408
Abyssal Circulation
¢ :::; ¢w., the western longitudinal extent of the source, the total zonal flux is
constant, westward, and equal to:
fo!h uHRdfJ= JfwoR 2 cos fJdcjJdfJ=S+.
1
source
(7.4.5)
Just enough more fluid flows westward in the southern branch of the
bidirectional jet than flows eastward in the northern branch to deliver to the
western boundary layer a net amount of flow equal to the flux of mass issuing
from the source. This is shown schematically in the figure where four
streamlines move westward while three streamlines return to the source. The
difference of one unit is provided by the source. In the western boundary layer
the recirculating portion (three units in the figure) turn northward to close the
recirculating, dipolar cell. The smaller portion of one unit, representing the flux
S+, turns southward in the western boundary layer where it flows southward
with no change in transport until it reaches the latitude band of the sink. In this
region the arguments given above for the source can be applied directly to the
flow in the latitude interval of the sink. Again, in the southern limb of the
dipolar flow to the sink the smaller Coriolis parameter provides more flow to
the sink than issues from it, and this excess is provided by the southward flux in
the western boundary current which terminates at the southern edge of the
latitude band containing the sink.
It is true that there is a net mass flux from source to sink through zonal jets
and the western boundary current. However, focusing on the mass balance
alone can be somewhat misleading as the results of the analysis shows. By far
the largest velocities are not connected to the requirements of simple mass flux
but are provoked by the reaction of the flow to the presence of vortex tube
stretching in the presence of a powerful potential vorticity constraint. The
dominant flow, in terms of its magnitude, is the recirculating flow, and, once
again, its direction at any location is not simply related to its position relative
to its source. In the western boundary current, for example, in the latitude
band of the source, most of the water moves northward even though the global
mass budget requires a southward boundary layer transport of the fluid from
the source to feed the sink in the south. In the regions of both the source and
the sink the strong recirculation implies that slightly less than half of the flow
moves towards the source and away from the sink.
The dipolar jets, with their relatively strong lateral shears, especially when
the north-south scale becomes small, are likely to be unstable, and the idealized
rectilinear flow is surely only an idealization of the more complex flow that is
more likely to result. Something of the kind can be inferred from the original
photographic evidence of the Stommel, Arons, and Faller (1958) experiment in
the case where the source and sink flow, analyzed, here was attempted. The
reader sees in the original illustration of the experiment a large billowing ink
cloud issuing westward from the source. It is not possible to reconstruct the
Abyssal Circulation
¢ :::; ¢w., the western longitudinal extent of the source, the total zonal flux is
constant, westward, and equal to:
fo!h uHRdfJ= JfwoR 2 cos fJdcjJdfJ=S+.
1
source
(7.4.5)
Just enough more fluid flows westward in the southern branch of the
bidirectional jet than flows eastward in the northern branch to deliver to the
western boundary layer a net amount of flow equal to the flux of mass issuing
from the source. This is shown schematically in the figure where four
streamlines move westward while three streamlines return to the source. The
difference of one unit is provided by the source. In the western boundary layer
the recirculating portion (three units in the figure) turn northward to close the
recirculating, dipolar cell. The smaller portion of one unit, representing the flux
S+, turns southward in the western boundary layer where it flows southward
with no change in transport until it reaches the latitude band of the sink. In this
region the arguments given above for the source can be applied directly to the
flow in the latitude interval of the sink. Again, in the southern limb of the
dipolar flow to the sink the smaller Coriolis parameter provides more flow to
the sink than issues from it, and this excess is provided by the southward flux in
the western boundary current which terminates at the southern edge of the
latitude band containing the sink.
It is true that there is a net mass flux from source to sink through zonal jets
and the western boundary current. However, focusing on the mass balance
alone can be somewhat misleading as the results of the analysis shows. By far
the largest velocities are not connected to the requirements of simple mass flux
but are provoked by the reaction of the flow to the presence of vortex tube
stretching in the presence of a powerful potential vorticity constraint. The
dominant flow, in terms of its magnitude, is the recirculating flow, and, once
again, its direction at any location is not simply related to its position relative
to its source. In the western boundary current, for example, in the latitude
band of the source, most of the water moves northward even though the global
mass budget requires a southward boundary layer transport of the fluid from
the source to feed the sink in the south. In the regions of both the source and
the sink the strong recirculation implies that slightly less than half of the flow
moves towards the source and away from the sink.
The dipolar jets, with their relatively strong lateral shears, especially when
the north-south scale becomes small, are likely to be unstable, and the idealized
rectilinear flow is surely only an idealization of the more complex flow that is
more likely to result. Something of the kind can be inferred from the original
photographic evidence of the Stommel, Arons, and Faller (1958) experiment in
the case where the source and sink flow, analyzed, here was attempted. The
reader sees in the original illustration of the experiment a large billowing ink
cloud issuing westward from the source. It is not possible to reconstruct the