Ventilation and Homogenization: A Unified Theory
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region acts to further reduce the potential vorticity gradient of the subducted,
ventilatedfluid. The reason for this can be understood easily by examining the
zonal section of the layer thicknesses at the outcrop line where the potential
vorticity in layer 2 is determined. This is shown in panel c of the figure. Only
layers 2 and 3 are present at the outcrop line. The dotted curve is the base of
layer 2 in the case when layer 3 is not in motion while the solid curve is for the
case where the presence of motion in the pool has been taken into account.
Again, because layer 2 now shares the Sverdrup transport with layer 3 the shear
across the interface between the two layers is reduced, and the east-west
variation of the thickness of layer 2 is thus reduced at the outcrop line. Since
the potential vorticity of the subducting fluid in layer 2 at the outcrop line is
fz/h2, the variation of q2 along the outcrop line, and hence everywhere south of
the outcrop line in the region west of the dotted curve in Fig. 4.9.2 is reduced.
Panel d shows a meridional section slicing through the pool region of the layer
depths in the two cases with (solid curves) and without (dashed curves) the
homogenized motion of layer 3. Liu et al. show that the reduction in the
potential vorticity in the ventilated layer above the pool is substantial. For the
parameters chosen the reduction is estimated to be of a factor of 2 or 3.
Thus the nonlinear interplay of the ventilated zone and the homogenized
region is substantial. The ventilated layers reduce the size of the pool region
and also reduce the circulation there below that which would be calculated in
the absence of ventilation. At the same time the effect of the pool region
substantially reduces the potential vorticity gradients in the ventilated zone.
Although the variability of the potential vorticity in the ventilated region and
the determination of this variation at the outcrop line form a conceptually
important part of the dynamics and of the solution, the flow in the subducted
layers of the ventilated region have weak gradients compared to the shadow
zone or the layer directly in contact with the Ekman pumping.
This has important interpretive significance because it implies that the
observation of a region of very low potential vorticity gradient does not in itself
specify the process that produced it. It could be due to the process of
homogenization, as is likely the case for deep layers, but for layers that are also
ventilated there are additional mechanisms, as we have seen in this section, that
can produce zones of weak potential vorticity gradients. This often makes the
observational inference of process problematical.
There are also other effects which tend to render the potential vorticity
gradients weak in subducting layers. We have, for the sake of analytical
simplicity, considered only the cases of outcrop lines that are oriented along
latitude circles. This is a reasonable approximation, but observations show that
the outcrop lines tend to tilt from northwest to southeast in the gyre.
Figure 3.11.3a, for example, shows the outcrop area for the a0 = 26.4 surface
stippled in gray. The relevant winter time outcrop line for the a0 = 26.5 surface
is also shown in Fig. 3.11.4a. In both cases the outcrop line slants northward as
one moves to the west. Since the potential vorticity of the nth layer along its
outcrop line is f fhn, the general increase in hn to the west along the outcrop
231
region acts to further reduce the potential vorticity gradient of the subducted,
ventilatedfluid. The reason for this can be understood easily by examining the
zonal section of the layer thicknesses at the outcrop line where the potential
vorticity in layer 2 is determined. This is shown in panel c of the figure. Only
layers 2 and 3 are present at the outcrop line. The dotted curve is the base of
layer 2 in the case when layer 3 is not in motion while the solid curve is for the
case where the presence of motion in the pool has been taken into account.
Again, because layer 2 now shares the Sverdrup transport with layer 3 the shear
across the interface between the two layers is reduced, and the east-west
variation of the thickness of layer 2 is thus reduced at the outcrop line. Since
the potential vorticity of the subducting fluid in layer 2 at the outcrop line is
fz/h2, the variation of q2 along the outcrop line, and hence everywhere south of
the outcrop line in the region west of the dotted curve in Fig. 4.9.2 is reduced.
Panel d shows a meridional section slicing through the pool region of the layer
depths in the two cases with (solid curves) and without (dashed curves) the
homogenized motion of layer 3. Liu et al. show that the reduction in the
potential vorticity in the ventilated layer above the pool is substantial. For the
parameters chosen the reduction is estimated to be of a factor of 2 or 3.
Thus the nonlinear interplay of the ventilated zone and the homogenized
region is substantial. The ventilated layers reduce the size of the pool region
and also reduce the circulation there below that which would be calculated in
the absence of ventilation. At the same time the effect of the pool region
substantially reduces the potential vorticity gradients in the ventilated zone.
Although the variability of the potential vorticity in the ventilated region and
the determination of this variation at the outcrop line form a conceptually
important part of the dynamics and of the solution, the flow in the subducted
layers of the ventilated region have weak gradients compared to the shadow
zone or the layer directly in contact with the Ekman pumping.
This has important interpretive significance because it implies that the
observation of a region of very low potential vorticity gradient does not in itself
specify the process that produced it. It could be due to the process of
homogenization, as is likely the case for deep layers, but for layers that are also
ventilated there are additional mechanisms, as we have seen in this section, that
can produce zones of weak potential vorticity gradients. This often makes the
observational inference of process problematical.
There are also other effects which tend to render the potential vorticity
gradients weak in subducting layers. We have, for the sake of analytical
simplicity, considered only the cases of outcrop lines that are oriented along
latitude circles. This is a reasonable approximation, but observations show that
the outcrop lines tend to tilt from northwest to southeast in the gyre.
Figure 3.11.3a, for example, shows the outcrop area for the a0 = 26.4 surface
stippled in gray. The relevant winter time outcrop line for the a0 = 26.5 surface
is also shown in Fig. 3.11.4a. In both cases the outcrop line slants northward as
one moves to the west. Since the potential vorticity of the nth layer along its
outcrop line is f fhn, the general increase in hn to the west along the outcrop