The fl-Spiral
201
whole notion of an interior in Sverdrup balance may become invalid. For now
we accept the provisional character of the solution.
In Fig. 4.4.4b we see the streamlines in the upper layer. The shadow zone
boundary is also shown. The streamlines in the upper layer cross the shadow
zone boundary. West of this boundary the upper layer shares the Sverdrup
transport with the lower layer. East of the shadow zone boundary the upper
layer carries the full Sverdrup transport. On the boundary, note the kink in the
upper layer streamfunction. The tangential velocity in both layers is
discontinuous at the shadow zone boundary. It is obviously true for the lower
layer flow. Since the total Sverdrup transport is continuous everywhere, the
upper layer flow must experience a compensating discontinuity to render the
total transport continuous.
Panel c of Fig. 4.4.4 shows the potential vorticity, q2 , in the lower layer
where it is conserved south of the outcrop line. Note the weakening of the
variation in q2 in the region of the ventilation south of the outcrop line. The
thickness of layer 2 varies much more strongly in regions where either layer 2
carries the full Sverdrup transport, as in the region north of the outcrop line, or
in the shadow zone where the upper layer carries the full Sverdrup transport,
and thus where the interface between layers 1 and 2 must vary strongly. This is
demonstrated in panels d and e, which show meridional and zonal cross
sections of the layer thicknesses. In panel d note the flattening of the base of the
thermocline south of the intersection with the shadow zone and the
simultaneous increase in the slope of the interface between the two layers.
The same behavior is evident in panel e, which shows a zonal cross section.
Note in particular that the layer thickness in the upper layer vanishes at the
eastern boundary. The strong east-west gradient of q2 in the shadow zone is
due to the rapid variation in h2 in the shadow zone region where z2 surfaces on
the eastern boundary. The overall shape of the base of the thermocline is
shown in the perspective representation of h in panel f. The bowl of the
thermocline and the ledge of the shadow zone are apparent.
4.5 The {3-Spiral
A careful examination of the streamline patterns in Fig. 4.4.4 shows that the
streamlines in layer 2 are always twisted clockwise with respect to streamlines
in layer 1 at the same geographical location. This can easily be observed where
the streamlines in layer 1 cross the shadow zone boundary, which is after all a
streamline in layer 2. The velocity vector spirals clockwise with increasing
depth in the subtropical gyre. This is a general feature of adiabatic flow in the
models of the subtropical gyre and can also be noted in the flow patterns
predicted by the Rhines and Young model discussed in Chapter 3. Stommel
and Schott (1977) pointed out this fact in an attempt to describe a method to
201
whole notion of an interior in Sverdrup balance may become invalid. For now
we accept the provisional character of the solution.
In Fig. 4.4.4b we see the streamlines in the upper layer. The shadow zone
boundary is also shown. The streamlines in the upper layer cross the shadow
zone boundary. West of this boundary the upper layer shares the Sverdrup
transport with the lower layer. East of the shadow zone boundary the upper
layer carries the full Sverdrup transport. On the boundary, note the kink in the
upper layer streamfunction. The tangential velocity in both layers is
discontinuous at the shadow zone boundary. It is obviously true for the lower
layer flow. Since the total Sverdrup transport is continuous everywhere, the
upper layer flow must experience a compensating discontinuity to render the
total transport continuous.
Panel c of Fig. 4.4.4 shows the potential vorticity, q2 , in the lower layer
where it is conserved south of the outcrop line. Note the weakening of the
variation in q2 in the region of the ventilation south of the outcrop line. The
thickness of layer 2 varies much more strongly in regions where either layer 2
carries the full Sverdrup transport, as in the region north of the outcrop line, or
in the shadow zone where the upper layer carries the full Sverdrup transport,
and thus where the interface between layers 1 and 2 must vary strongly. This is
demonstrated in panels d and e, which show meridional and zonal cross
sections of the layer thicknesses. In panel d note the flattening of the base of the
thermocline south of the intersection with the shadow zone and the
simultaneous increase in the slope of the interface between the two layers.
The same behavior is evident in panel e, which shows a zonal cross section.
Note in particular that the layer thickness in the upper layer vanishes at the
eastern boundary. The strong east-west gradient of q2 in the shadow zone is
due to the rapid variation in h2 in the shadow zone region where z2 surfaces on
the eastern boundary. The overall shape of the base of the thermocline is
shown in the perspective representation of h in panel f. The bowl of the
thermocline and the ledge of the shadow zone are apparent.
4.5 The {3-Spiral
A careful examination of the streamline patterns in Fig. 4.4.4 shows that the
streamlines in layer 2 are always twisted clockwise with respect to streamlines
in layer 1 at the same geographical location. This can easily be observed where
the streamlines in layer 1 cross the shadow zone boundary, which is after all a
streamline in layer 2. The velocity vector spirals clockwise with increasing
depth in the subtropical gyre. This is a general feature of adiabatic flow in the
models of the subtropical gyre and can also be noted in the flow patterns
predicted by the Rhines and Young model discussed in Chapter 3. Stommel
and Schott (1977) pointed out this fact in an attempt to describe a method to