398
Abyssal Circulation
Fig. 7.3.1. Circulation in a spherical
sector driven by the source So in the
apex of the basin and uniform upwelling at the upper surface of the abyss.
To determine the transport in the western boundary current a mass balance
is made for the area north of the
arbitrarily chosen latitude ()
the vertical motion through the interface into the thermocline. Thus the
northward flux of the interior velocity T1 is, using (7.3.6):
(7.3.10)
while the fluid entering the thermocline and leaving the abyss in that subsector
is:
(7.3.11)
If Tw is the northward transport of the western boundary current, and So is the
source strength, the mass balance implies that:
or, using (7.3.10) and (7.3.11):
Tw = -2woR 2 (4Je- c/Jw) sin()+ [woR 2 (4Je- c/Jw)- So].
If the mass is balanced over this northern hemispheric sector:
r/2r"·
So= Jo }"' woR 2 cos()dqyd() = woR 2 (4Je- c/Jw)·
0 c/Jw
(7.3.12)
(7.3.13)
(7.3.14)
In this case, where the sector is isolated from the rest of the ocean, the two
terms in the square bracket in (7.3.13) exactly balance and: