402
Abyssal Circulation
stagnation point in the western boundary layer moves only slightly, i.e., to
28°N from 30°N. If 8n becomes small on the other hand (e.g., the Indian
Ocean), the latitude where the boundary current changes direction becomes
1/28n. If, instead, the two sources are equal, i.e., if Sn = Ss = S:
-
2("' _A. ){sin8n+sin8s_2. 8}
Tw - woR '+'e '+'w
2
Sill
.
(7.3.23)
If the southern boundary of the region lies in the southern hemisphere,
sines< 0. If the domain is symmetric, i.e., if es =-en the first term in the final
bracket of (7.3.23) will vanishes, and the boundary-layer transport vanishes
only on the equator. In this case, where both the source strength and the
geometry of the two hemispheres are perfect mirror images of each other, there
is no interchange across the equator in either the interior or boundary layer.
The situation is shown in Fig. 7.3.2. Note the need in general for northern and
southern boundary layers required to close the flow produced by the
circulation in the interior.
When the sources and each of the hemispheric basins are mirror images,
the two hemispheres are isolated from each other. When the symmetry is
broken, either by unequal source strengths or by dissimilar basin geometries in
the two hemispheres, there results a flux across the equator in the western
boundary current, and the two hemispheres are in communication. This lack of
symmetry is certainly the more realistic situation and therefore we expect to see
cross-equatorward transport in the western boundary layer in all basins.
A further illuminating example presented by Stommel and Arons in their
original paper is shown in Fig. 7.3.3. A hemispheric sector is partly blocked by
a barrier at the longitude ¢* which stretches from the apex to a latitude 8*. The
barrier is meant to represent a continent, and it is of interest to see its effect on
the deep circulation driven by a source, S0, placed to the south of the continent.
The source can be thought of either as the actual location of production of
deep water or as the point of entry of fluid from the western boundary layer
into the basin.
The interior meridional flow is still given everywhere by (7.3.6). Consider
the region north of 8 = 8*. There are two subsectors, one on each side of the
barrier. The total upwelling into the thermocline for the entire region north of
8 is given by (7.3.11). For the subsector to the right of the continent and in the
region north of the latitude 8 = 8*, the total mass balance for the region
¢ 2: ¢* is:
(7.3.24)
so that the boundary layer transport, T :, on the eastern side of the continent is
given by:
(7.3.25)
Abyssal Circulation
stagnation point in the western boundary layer moves only slightly, i.e., to
28°N from 30°N. If 8n becomes small on the other hand (e.g., the Indian
Ocean), the latitude where the boundary current changes direction becomes
1/28n. If, instead, the two sources are equal, i.e., if Sn = Ss = S:
-
2("' _A. ){sin8n+sin8s_2. 8}
Tw - woR '+'e '+'w
2
Sill
.
(7.3.23)
If the southern boundary of the region lies in the southern hemisphere,
sines< 0. If the domain is symmetric, i.e., if es =-en the first term in the final
bracket of (7.3.23) will vanishes, and the boundary-layer transport vanishes
only on the equator. In this case, where both the source strength and the
geometry of the two hemispheres are perfect mirror images of each other, there
is no interchange across the equator in either the interior or boundary layer.
The situation is shown in Fig. 7.3.2. Note the need in general for northern and
southern boundary layers required to close the flow produced by the
circulation in the interior.
When the sources and each of the hemispheric basins are mirror images,
the two hemispheres are isolated from each other. When the symmetry is
broken, either by unequal source strengths or by dissimilar basin geometries in
the two hemispheres, there results a flux across the equator in the western
boundary current, and the two hemispheres are in communication. This lack of
symmetry is certainly the more realistic situation and therefore we expect to see
cross-equatorward transport in the western boundary layer in all basins.
A further illuminating example presented by Stommel and Arons in their
original paper is shown in Fig. 7.3.3. A hemispheric sector is partly blocked by
a barrier at the longitude ¢* which stretches from the apex to a latitude 8*. The
barrier is meant to represent a continent, and it is of interest to see its effect on
the deep circulation driven by a source, S0, placed to the south of the continent.
The source can be thought of either as the actual location of production of
deep water or as the point of entry of fluid from the western boundary layer
into the basin.
The interior meridional flow is still given everywhere by (7.3.6). Consider
the region north of 8 = 8*. There are two subsectors, one on each side of the
barrier. The total upwelling into the thermocline for the entire region north of
8 is given by (7.3.11). For the subsector to the right of the continent and in the
region north of the latitude 8 = 8*, the total mass balance for the region
¢ 2: ¢* is:
(7.3.24)
so that the boundary layer transport, T :, on the eastern side of the continent is
given by:
(7.3.25)