Ventilation and Homogenization: A Unified Theory
D~ +Hf = - 2
13
12 fr!>' wE(¢',8)Rcos8 d¢'.
1'3 }q,
219
( 4.8.5)
This implies that on the outcrop line h4 is a constant. Thus there is no flow
across the outcrop line in layer 4 from layer 3 in this solution.
If the Ekman suction is strong enough, the thickness of layer 4 also
vanishes on a curve 4(8) which lies everywhere within, i.e., northwestward of,
the previous outcrop line for layer 3. The same is subsequently true for deeper
layers. One isopycnal interface after another is pulled to the surface leading to
a horizontal "jelly roll" pattern, as shown in Fig. 4.8.la, for the flow in which
only the exposed density surface is in motion.
The highly artificial character of this solution is evident. Quite apart from
the question of whether adiabatic dynamics is valid in the subpolar gyre, where
strong buoyancy loss to the atmosphere is observed, the direction of
information flow which is upward and from the west leads us to expect that
the solution obtained is nonunique. In distinction to the subtropical gyre,
where information is passed downward and southward from the outcrop lines,
and where alterations of the solution in the west did not affect the solution
already found in the eastern part of the ocean, our circulation solution for the
subpolar gyre is very vulnerable to effects of altering the solution in the west. If,
for example, we imagine flow in layer 4 to differ from zero near the western
boundary and to enter the subpolar gyre from the western boundary, traveling
along lines of constant q4 , we would have to recalculate the circulation that we
have assumed in layer 3. Among other things this would alter the position of
the outcrop line, which is fundamental to the solution. If we then ask what the
effect of possible motion in layer 5 is, this would again require an entire
reiteration of the total solution. The fact that information flows eastward along
the intergyre boundary contaminates the calculation of the position of the
outcrop line and renders the solution fundamentally nonunique. Only a full
solution resolving the western boundary current can resolve the issue. At this
time such solutions are lacking, and the state of the theory of the subpolar gyre
must be considered unsatisfactory.
4.9 Ventilation and Homogenization: A Unified Theory
We have discussed two mechanisms by which the thermocline can be set into
motion. The first, discussed in Chapter 3, involves the Rhines and Young
recirculation theory for fluid layers that are isolated from sources of potential
vorticity such as subduction and ventilation. In such unventilated layers the
motion is deduced by appealing to the principle of homogenization of potential
vorticity within closed isolines of potential vorticity. The wrapping of the
isolines and their closure is produced by the motion itself. We saw that
D~ +Hf = - 2
13
12 fr!>' wE(¢',8)Rcos8 d¢'.
1'3 }q,
219
( 4.8.5)
This implies that on the outcrop line h4 is a constant. Thus there is no flow
across the outcrop line in layer 4 from layer 3 in this solution.
If the Ekman suction is strong enough, the thickness of layer 4 also
vanishes on a curve 4(8) which lies everywhere within, i.e., northwestward of,
the previous outcrop line for layer 3. The same is subsequently true for deeper
layers. One isopycnal interface after another is pulled to the surface leading to
a horizontal "jelly roll" pattern, as shown in Fig. 4.8.la, for the flow in which
only the exposed density surface is in motion.
The highly artificial character of this solution is evident. Quite apart from
the question of whether adiabatic dynamics is valid in the subpolar gyre, where
strong buoyancy loss to the atmosphere is observed, the direction of
information flow which is upward and from the west leads us to expect that
the solution obtained is nonunique. In distinction to the subtropical gyre,
where information is passed downward and southward from the outcrop lines,
and where alterations of the solution in the west did not affect the solution
already found in the eastern part of the ocean, our circulation solution for the
subpolar gyre is very vulnerable to effects of altering the solution in the west. If,
for example, we imagine flow in layer 4 to differ from zero near the western
boundary and to enter the subpolar gyre from the western boundary, traveling
along lines of constant q4 , we would have to recalculate the circulation that we
have assumed in layer 3. Among other things this would alter the position of
the outcrop line, which is fundamental to the solution. If we then ask what the
effect of possible motion in layer 5 is, this would again require an entire
reiteration of the total solution. The fact that information flows eastward along
the intergyre boundary contaminates the calculation of the position of the
outcrop line and renders the solution fundamentally nonunique. Only a full
solution resolving the western boundary current can resolve the issue. At this
time such solutions are lacking, and the state of the theory of the subpolar gyre
must be considered unsatisfactory.
4.9 Ventilation and Homogenization: A Unified Theory
We have discussed two mechanisms by which the thermocline can be set into
motion. The first, discussed in Chapter 3, involves the Rhines and Young
recirculation theory for fluid layers that are isolated from sources of potential
vorticity such as subduction and ventilation. In such unventilated layers the
motion is deduced by appealing to the principle of homogenization of potential
vorticity within closed isolines of potential vorticity. The wrapping of the
isolines and their closure is produced by the motion itself. We saw that