Stommel-Arons Theory: Abyssal Flow on the Sphere
399
Tw = -2So sin 0.
(7.3.15)
The western boundary layer transport is southward for all () ~ 0. At the
pole the transport is exactly twice the source strength since the boundary
current must carry southward the fluid issuing from the source as well as all of
theinterior flow impinging on the apex. This interior flux, which comprises a
basinwide recirculation, has a northward mass flux at the apex equal to the
source strength. Thus at the apex half the mass flux of the boundary layer
comes from the source and half from the recirculating interior flow. The
interior is fed from the western boundary current as the current flows
southward, as indicated in Fig. 7.3.1. The transport of the western boundary
current falls to zero as the current approaches the equator. During its flow
southward the western boundary current loses a total mass flux equal to 2So.
One half of this flux is recirculated in the interior and ends up at the apex to
return through the western boundary current. The other half is lost through the
interface to the thermocline and is directly replaced in the western boundary
layer at the apex by the source.
Of course there is no reason why the sector need be isolated from the other
hemisphere. That is, there is no a priori reason why the balance in (7.3.14) need
apply if there are sources or sinks of fluid in the other hemisphere. The interior
flow is still zero at the equator but the transport of the western boundary
current at the equator, from (7.3.13) would be:
(7.3.16)
If the upwelling to the thermocline is greater than the source strength at the
pole, there must be an import of fluid across the equator from the south, and
Tw is positive. If the source strength is larger than the upwelling, the reverse is
true, and the boundary current flows across the equator from the northern to
southern hemispheres. This is likely to be the situation in the North Atlantic.
On the other hand, if we consider a similar sector in which there is no
source at the apex, all the water must be imported from the southern
hemisphere. In such a case So would be zero and Tw is given by:
(7.3.17)
instead of (7.3.15). This might be the case in a simple model of the North
Pacific which is thought to have no local sources of deep water (Warren 1981).
The interior flow is the same as in the previous example. However, now at the
equator the boundary current is positive as the current delivers the necessary
flow to the northern hemisphere sector. As the current flows northward, its
mass is exhausted as the flow through the upper surface of the abyss into the
thermocline draws fluid from the boundary layer. In fact at 30°N the transport
vanishes. North of this latitude the boundary current actually moves
southward, driven by the cyclonic recirculation of the interior flow.
399
Tw = -2So sin 0.
(7.3.15)
The western boundary layer transport is southward for all () ~ 0. At the
pole the transport is exactly twice the source strength since the boundary
current must carry southward the fluid issuing from the source as well as all of
theinterior flow impinging on the apex. This interior flux, which comprises a
basinwide recirculation, has a northward mass flux at the apex equal to the
source strength. Thus at the apex half the mass flux of the boundary layer
comes from the source and half from the recirculating interior flow. The
interior is fed from the western boundary current as the current flows
southward, as indicated in Fig. 7.3.1. The transport of the western boundary
current falls to zero as the current approaches the equator. During its flow
southward the western boundary current loses a total mass flux equal to 2So.
One half of this flux is recirculated in the interior and ends up at the apex to
return through the western boundary current. The other half is lost through the
interface to the thermocline and is directly replaced in the western boundary
layer at the apex by the source.
Of course there is no reason why the sector need be isolated from the other
hemisphere. That is, there is no a priori reason why the balance in (7.3.14) need
apply if there are sources or sinks of fluid in the other hemisphere. The interior
flow is still zero at the equator but the transport of the western boundary
current at the equator, from (7.3.13) would be:
(7.3.16)
If the upwelling to the thermocline is greater than the source strength at the
pole, there must be an import of fluid across the equator from the south, and
Tw is positive. If the source strength is larger than the upwelling, the reverse is
true, and the boundary current flows across the equator from the northern to
southern hemispheres. This is likely to be the situation in the North Atlantic.
On the other hand, if we consider a similar sector in which there is no
source at the apex, all the water must be imported from the southern
hemisphere. In such a case So would be zero and Tw is given by:
(7.3.17)
instead of (7.3.15). This might be the case in a simple model of the North
Pacific which is thought to have no local sources of deep water (Warren 1981).
The interior flow is the same as in the previous example. However, now at the
equator the boundary current is positive as the current delivers the necessary
flow to the northern hemisphere sector. As the current flows northward, its
mass is exhausted as the flow through the upper surface of the abyss into the
thermocline draws fluid from the boundary layer. In fact at 30°N the transport
vanishes. North of this latitude the boundary current actually moves
southward, driven by the cyclonic recirculation of the interior flow.