220
Theory of the Ventilated Thermocline
observational and numerical studies seem to validate these ideas, at least for
layers which are deep enough in the subtropical gyre to remain unaffected
directly by Ekman pumping in the gyre. On the other hand, shallower density
layers which outcrop in the subtropical gyre are ventilated and set into motion
by the process of subduction even in regions where they are shielded from the
direct action of Ekman pumping by overlying layers. These two theoretical
ideas are complementary rather than dichotomous since they apply to different
levels in the thermocline. At first glance one should be able to unite the two
theories by simply stacking the ventilated thermocline on top of the
homogenized, unventilated layers in which the fluid recirculates without direct
contact with the Ekman layer. A little reflection shows that although this is
roughly correct, the situation is actually a good deal more complex. This is
because the interaction between the two regions in the vertical is nonlinear. At
each geographical position the sum of the transports in the ventilated and
unventilated layers must equal the Sverdrup transport. The expression for the
Sverdrup transport in terms of the interface depths, for example, is given by
(4.3.15) and thus nonlinearly couples all of the layer depths. If we wish to
consider a unified model containing both mechanisms we must simultaneously
consider ventilation and recirculation. This unification was achieved by
Pedlosky and Young (1983) and more recently extended by Liu et al. (1993).
We discuss the relevant ideas here in the simplest context that contains
both mechanisms. Thus we return to the model of Section 4.4 whose
configuration is given in Fig. 4.4.1. Layer 3 in the earlier treatment of Section
4.4 was assumed to be at rest since it was not directly forced anywhere in the
subtropical gyre. We saw in Chapter 3 that although such a presupposition can
lead to consistent solutions, the resulting flows are not necessarily the most
likely to be observed if closed potential vorticity contours appear in the deeper,
unventilated layer. In this section we investigate whether layer 3 can be put into
motion, and if so what that motion would be. Since layer 3 lies under two
ventilated layers, one of which subducts at 8 = 82, we are therefore taking up
the question of whether the ventilated thermocline solution already found in
Section 4.4 is unique, or whether layer 3 can move and so affect and modify the
circulation in layers 1 and 2. At the same time, by discussing the possibility of
recirculation of the deep layers in the context of planetary scale dynamics we
are also relaxing the constraints of Chapter 3 required by quasi-geostrophy and
can consistently allow large excursions, over the scale of the gyre, of the
interface depths.
As we reconsider the model of Fig. 4.4.1, we again start our analysis in the
region north of the first outcrop line at 8 = 82 where f = h. Iflayer 3 is going
to be set into motion by the process of potential vorticity homogenization, this
can occur only if the potential vorticity isolines in layer 3 are sufficiently
distorted, as described in Chapter 3, so that they elude the eastern boundary
and curl around instead to intersect the western boundary or close on
themselves in the interior. Near the eastern boundary, as we showed above, the
distortions of the interface of deeper layers are small, and we can anticipate
Theory of the Ventilated Thermocline
observational and numerical studies seem to validate these ideas, at least for
layers which are deep enough in the subtropical gyre to remain unaffected
directly by Ekman pumping in the gyre. On the other hand, shallower density
layers which outcrop in the subtropical gyre are ventilated and set into motion
by the process of subduction even in regions where they are shielded from the
direct action of Ekman pumping by overlying layers. These two theoretical
ideas are complementary rather than dichotomous since they apply to different
levels in the thermocline. At first glance one should be able to unite the two
theories by simply stacking the ventilated thermocline on top of the
homogenized, unventilated layers in which the fluid recirculates without direct
contact with the Ekman layer. A little reflection shows that although this is
roughly correct, the situation is actually a good deal more complex. This is
because the interaction between the two regions in the vertical is nonlinear. At
each geographical position the sum of the transports in the ventilated and
unventilated layers must equal the Sverdrup transport. The expression for the
Sverdrup transport in terms of the interface depths, for example, is given by
(4.3.15) and thus nonlinearly couples all of the layer depths. If we wish to
consider a unified model containing both mechanisms we must simultaneously
consider ventilation and recirculation. This unification was achieved by
Pedlosky and Young (1983) and more recently extended by Liu et al. (1993).
We discuss the relevant ideas here in the simplest context that contains
both mechanisms. Thus we return to the model of Section 4.4 whose
configuration is given in Fig. 4.4.1. Layer 3 in the earlier treatment of Section
4.4 was assumed to be at rest since it was not directly forced anywhere in the
subtropical gyre. We saw in Chapter 3 that although such a presupposition can
lead to consistent solutions, the resulting flows are not necessarily the most
likely to be observed if closed potential vorticity contours appear in the deeper,
unventilated layer. In this section we investigate whether layer 3 can be put into
motion, and if so what that motion would be. Since layer 3 lies under two
ventilated layers, one of which subducts at 8 = 82, we are therefore taking up
the question of whether the ventilated thermocline solution already found in
Section 4.4 is unique, or whether layer 3 can move and so affect and modify the
circulation in layers 1 and 2. At the same time, by discussing the possibility of
recirculation of the deep layers in the context of planetary scale dynamics we
are also relaxing the constraints of Chapter 3 required by quasi-geostrophy and
can consistently allow large excursions, over the scale of the gyre, of the
interface depths.
As we reconsider the model of Fig. 4.4.1, we again start our analysis in the
region north of the first outcrop line at 8 = 82 where f = h. Iflayer 3 is going
to be set into motion by the process of potential vorticity homogenization, this
can occur only if the potential vorticity isolines in layer 3 are sufficiently
distorted, as described in Chapter 3, so that they elude the eastern boundary
and curl around instead to intersect the western boundary or close on
themselves in the interior. Near the eastern boundary, as we showed above, the
distortions of the interface of deeper layers are small, and we can anticipate