Dipole Circulation Associated with Isolated Sources
405
associated with circulation were refined in a later paper (Stommel and Arons
1960b), but the pattern of flow remains similar to that shown in the figure (see
also Kuo and Veronis 1970).
The original figure of Stommel's is shown because it highlights an
important point. The patterns of flow described in the theory assume that the
ocean floor is fiat. As noted earlier, the presence of the great oceanic ridge
systems is expected to disturb the low patterns considerably. The ridge system
is indicated in Stommel's figure by the shaded areas, but the streamlines are
drawn as if the barriers to the deep flow presented by the ridges were not
present. The flow in the figure moves with serene indifference to the presence of
the topographic barriers. In Section 7.5 we take up the question of the effect of
the ridges and their gaps on the Stommel-Arons circulation. However, first we
consider in more detail the circulation associated with isolated sources and
sinks within the domain of the basin.
7.4 Dipole Circulation Associated with Isolated Sources
In Section 7.2 we described an experimental situation in a rotating pie-shaped
sector in which a source and sink are placed at different radii on the eastern
boundary of the sector, and argued on the basis of mass balance considerations
that the flow of mass from source to sink takes place in purely zonal jets which
are connected to the western boundary current. This picture, in which the flow
moves zonally from the source and then to the sink, is only a partial picture of
the circulation. In this section we reexamine the situation more carefully within
the context of the Stommel-Arons theory on the sphere.
Consider the situation shown in Fig. 7 .4.1. A source of finite extent has a
total strength S+ and feeds the abyss by pumping fluid downward in the zone
indicated by the upper circle. South of the source lies a sink with an equal and
opposite total strength, i.e., S_ = -S+. Outside of these zones the vertical
pumping velocity w0 is zero. What is the circulation produced by such a
distribution?
The meridional velocity is given by (7.3.6) and is zero except in the regions
of the source and sink. In the region of the source, where w0 < 0, the
meridional flow (assuming the source is in the northern hemisphere) is
southward while under the sink where w0 > 0, the meridional flow is
northward as indicated in the figure. Elsewhere the interior flow can only be
zonal and given by (7.3.8) while the pressure anomaly is given by (7.3.7). Note
that the pressure disturbance and zonal velocity are both zero east of the source
and sink. The pressure anomaly is also zero west of the source and sink outside
the latitude bands containing the source and sink. This has important
implications. If the zonal flow from the source to the western boundary were
unidirectional, for example, strictly westward, the pressure west of the source
would have to increase monotonically across the latitude interval of the source
405
associated with circulation were refined in a later paper (Stommel and Arons
1960b), but the pattern of flow remains similar to that shown in the figure (see
also Kuo and Veronis 1970).
The original figure of Stommel's is shown because it highlights an
important point. The patterns of flow described in the theory assume that the
ocean floor is fiat. As noted earlier, the presence of the great oceanic ridge
systems is expected to disturb the low patterns considerably. The ridge system
is indicated in Stommel's figure by the shaded areas, but the streamlines are
drawn as if the barriers to the deep flow presented by the ridges were not
present. The flow in the figure moves with serene indifference to the presence of
the topographic barriers. In Section 7.5 we take up the question of the effect of
the ridges and their gaps on the Stommel-Arons circulation. However, first we
consider in more detail the circulation associated with isolated sources and
sinks within the domain of the basin.
7.4 Dipole Circulation Associated with Isolated Sources
In Section 7.2 we described an experimental situation in a rotating pie-shaped
sector in which a source and sink are placed at different radii on the eastern
boundary of the sector, and argued on the basis of mass balance considerations
that the flow of mass from source to sink takes place in purely zonal jets which
are connected to the western boundary current. This picture, in which the flow
moves zonally from the source and then to the sink, is only a partial picture of
the circulation. In this section we reexamine the situation more carefully within
the context of the Stommel-Arons theory on the sphere.
Consider the situation shown in Fig. 7 .4.1. A source of finite extent has a
total strength S+ and feeds the abyss by pumping fluid downward in the zone
indicated by the upper circle. South of the source lies a sink with an equal and
opposite total strength, i.e., S_ = -S+. Outside of these zones the vertical
pumping velocity w0 is zero. What is the circulation produced by such a
distribution?
The meridional velocity is given by (7.3.6) and is zero except in the regions
of the source and sink. In the region of the source, where w0 < 0, the
meridional flow (assuming the source is in the northern hemisphere) is
southward while under the sink where w0 > 0, the meridional flow is
northward as indicated in the figure. Elsewhere the interior flow can only be
zonal and given by (7.3.8) while the pressure anomaly is given by (7.3.7). Note
that the pressure disturbance and zonal velocity are both zero east of the source
and sink. The pressure anomaly is also zero west of the source and sink outside
the latitude bands containing the source and sink. This has important
implications. If the zonal flow from the source to the western boundary were
unidirectional, for example, strictly westward, the pressure west of the source
would have to increase monotonically across the latitude interval of the source