Continuous Models of the Ventilated Thermocline
261
pumping is a function only of latitude. From a physical point of view we have
defined the subtropical gyre as the region in which the Ekman pumping is
downward so that the subsurface density is determined by the surface values.
This would seem to identify the zero line of the Ekman pumping with the
boundary of the subtropical gyre. On the other hand, the zero line of the
Sverdrup transport divides the horizontal circulation into separate and welldefined gyres. Huang chose the first definition to define the northern gyre
boundary. Although the meridional velocity vanishes on the zero line of
Ekman pumping, the zonal velocity does not, and therefore there is horizontal
flow carrying fluid across the gyre boundary defined in this way. Huang specifies
the potential vorticity of that flow from hydrographic data.
Figure 4.11.4c shows the position of the outcrop lines for the density
surfaces used in the calculation. Note that the outcrop lines slope northwestsoutheast. Figure 4.11.4d shows the mixed layer depth. It increases from about
50 m near the southern boundary of the gyre to 400 m in the northeast corner
of the basin.
Figure 4.11.5 shows the salient features of the solution. In panel a we see
the overall depth of the thermocline as calculated by Huang (1989b). The
thermocline increases in depth to the northwest. It is realistically shallow in the
southern part of the gyre, with depths less than 1 km. Only north of 30° does
the thermocline reach a depth exceeding 1.5 km. On shallow density surfaces,
such as the ae = 26.2 surface shown in panel b, the shadow zone is very small.
Note that on this surface most of the streamlines originate at the outcrop line.
That is, on this shallow surface most of the layer is ventilated, and the western
pool is very small, as we would anticipate from our discussion of the layer
models. The effect of the sloping mixed layer base and the zonal variation of
density is evident in panel c. The outcrop line is quite far north but at least half
of the transport on this surface occurs in a relatively narrow zone in the eastern
part of the basin and enters the thermocline through the sloping mixed layer
base. Even on this surface the ventilation process in dominant. Deeper
surfaces, ae = 27.1 and ae = 27.7, are shown in the final panels. In the former
most of the flow originates from the gyre boundary. In the latter case the
shadow zone occupies most of the density surface, and the flow shrinks to a
narrow band of slow moving water and carries very little transport (0.2
sverdrups). Figure 4.11.4f shows a zonal cross section of the density field. The
density surfaces are flat in the shadow zone in the east. Note that the density
surfaces intersect the eastern wall at nonzero depths.
The continuous model, and its numerical finite-difference form, is a
limiting case of the layer models discussed in earlier sections of this chapter.
The successful implementation of the continuous model not only allows
precise predictions of thermocline structure and velocity, given the surface
wind stress and the surface density field, but also verifies the essential validity
of the physical processes seen in a more accessible form in the low-order layer
models.
261
pumping is a function only of latitude. From a physical point of view we have
defined the subtropical gyre as the region in which the Ekman pumping is
downward so that the subsurface density is determined by the surface values.
This would seem to identify the zero line of the Ekman pumping with the
boundary of the subtropical gyre. On the other hand, the zero line of the
Sverdrup transport divides the horizontal circulation into separate and welldefined gyres. Huang chose the first definition to define the northern gyre
boundary. Although the meridional velocity vanishes on the zero line of
Ekman pumping, the zonal velocity does not, and therefore there is horizontal
flow carrying fluid across the gyre boundary defined in this way. Huang specifies
the potential vorticity of that flow from hydrographic data.
Figure 4.11.4c shows the position of the outcrop lines for the density
surfaces used in the calculation. Note that the outcrop lines slope northwestsoutheast. Figure 4.11.4d shows the mixed layer depth. It increases from about
50 m near the southern boundary of the gyre to 400 m in the northeast corner
of the basin.
Figure 4.11.5 shows the salient features of the solution. In panel a we see
the overall depth of the thermocline as calculated by Huang (1989b). The
thermocline increases in depth to the northwest. It is realistically shallow in the
southern part of the gyre, with depths less than 1 km. Only north of 30° does
the thermocline reach a depth exceeding 1.5 km. On shallow density surfaces,
such as the ae = 26.2 surface shown in panel b, the shadow zone is very small.
Note that on this surface most of the streamlines originate at the outcrop line.
That is, on this shallow surface most of the layer is ventilated, and the western
pool is very small, as we would anticipate from our discussion of the layer
models. The effect of the sloping mixed layer base and the zonal variation of
density is evident in panel c. The outcrop line is quite far north but at least half
of the transport on this surface occurs in a relatively narrow zone in the eastern
part of the basin and enters the thermocline through the sloping mixed layer
base. Even on this surface the ventilation process in dominant. Deeper
surfaces, ae = 27.1 and ae = 27.7, are shown in the final panels. In the former
most of the flow originates from the gyre boundary. In the latter case the
shadow zone occupies most of the density surface, and the flow shrinks to a
narrow band of slow moving water and carries very little transport (0.2
sverdrups). Figure 4.11.4f shows a zonal cross section of the density field. The
density surfaces are flat in the shadow zone in the east. Note that the density
surfaces intersect the eastern wall at nonzero depths.
The continuous model, and its numerical finite-difference form, is a
limiting case of the layer models discussed in earlier sections of this chapter.
The successful implementation of the continuous model not only allows
precise predictions of thermocline structure and velocity, given the surface
wind stress and the surface density field, but also verifies the essential validity
of the physical processes seen in a more accessible form in the low-order layer
models.