pref da/dz) where a is the potential density on a shallow density surface in the Pacific (left; a = 26.5 ; the depth of this surface is plotted in Fig. 9.8) and on a deeper density surface (right; a = 27.5). Note that da/dz < 0 because the ocean is stably stratified and so (-f /pref da/dz) is positive in the northern hemisphere and negative in the southern hemisphere.

If we focus on one particular layer then, away from the direct influence of Ekman pumping, f /h will be conserved following that column of fluid around the ocean. What do the f /h contours look like in the ocean? Some are plotted in Fig. 10.24 for chosen density surfaces in the Pacific. In fact what is actually plotted is (-f /pref da/dz), a "continuous" version of f /h,9 where a is the potential density. On the a _ 26.5 surface in the North Pacific, for example, which is everywhere rather shallow (see Fig. 9.8) the f/h contours sweep around and turn back on themselves. Variations in h dominate over f, allowing the strong circulatory flow of the gyre to persist within the thermocline without violation of the Taylor-Proudman theorem. On the a _ 27.5 surface, much deeper in the water column (see Fig. 9.7), f/h contours are more zonal and they intersect the coast. On these deeper surfaces, variations in f are much more important than variations in h. Since interior fluid columns conserve their f /h, there can be little flow deep down, because the columns would run into the coast. So the deep ocean interior is, in the mean, largely quiescent. However, as we shall see in Section 11.3 and 11.4, a weak abyssal circulation does exist, fed by deep western boundary currents driven by convective sources at the poles. This is particularly true in the Atlantic Ocean (see, e.g., Fig. 11.24).

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