Western intensification
151
0
d
1
x
y
C
A
ψ = constant
wind-stress vector τ =(τ x ,τ y ) satisfy the relation
δ S
L
C
u · ds =
C
τ · ds
and provide a physical explanation of the result.
(6.4) Fofonoff inertial flow
Consider a general pure inertial quasi-geostrophic flow in a homogeneous
ocean. This flow satisfies the barotropic vorticity equation with zero wind
stress (T = 0) and without frictional effects (δ S = δ M =0).
a. Show that the resulting equation is given by
u ·∇
δ I
L
2
∇
2 ψ + y
=0
where u is the horizontal velocity vector. Give a physical interpretation of this
vorticity balance.
Consider now an inertial current and the situation that the ocean is bounded
at x =0by a coast. The flow is purely zonal for x →∞and it has a
dimensionless horizontal velocity field given by u = −1 and v =0.
b. Demonstrate that in this case, the absolute vorticity is a linear function of
the streamfunction.
c. Consider the western boundary layer (with δ I ≪ L) and show that the total
solution is given by
ψ W (x, y)=(y − y 0 )(1 − e
−xL/δ I )