410
y
Y1s
Y2n
Y2s
Y3n
Y3s
X=Xr
Abyssal Circulation
Y=Yn
Y=Ys
Fig. 7.5.1. Abyssal basin with its idealized ridge system. The ridge system, at x = Xt, has gaps at the
locations shown. The jth ridge element extends from y = y 1 • to y = YJn
the vorticity equation is written in terms of the geostrophic streamfunction
(7.5.1).
The pumping velocity wo is an arbitrary function of latitude and longitude.
However, the longitudinal dependence is relatively inconsequential for the
present argument. The dependence on latitude is important, and it is imagined
that the pumping velocity would, in the absence of the ridge, produce a largescale closed gyre. That is, it is anticipated that the interior streamfunction has a
minimum within the basin representing the center of a large cyclonic gyre of the
type anticipated in the Stommel-Arons theory.
The presence of the ridge produces boundary-layer structures on the
eastern side of the ridges (the western side of the eastern subbasin). To describe
these boundary layers with maximum simplicity a bottom friction model is
used so that the entire dynamics is governed by the vorticity balance:
{3v = fwo- r(av- au)
H
ax ay
(7.5.2)
where r is a parameter which measures the effect of bottom friction. The
bottom friction is imagined to be negligible outside western boundary layers
which requires that:
r
{3( - ) « 1.
Xe
Xt
(7.5.3)
When the velocities are written in terms of the geostrophic streamfunction
(7.5.2) becomes: