A Midocean Example
121
WE = -ocx r < r1
= 0
r > r1
(3.6.1)
where r = Jx2 + y 2 • We can think of IX as being the amplitude of the Ekman
pumping, W0, divided by the disk's radius, r1, so that within the "disk" of
forcing, WE= -Wo(xfrt).
The Sverdrup streamfunction is given by (3.5.8). The integral is zero for all
x east of the eastern edge of the circle r = r1 and for all values of IYI > r1.
Within the latitude limits -r1 :=::; y :=::; r1 the Sverdrup solution is thus given by
the integral from the point x to the eastern rim of the circle at:
X(y) = Jrf- y2.
(3.6.2)
Thus:
,/, -~
'd'
f
1
X(y)
'f'BX X
fJH X
(3.6.3)
or:
IX /o [ ( )2 2]
t/ln = 2f3H X y -x
= IX/o [r2 -xz- Y2] r < rl
2{3H 1
(3.6.4)
= 0 r > r1.
It is important to note that because of the antisymmetric form of the
Ekman pumping the Sverdrup transport is equal to zero outside the circle of
forcing and yields a barotropic flow with circular streamlines within the disk of
radius r1•
Now that t/Jn is determined, the geostrophic contours can be easily
calculated. Within the disk of radius r1 they are given by the contours of:
A
IX/oF[ 2 ~ .2]
qz = {Jy + 2f3H r I - - Y r < r1
(3.6.5)
= {Jy r > r1.
Inside the disk the geostrophic contours are circles centered on x = 0, y = y0,
where:
(3.6.6)
i.e., inside the disk: