288
Buoyancy Forced Circulation and Cross-Gyre Flow
Figure 5.2.5 shows a cross-gyre solution calculated by Schopp and Arhan
(1986) for the case of deep northward flow. The pool to the west of this region
is kept at rest for simplicity. Schopp and Arhan continued the solution into the
subpolar gyre, assuming that potential vorticity is conserved even there, although it is problematic whether this is true. One of the consequences of this
continuation is a prediction of the outcrop line in which layer 3 becomes
exposed to the Ekman suction of the subpolar gyre. This is shown in panel a of
the figure in which the "inverted V" in the subpolar gyre is the outcrop line.
Panel b shows the flow of fluid across the gyre from south to north in the
narrow band defined by the window. In their calculation Schopp and Arhan
take Hz= 0 so that the window extends all the way to the eastern boundary.
Panels c-e show zonal sections of the layer thicknesses in the subpolar gyre, on
the intergyre boundary, and in the subtropical gyre, respectively. Schopp and
Arhan applied their solution to the eastern North Atlantic and estimated a flux
of about 4.25x 10 6 m 3 s- 1 (4.25 sverdrups) to cross the intergyre boundary.
Chen and Dewar (1993) have extended the theory of cross-gyre communication to a model with three moving layers. As might be expected, the presence of three layers increases the richness of the structure of the possible crossgyre communication. Just as in the case of pools of unventilated flow which are
nested, one beneath the other, and shrink in size to the northwest, the presence
of additional layers allows deeper windows which can appear to the west of the
window that we have discussed. Chen and Dewar call attention to the observed
structure of potential in layer between the ao = 27.3 and 27.6 surfaces in the
North Atlantic and shown in Fig. 5.2.6. The contours stretch from the subpolar to the subtropical gyre, and the region shown has been described by
McDowell et al. (1982) as a flow linking subpolar water in Irminger Sea with
the subtropical gyre. This would be an example of southward flow through the
window.
We therefore have, from a purely theoretical point of view, an additional
nonuniqueness in the solution for the circulation structure. Solutions with
cross-gyre communication are possible whenever the wind forcing is strong
enough to produce unventilated pools with geostrophic contours (potential
vorticity isolines) which meet the intergyre boundary. However, a solution in
which the window, while possibly open, remains closed, is also always a possible steady solution. That is, a solution with hz = Hz and h3 = H3 on the line
of zero D6 is consistent. The nonuniqueness is a consequence of our use of
nondissipative, steady dynamics and could be resolved by relaxing either of
these idealizations.
Schopp (1988) described a heuristic model of the time-dependent dynamics
of the nonlinear Rossby waves on the intergyre boundary (see also Dewar
1987) and obtained an equation similar to the classical KdV equation (Korteweg and de Vreis 1895) . He chose, as initial conditions on the boundary, to
have the interface between the layers initially flat and then to lower the interface at the western boundary (as if there were heating in the west) and raise
it at the eastern boundary (cooling there) and held at that position during the
Buoyancy Forced Circulation and Cross-Gyre Flow
Figure 5.2.5 shows a cross-gyre solution calculated by Schopp and Arhan
(1986) for the case of deep northward flow. The pool to the west of this region
is kept at rest for simplicity. Schopp and Arhan continued the solution into the
subpolar gyre, assuming that potential vorticity is conserved even there, although it is problematic whether this is true. One of the consequences of this
continuation is a prediction of the outcrop line in which layer 3 becomes
exposed to the Ekman suction of the subpolar gyre. This is shown in panel a of
the figure in which the "inverted V" in the subpolar gyre is the outcrop line.
Panel b shows the flow of fluid across the gyre from south to north in the
narrow band defined by the window. In their calculation Schopp and Arhan
take Hz= 0 so that the window extends all the way to the eastern boundary.
Panels c-e show zonal sections of the layer thicknesses in the subpolar gyre, on
the intergyre boundary, and in the subtropical gyre, respectively. Schopp and
Arhan applied their solution to the eastern North Atlantic and estimated a flux
of about 4.25x 10 6 m 3 s- 1 (4.25 sverdrups) to cross the intergyre boundary.
Chen and Dewar (1993) have extended the theory of cross-gyre communication to a model with three moving layers. As might be expected, the presence of three layers increases the richness of the structure of the possible crossgyre communication. Just as in the case of pools of unventilated flow which are
nested, one beneath the other, and shrink in size to the northwest, the presence
of additional layers allows deeper windows which can appear to the west of the
window that we have discussed. Chen and Dewar call attention to the observed
structure of potential in layer between the ao = 27.3 and 27.6 surfaces in the
North Atlantic and shown in Fig. 5.2.6. The contours stretch from the subpolar to the subtropical gyre, and the region shown has been described by
McDowell et al. (1982) as a flow linking subpolar water in Irminger Sea with
the subtropical gyre. This would be an example of southward flow through the
window.
We therefore have, from a purely theoretical point of view, an additional
nonuniqueness in the solution for the circulation structure. Solutions with
cross-gyre communication are possible whenever the wind forcing is strong
enough to produce unventilated pools with geostrophic contours (potential
vorticity isolines) which meet the intergyre boundary. However, a solution in
which the window, while possibly open, remains closed, is also always a possible steady solution. That is, a solution with hz = Hz and h3 = H3 on the line
of zero D6 is consistent. The nonuniqueness is a consequence of our use of
nondissipative, steady dynamics and could be resolved by relaxing either of
these idealizations.
Schopp (1988) described a heuristic model of the time-dependent dynamics
of the nonlinear Rossby waves on the intergyre boundary (see also Dewar
1987) and obtained an equation similar to the classical KdV equation (Korteweg and de Vreis 1895) . He chose, as initial conditions on the boundary, to
have the interface between the layers initially flat and then to lower the interface at the western boundary (as if there were heating in the west) and raise
it at the eastern boundary (cooling there) and held at that position during the