Singular nature of the SAF experiments

Physically, every source has a finite dimension, i.e., it is a continuously distributed source. In fact, flow patterns obtained by releasing dye from the eastern boundary, as depicted in Figure 5.48a, are not in the form of a few clearly marked streamlines; instead, the flows appear in the form of clouds. These clouds may be interpreted as mini-gyres driven by the source and sink. Using the principle of vorticity balance, the local source/sink should induce the mini-gyres (Fig. 5.50). The net transportation of mass from the source to the sink is accomplished by the "equatorward" western boundary current along the left edge of the sector.

Fig. 5.50 Sketch of the mini-gyres driven by distributed source (+) and sink (—).

Fig. 5.50 Sketch of the mini-gyres driven by distributed source (+) and sink (—).

Source-sink driven flow on a sphere

The source-sink driven flow on a sphere was discussed by Stommel and Arons (1960a). The model consists of a single homogeneous layer of depth h covering the surface of the Earth, and the free surface elevation is Z. The basic equations for a steady circulation are g dZ

a d0

dk 80

The notation used in their original paper is different from the current common notations in oceanography; thus, we will adopt the latter, i.e., 0 < k < 2n is the longitude and -n/2 < 0 < n/2 is the latitude. In addition, Q is defined as positive (negative) for distributed source (sink) of deep water. In the following analysis, we will assume that there is no bottom topography and the free surface satisfies the following relation, Z ^ h, so that h can be treated as approximately constant. By cross-differentiating Eqns. (5.68, 5.69), subtracting and using Eqn. (5.70), we obtain

h which corresponds to the Sverdrup relation in the wind-driven circulation. For example, a distributed source with Q > 0 drives a southward flow in the interior. Substituting Eqn. (5.71) into Eqn. (5.68) gives dZ 2wa2 sin2 0

dk gh

Note that for the steady case, mass conservation requires the source distribution to satisfy

Evaporation-precipitation hemispheres with no boundaries

Assume a simple pattern of evaporation and precipitation

The solution is

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