62
/
t v (x, y2)
______ t _______ Y2
R
-------~------- Y1
v (x, Y1)
Homogeneous Models of the Ocean Circulation
- u
Fig. 2.11.1. Open region R covering a
segment of the western boundary-layer
region over which the vorticity equation
is integrated
X=O
(2.11.3)
Thus, in the region R the vorticity balance depends locally on a competition
between advection and dissipation. The flux of planetary vorticity, which is the
second term on the right side of (2.11.3), brings negative (anticyclonic) vorticity
into the boundary layer in the subtropical gyre since 1/J 1 is positive there and
zero on the eastern boundary. Since the velocity is nondivergent:
Jh \1 · (ilf) dx dy = Jh vf3 dx dy = Jh f3 ~~ dx dy
1
Y2
=
f31/11(0,y)dy
YI
(2.11.4)
which shows the relation between the f3 term in (2.11.3) and the total flux of
planetary vorticity into R.
This flux into the layer is balanced in a steady state by a frictional flux
through the side wall and consumption of vorticity through the bottom and by
an inertial flux out of R [the first term on the right side of (2.11.3)]. It is