Theory of the Ventilated Thermocline
Properties of the Two-Layer Solution
The solution that we have obtained so far is composed of flow in two regions,
the shadow zone and the ventilated region in layer 2. There is a strong variation
of structure from one region to the other, and this immediately demonstrates
the non-self-similar nature of the flow. The ideal fluid flow has critical curves, in
the two-layer model, for example, this is the shadow zone boundary across
which the solution possesses weak discontinuities, for example, the jump in the
slope of the interface surfaces.
Figure 4.4.4 shows various images of the solution. In this example the
Ekman pumping has been chosen in the form:
wE=- Wo JJ sin(rrf/fo)
h
(4.4.25)
which diverges linearly at the equator but leaves Dij finite, in fact zero, at the
equator. In the figures shown the depth is scaled with H 2 , the depth of the
thermocline on the eastern boundary. W0 has been chosen to be
1.5 x 10- 4 cmjs, the ocean width is 3000 km and y 2 has been taken as
1 em s- 2 • H 2 is taken to be 670 m. This yields:
D2
--% = 2(1 -
e) sin(rc/ / /o).
H2
(4.4.26)
Figure 4.4.4a shows the streamlines in the lower layer. As anticipated by
the previous discussion, the region east of the shadow zone is at rest. The flow
in the lower layer consists of a giant anticyclonic circulation exiting from the
western boundary in the north and reentering it in the south. We recall that this
interior solution assumes that the western boundary layer accepts the interior
flow and returns it as required by the solution but our discussion of the simpler
one-layer model in Chapter 2 reminds us that the physics of the western
boundary current is not that simple and accommodating. We must expect at
least a portion of the present solution, in the western region, to be sharply
altered by the presence of a western current that may detach from the
boundary and impinge on the interior. Or, for small enough dissipation, the
Fig. 4.4.4a-f. Circulation pattern for the two-layer model. The outcrop line is purely zonal and is
indicated by the crosses extending the width of the basin. The shadow zone boundary is delineated
by asterisks which initiate at the eastern boundary and pull away from the boundary at the
intersection of the outcrop line with the eastern wall. a Streamlines (and h) in the lower layer. The
shaded region is the "pool" region of constant potential vorticity described in Section 4.6. b
Streamlines of the flow in the upper layer. Note the kink in the upper layer streamlines as they cross
the shadow zone boundary. c Potential vorticity of the lower layer. Note the decrease in the
variation of q2 in the ventilated region. d Meridional cross section showing the layer thicknesses. e
Zonal cross-section of the layer thicknesses. f Perspective view of the base of the thermocline. Note
the region of the shadow zone in which the base of the thermocline is flat