28
Homogeneous Models of the Ocean Circulation
fwE
- n
- ~---L...-1 y X
t 0 E
_
Fig. 2.2.1. Schematic cross section of the homogeneous model. The model decribes the motion in a
layer of thickness D surmounted by a mixed layer in which the wind-driven turbulent stresses drive
an Ekman transport whose divergence yields the Ekman vertical velocity wE. The layer is bounded
below by a viscous Ekman layer that couples the flow to the bottom and helps dissipate the motion
ot/J
U = - -
oy'
where:
V=
ot/J
OX
(2.2.2)
(2.2.3)
The fluid pressure is p, its density is p, and fo is the Corio lis parameter at the
central latitude of the gyre.
On the f3 plane the vorticity equation takes a particularly simple form.
Since the horizontal velocity is independent of depth, the only way in which the
total vorticity can be altered in the geostrophic region between the upper and
lower boundary layers is by vortex tube stretching of the total vorticity or by
lateral diffusion of the relative vorticity. Thus if:
C=ov_ou
ox oy
is the relative vorticity, it satisfies the equation:
(2.2.4)
(2.2.5)
The first term on the right side is the vorticity production by the stretching of
the total vortex filaments by the vertical velocity while the second term is the
lateral diffusion of vorticity. Since f3y «fo by the f3 plane approximation, and
C « fo by the geostrophic approximation:
Homogeneous Models of the Ocean Circulation
fwE
- n
- ~---L...-1 y X
t 0 E
_
Fig. 2.2.1. Schematic cross section of the homogeneous model. The model decribes the motion in a
layer of thickness D surmounted by a mixed layer in which the wind-driven turbulent stresses drive
an Ekman transport whose divergence yields the Ekman vertical velocity wE. The layer is bounded
below by a viscous Ekman layer that couples the flow to the bottom and helps dissipate the motion
ot/J
U = - -
oy'
where:
V=
ot/J
OX
(2.2.2)
(2.2.3)
The fluid pressure is p, its density is p, and fo is the Corio lis parameter at the
central latitude of the gyre.
On the f3 plane the vorticity equation takes a particularly simple form.
Since the horizontal velocity is independent of depth, the only way in which the
total vorticity can be altered in the geostrophic region between the upper and
lower boundary layers is by vortex tube stretching of the total vorticity or by
lateral diffusion of the relative vorticity. Thus if:
C=ov_ou
ox oy
is the relative vorticity, it satisfies the equation:
(2.2.4)
(2.2.5)
The first term on the right side is the vorticity production by the stretching of
the total vortex filaments by the vertical velocity while the second term is the
lateral diffusion of vorticity. Since f3y «fo by the f3 plane approximation, and
C « fo by the geostrophic approximation: