138
Vertical Structure: Baroclinic Quasi-Geostrophic Models
(3.9.3)
so that the geostrophic contours are given by the isolines of:
(J2 = f3y + Fl/JB
= f3y- fo;~(y) F(xe - x)
(3.9.4)
where F = f5Hfy 1H ,H2 = 1/L~ and y 1 is the reduced gravity associated with
the interface between layers 1 and 2.
Consider the geostrophic contour that originates at the eastern boundary
at the latitude Ye· The value of q2 for this contour is f3Ye and the isoline of this
geostrophic contour thus satisfies:
(xe- x) = f32~Ye - y)H .
foF[-wE(y)]
(3.9.5)
Recall from (3.5.14) that q2 is equal to q2, the potential vorticity in layer 2,
if layer 2 is motionless. This gives us a physically immediate way to think about
the q2 isolines.
If we momentarily imagine then, that the Sverdrup circulation were limited
to the upper layer, the anticyclonic swirl in the subtropical gyre would depress
the interface between layer 1, which is in motion, and layer 2, which is at rest
and whose base must therefore be level. The thickness of layer 2 would thus
decrease westward from the eastern boundary. Its upper surface has been
depressed downward by the motion of the upper layer, and its lower surface is
flat. An isoline of constant q2 = f /h2 must therefore trend southward as it
strikes westward from the eastern boundary so that the decrease in f offsets the
decrease in h2 . If the isolines are diverted southward strongly enough, this can
open up a region in the northwest, shielded from the eastern boundary, in
which motion in layer 2 is no longer prohibited. Baroclinic Rossby waves from
the eastern boundary are guided around, and prevented from penetrating, a
zone in which contours of q2 are disconnected from the eastern boundary.
Although each point of the eastern boundary is a point of origin of a fh
isoline, not every point in the basin is bathed by isolines starting from the
eastern boundary if the distortion of the geostrophic contours is strong enough.
As an example, consider the Ekman pumping:
w. 0 y
WE=- osmnL.
(3.9.6)
The geostrophic contours are given by the isolines of:
Vertical Structure: Baroclinic Quasi-Geostrophic Models
(3.9.3)
so that the geostrophic contours are given by the isolines of:
(J2 = f3y + Fl/JB
= f3y- fo;~(y) F(xe - x)
(3.9.4)
where F = f5Hfy 1H ,H2 = 1/L~ and y 1 is the reduced gravity associated with
the interface between layers 1 and 2.
Consider the geostrophic contour that originates at the eastern boundary
at the latitude Ye· The value of q2 for this contour is f3Ye and the isoline of this
geostrophic contour thus satisfies:
(xe- x) = f32~Ye - y)H .
foF[-wE(y)]
(3.9.5)
Recall from (3.5.14) that q2 is equal to q2, the potential vorticity in layer 2,
if layer 2 is motionless. This gives us a physically immediate way to think about
the q2 isolines.
If we momentarily imagine then, that the Sverdrup circulation were limited
to the upper layer, the anticyclonic swirl in the subtropical gyre would depress
the interface between layer 1, which is in motion, and layer 2, which is at rest
and whose base must therefore be level. The thickness of layer 2 would thus
decrease westward from the eastern boundary. Its upper surface has been
depressed downward by the motion of the upper layer, and its lower surface is
flat. An isoline of constant q2 = f /h2 must therefore trend southward as it
strikes westward from the eastern boundary so that the decrease in f offsets the
decrease in h2 . If the isolines are diverted southward strongly enough, this can
open up a region in the northwest, shielded from the eastern boundary, in
which motion in layer 2 is no longer prohibited. Baroclinic Rossby waves from
the eastern boundary are guided around, and prevented from penetrating, a
zone in which contours of q2 are disconnected from the eastern boundary.
Although each point of the eastern boundary is a point of origin of a fh
isoline, not every point in the basin is bathed by isolines starting from the
eastern boundary if the distortion of the geostrophic contours is strong enough.
As an example, consider the Ekman pumping:
w. 0 y
WE=- osmnL.
(3.9.6)
The geostrophic contours are given by the isolines of: