232
Theory of the Ventilated Thermocline
line tends to be offset by the increase in/along such a slanting outcrop line and
thus reduces the variation in the potential vorticity of the subducted fluid. This
leads to the ventilated layer having even weaker gradients in the region on
ventilation than hitherto calculated. Indeed, it is possible that a sloping
outcrop line can lead to ventilated, subducting fluid having completely uniform
potential vorticity. We can easily find the shape of such a line.
Suppose we consider the two layer model again and consider the potential
vorticity at the first outcrop line. Let the position of the outcrop line be given
by:
f = h(¢).
(4.9.28)
Then for the potential vorticity to be constant along the outcrop line we would
have:
f
h fe
hz
h
Hz
(4.9.29)
where fe is the value of h on the eastern boundary. Along the outcrop line his
equal to hz and is given by (4.9.2) so an implicit equation for h(¢) is given by:
h(¢) = (Dij(¢~h) + 1)1/Z
fe
Hz
(4.9.30)
which can be used to solve for h(¢). Figure 4.9.4 shows the outcrop line for
the case in which the Ekman pumping is again sinusoidal and fe/ fo is 0.4. The
outcrop line slopes most strongly in the northwest-southeast direction near the
eastern boundary as in the observations, rendering the subducted fluid in this
idealized case entirely uniform. Of course this does not explain why the outcrop
line should slope in that sense. To the degree that the clockwise circulation
itself advects the surface density field in a clockwise fashion we might expect
such a tilt. Pedlosky et al. (1984), in a simple model in which the surface density
field was determined by the flow and its interaction with atmospheric heat
fluxes, suggested the way in which the coupled dynamics of an active mixed
layer could lead to such slopes of the outcrop line.
When the recirculation theory and the ventilation theory are unified, an
elegant structure is predicted for the thermocline. Starting with the deepest
unventilated layers that do not outcrop in the subtropical gyre, the circulation
occupies a small bowl in the northwest corner of the basin, as we saw in
Chapter 3. As we proceed higher in the water column, this bowl expands in size
in both latitude and longitude but is always detached from the eastern
boundary. Within the bowl potential vorticity is uniform. At higher levels and
lower densities, whose surfaces outcrop in the gyre, the circulation is ventilated
and laterally more extensive. The potential vorticity is inhomogeneous,
although it may be weakly so, in the ventilated regions. In the northwest
portions of the ventilated zones regions of homogenized potential vorticity may
occur. These are more extensive on the deeper ventilated layers, and the
Theory of the Ventilated Thermocline
line tends to be offset by the increase in/along such a slanting outcrop line and
thus reduces the variation in the potential vorticity of the subducted fluid. This
leads to the ventilated layer having even weaker gradients in the region on
ventilation than hitherto calculated. Indeed, it is possible that a sloping
outcrop line can lead to ventilated, subducting fluid having completely uniform
potential vorticity. We can easily find the shape of such a line.
Suppose we consider the two layer model again and consider the potential
vorticity at the first outcrop line. Let the position of the outcrop line be given
by:
f = h(¢).
(4.9.28)
Then for the potential vorticity to be constant along the outcrop line we would
have:
f
h fe
hz
h
Hz
(4.9.29)
where fe is the value of h on the eastern boundary. Along the outcrop line his
equal to hz and is given by (4.9.2) so an implicit equation for h(¢) is given by:
h(¢) = (Dij(¢~h) + 1)1/Z
fe
Hz
(4.9.30)
which can be used to solve for h(¢). Figure 4.9.4 shows the outcrop line for
the case in which the Ekman pumping is again sinusoidal and fe/ fo is 0.4. The
outcrop line slopes most strongly in the northwest-southeast direction near the
eastern boundary as in the observations, rendering the subducted fluid in this
idealized case entirely uniform. Of course this does not explain why the outcrop
line should slope in that sense. To the degree that the clockwise circulation
itself advects the surface density field in a clockwise fashion we might expect
such a tilt. Pedlosky et al. (1984), in a simple model in which the surface density
field was determined by the flow and its interaction with atmospheric heat
fluxes, suggested the way in which the coupled dynamics of an active mixed
layer could lead to such slopes of the outcrop line.
When the recirculation theory and the ventilation theory are unified, an
elegant structure is predicted for the thermocline. Starting with the deepest
unventilated layers that do not outcrop in the subtropical gyre, the circulation
occupies a small bowl in the northwest corner of the basin, as we saw in
Chapter 3. As we proceed higher in the water column, this bowl expands in size
in both latitude and longitude but is always detached from the eastern
boundary. Within the bowl potential vorticity is uniform. At higher levels and
lower densities, whose surfaces outcrop in the gyre, the circulation is ventilated
and laterally more extensive. The potential vorticity is inhomogeneous,
although it may be weakly so, in the ventilated regions. In the northwest
portions of the ventilated zones regions of homogenized potential vorticity may
occur. These are more extensive on the deeper ventilated layers, and the