286
Buoyancy Forced Circulation and Cross-Gyre Flow
imum of the Ross by wave speed curve with the Sverdrup transport line determines the western boundary of the window at tfJ = t/J2• A little algebra shows that:
( hzh 3 )
= [
1 +rz3(Hz/H)z z] yil +rz 3
H2 max
rz3+{l+v'l+rz3}
(5.2.24)
where rz3 = Yz/YJ.
For an Ekman pumping independent of longitude this would lead to a
window of width:
(5.2.25)
There is no a priori reason necessarily to expect the flow in the lower layer
through the window to be southward. Northward flow seems equally likely.
However, northward flow in the lower layer would require that the base of
layer 3 at z = -h deepens westward. The right side of (5.2.22) must then increase ash decreases so that the window opens west of its eastern limit when
the two sides of (5.2.22) are equated. We can see from the figure that for the
parameters chosen the Rossby speed would decrease as h decreases from H, and
that no solution would be possible. This, however, is a function of the parameters which represent the stratification at the inter-gyre boundary, i.e., rz3
and the ratio of the layer depths.
Consider the function I= hzh3 which is the right side of (5.2.22) aside from
a constant factor. Its variation ash is varied is given by:
(5.2.26)
On the intergyre boundary, where the Ekman pumping is zero, the Sverdrup
relation (5.2.5) allows (5.2.26) to be written:
M = __!__h [rz3h~ + 2hzh- hz]c5h
rz3 z
(5.2.27)
where we use h3 = h - hz to eliminate h3 in arriving at (5.2.27). At the eastern
edge of the window each of the layer thicknesses take on their rest values, for
example, h =Hand hz =Hz. In order for the window to extend westward M
must be positive regardless of the sign of c5h since Us increases westward. Thus,
if c5h > 0 (southward lower layer flow in the window) the square bracket in
(5.2.27) must be positive, which requires that:
Hz Jl + r23 -1
->
.
Hrz3
(5.2.28)
If Hz/ H is less than this critical value, southward flow in the lower layer
across the intergyre boundary is not possible. On the other hand, when Hz/ His
Buoyancy Forced Circulation and Cross-Gyre Flow
imum of the Ross by wave speed curve with the Sverdrup transport line determines the western boundary of the window at tfJ = t/J2• A little algebra shows that:
( hzh 3 )
= [
1 +rz3(Hz/H)z z] yil +rz 3
H2 max
rz3+{l+v'l+rz3}
(5.2.24)
where rz3 = Yz/YJ.
For an Ekman pumping independent of longitude this would lead to a
window of width:
(5.2.25)
There is no a priori reason necessarily to expect the flow in the lower layer
through the window to be southward. Northward flow seems equally likely.
However, northward flow in the lower layer would require that the base of
layer 3 at z = -h deepens westward. The right side of (5.2.22) must then increase ash decreases so that the window opens west of its eastern limit when
the two sides of (5.2.22) are equated. We can see from the figure that for the
parameters chosen the Rossby speed would decrease as h decreases from H, and
that no solution would be possible. This, however, is a function of the parameters which represent the stratification at the inter-gyre boundary, i.e., rz3
and the ratio of the layer depths.
Consider the function I= hzh3 which is the right side of (5.2.22) aside from
a constant factor. Its variation ash is varied is given by:
(5.2.26)
On the intergyre boundary, where the Ekman pumping is zero, the Sverdrup
relation (5.2.5) allows (5.2.26) to be written:
M = __!__h [rz3h~ + 2hzh- hz]c5h
rz3 z
(5.2.27)
where we use h3 = h - hz to eliminate h3 in arriving at (5.2.27). At the eastern
edge of the window each of the layer thicknesses take on their rest values, for
example, h =Hand hz =Hz. In order for the window to extend westward M
must be positive regardless of the sign of c5h since Us increases westward. Thus,
if c5h > 0 (southward lower layer flow in the window) the square bracket in
(5.2.27) must be positive, which requires that:
Hz Jl + r23 -1
->
.
Hrz3
(5.2.28)
If Hz/ H is less than this critical value, southward flow in the lower layer
across the intergyre boundary is not possible. On the other hand, when Hz/ His