Numerical and Observational Evidence
159
again, appears unlikely a priori, that such ventilated layers would satisfy the
conditions of the theorem.
Numerical Experiments
With this a priori uncertainty we are left to ask whether observations can
decide the issue. Two types of "observations" are relevant. The first of these
are the results of numerical experiments. Although numerical calculations
cannot reproduce the natural ocean with sufficient fidelity to substitute for
direct observations and with which they should never be confused, they can be
used to help us test dynamical issues not tractable by analytical methods. Thus,
for example, numerical experiments do contain western boundary currents,
and within the physics of each experiment, whether it is a faithful reproduction
of the natural ocean or not, it is possible to see whether the process of potential
vorticity homogenization is disrupted by a western boundary current in which
substantial dissipation is allowed a priori. In particular, quasi-geostrophic
experiments are particularly illuminating since they do not allow for isopycnal
outcropping, and thus, within the model, the absence of potential vorticity
sources during the journey of fluid through the interior in the lower layers
allows us to concentrate on the possible role of the western boundary current in
upsetting the process of potential vorticity homogenization.
A series of several numerical experiments with the quasi-geostrophic model
each has demonstrated the ability of the homogenization of potential vorticity
to proceed even with the western boundary current forced to act as a conduit
for the closure of the circulation and the potential vorticity isolines. Figure
3.11.1 shows the circulation pattern in the three-layer quasi-geostrophic model
as calculated by Rhines and Schopp (1991). In this model layer I is directly
forced by the Ekman pumping, and layer 3 is too deep (4000 m) to have closed
geostrophic contours in the interior, and its circulation is limited to very small
weak local gyres driven by strong inertial effects associated with the western
boundary current. Layer 2, on the other hand, does have closed geostrophic
contours, and in fact we see that layer 2 shows a large region in which q2 is
essentially homogenized. The isolines of q2 are expelled from the center of the
gyre which is left with a plateau of uniform potential vorticity. Rhines and
Schopp show that this zone is determined almost exactly by the expected shape
of the analytically determined pool region. A detailed analysis of the calculated
western boundary current by the same authors showed it to have a multiple
layer structure. Over most of the width of the western boundary current most
of the streamlines pass through the current in an outer boundary layer in which
friction is unimportant. The potential vorticity of only a small inner region is
substantially affected by dissipation. Thus a posteriori the most important
requirements of the potential vorticity homogenization process are met on
most streamlines. The mixing of potential vorticity within the pool turns out
not to be small, but as we remarked above, it is necessary only that it be small
159
again, appears unlikely a priori, that such ventilated layers would satisfy the
conditions of the theorem.
Numerical Experiments
With this a priori uncertainty we are left to ask whether observations can
decide the issue. Two types of "observations" are relevant. The first of these
are the results of numerical experiments. Although numerical calculations
cannot reproduce the natural ocean with sufficient fidelity to substitute for
direct observations and with which they should never be confused, they can be
used to help us test dynamical issues not tractable by analytical methods. Thus,
for example, numerical experiments do contain western boundary currents,
and within the physics of each experiment, whether it is a faithful reproduction
of the natural ocean or not, it is possible to see whether the process of potential
vorticity homogenization is disrupted by a western boundary current in which
substantial dissipation is allowed a priori. In particular, quasi-geostrophic
experiments are particularly illuminating since they do not allow for isopycnal
outcropping, and thus, within the model, the absence of potential vorticity
sources during the journey of fluid through the interior in the lower layers
allows us to concentrate on the possible role of the western boundary current in
upsetting the process of potential vorticity homogenization.
A series of several numerical experiments with the quasi-geostrophic model
each has demonstrated the ability of the homogenization of potential vorticity
to proceed even with the western boundary current forced to act as a conduit
for the closure of the circulation and the potential vorticity isolines. Figure
3.11.1 shows the circulation pattern in the three-layer quasi-geostrophic model
as calculated by Rhines and Schopp (1991). In this model layer I is directly
forced by the Ekman pumping, and layer 3 is too deep (4000 m) to have closed
geostrophic contours in the interior, and its circulation is limited to very small
weak local gyres driven by strong inertial effects associated with the western
boundary current. Layer 2, on the other hand, does have closed geostrophic
contours, and in fact we see that layer 2 shows a large region in which q2 is
essentially homogenized. The isolines of q2 are expelled from the center of the
gyre which is left with a plateau of uniform potential vorticity. Rhines and
Schopp show that this zone is determined almost exactly by the expected shape
of the analytically determined pool region. A detailed analysis of the calculated
western boundary current by the same authors showed it to have a multiple
layer structure. Over most of the width of the western boundary current most
of the streamlines pass through the current in an outer boundary layer in which
friction is unimportant. The potential vorticity of only a small inner region is
substantially affected by dissipation. Thus a posteriori the most important
requirements of the potential vorticity homogenization process are met on
most streamlines. The mixing of potential vorticity within the pool turns out
not to be small, but as we remarked above, it is necessary only that it be small