278
Buoyancy Forced Circulation and Cross-Gyre Flow
In fact, and as we have noted above, diagnostic studies of the subpolar
gyre, for example Luyten et al. (1985), imply that there the cross-isopycnal flux
is locally large compared to the Ekman pumping with the consequence that
potential vorticity can no longer be considered conserved. To discuss the dynamics of the subpolar gyre and go beyond the simple model of Section 4.8 we
must construct an alternative dynamical framework.
At the same time, one of the implicit assumptions we have used throughout
our discussion has been the identification of the barotropic boundary of the
gyre, defined on the basis of the Sverdrup transport, with the gyre boundary at
every level (or in every layer). When the Ekman pumping is a function only of
latitude, this boundary is given unambiguously as the latitude circle where WE
vanishes. In this case the Sverdrup function D~, given by ( 4.4.5), also vanishes
there. The situation is more complex when WE is a function oflongitude as well.
This is perhaps the more realistic situation. In the North Atlantic, for example,
the line on which the Ekman pumping vanishes stretches from about 40°N on
the western side of the ocean to about 55°N on the eastern side (see
Fig. 4.11.4a). The zero lines of Ekman pumping and D6 no longer coincide.
Because of the integration from the east in its definition, the zero line of D6 lies
to the west and north of the zero line of WE.
In the solutions that we have so far found, the isopycnal depths are all
constant on the line where D6 is zero and therefore this line is the most obvious
defining boundary of the gyre since no geostrophic flow crosses this line in
those solutions. In the case in which the line D6 = 0 lies west and north of the
zero line of Ekman pumping, a zone between the two lines opens up in which
the meridional velocity in the subtropical gyre is northward. Flow can cross the
zero Ekman pumping line when it is tilted with respect to a latitude circle since
only the meridional flow is zero there but the Sverdrup zonal flow is nonzero
and thus crosses the tilted line of WE= 0. This can lead to very interesting
changes in the gyre circulation structure (see, for example, Rhines and Schopp
1991) although the basic theory is not fundamentally altered.
A more fundamental question is whether the gyre flow can actually cross
the line D~ = 0. This, as we noted, is the natural definition of the gyre
boundary when we consider the geostrophic transport or the barotropic velocity. The question arises as to whether a solution also exists in which there is
baroclinic flow across the line D6 = 0 which at the same time has zero transport
across that line. That is, can there be a purely internal mode of fluid interchange between the subtropical and subpolar gyres in which, at each latitude
and longitude along the boundary, there is no net transport of mass? Such a net
interchange in which, say, warm water is going northward while cold water is
going southward across the gyre boundary would yield a net heat flux even in
the absence of a net mass flux.
We see below that both the problem of nonadiabatic motion, in which
potential vorticity is not conserved, and the problem of cross-gyre flow involve
the question of the flow of information in the gyre. We begin by discussing the
question of cross-gyre flow.
Buoyancy Forced Circulation and Cross-Gyre Flow
In fact, and as we have noted above, diagnostic studies of the subpolar
gyre, for example Luyten et al. (1985), imply that there the cross-isopycnal flux
is locally large compared to the Ekman pumping with the consequence that
potential vorticity can no longer be considered conserved. To discuss the dynamics of the subpolar gyre and go beyond the simple model of Section 4.8 we
must construct an alternative dynamical framework.
At the same time, one of the implicit assumptions we have used throughout
our discussion has been the identification of the barotropic boundary of the
gyre, defined on the basis of the Sverdrup transport, with the gyre boundary at
every level (or in every layer). When the Ekman pumping is a function only of
latitude, this boundary is given unambiguously as the latitude circle where WE
vanishes. In this case the Sverdrup function D~, given by ( 4.4.5), also vanishes
there. The situation is more complex when WE is a function oflongitude as well.
This is perhaps the more realistic situation. In the North Atlantic, for example,
the line on which the Ekman pumping vanishes stretches from about 40°N on
the western side of the ocean to about 55°N on the eastern side (see
Fig. 4.11.4a). The zero lines of Ekman pumping and D6 no longer coincide.
Because of the integration from the east in its definition, the zero line of D6 lies
to the west and north of the zero line of WE.
In the solutions that we have so far found, the isopycnal depths are all
constant on the line where D6 is zero and therefore this line is the most obvious
defining boundary of the gyre since no geostrophic flow crosses this line in
those solutions. In the case in which the line D6 = 0 lies west and north of the
zero line of Ekman pumping, a zone between the two lines opens up in which
the meridional velocity in the subtropical gyre is northward. Flow can cross the
zero Ekman pumping line when it is tilted with respect to a latitude circle since
only the meridional flow is zero there but the Sverdrup zonal flow is nonzero
and thus crosses the tilted line of WE= 0. This can lead to very interesting
changes in the gyre circulation structure (see, for example, Rhines and Schopp
1991) although the basic theory is not fundamentally altered.
A more fundamental question is whether the gyre flow can actually cross
the line D~ = 0. This, as we noted, is the natural definition of the gyre
boundary when we consider the geostrophic transport or the barotropic velocity. The question arises as to whether a solution also exists in which there is
baroclinic flow across the line D6 = 0 which at the same time has zero transport
across that line. That is, can there be a purely internal mode of fluid interchange between the subtropical and subpolar gyres in which, at each latitude
and longitude along the boundary, there is no net transport of mass? Such a net
interchange in which, say, warm water is going northward while cold water is
going southward across the gyre boundary would yield a net heat flux even in
the absence of a net mass flux.
We see below that both the problem of nonadiabatic motion, in which
potential vorticity is not conserved, and the problem of cross-gyre flow involve
the question of the flow of information in the gyre. We begin by discussing the
question of cross-gyre flow.