A History of Thermocline Theory
147
A key feature of this first model was that all layer thicknesses vanished on
the eastern boundary to satisfy the no-normal flow condition there. This particularly
troubled Hank and he insisted that there ought to be some way to save a finite layer
thickness on the eastern boundary. Why couldn’t the subducted layer just be motionless near the eastern boundary? It was a good question like all of Hank’s were and
due to his insistence I was moved to try to find a solution that could accomplish that.
I settled on knitting together two solutions, one in which, for a two-layer model, the
second layer was first arbitrarily at rest near the eastern wall and one in which the
lower layer was in motion due to the subduction from the outcrop line and then sought
to satisfy the compatibility condition that the layer thicknesses be continuous at the
joining line between them. Of course it turned out that the joining line was just the
trajectory of the easternmost path issuing from the outcrop line on the eastern boundary so that the total solution had a natural but non-self-similar form. This trajectory
defined what we called the Shadow Zone in analogy with optics. If one thought of the
subducted fluid as ventilating the lower thermocline, this was the region not reached
by any ventilated pathway. It remained in the shadow of the eastern boundary and
was not illuminated by “rays” from the outcrop line and so did not carry potential
vorticity information from the outcrop line. At this point the choice of the eastern
region as stagnant was arbitrary and I will return to that point later. Continuing the
solution with the Shadow Zone past the second outcrop line to the south led to a
complex foliation of the solution and an increasing departure from the ideas that the
thermocline could have a self-similar structure. Additional special domains appeared
naturally in the model. An isolated region near the western boundary of the model was
formed by a streamline in the subducted fluid that emanated from the intersection of
the western boundary and the outcrop line. It seemed unlikely to us that such a zone
would be at rest and with the Rhines and Young ideas in mind we entirely arbitrarily
assigned that zone a constant potential vorticity equal to the potential vorticity on the
bounding streamline. The idea was simply that eddy mixing and recirculation in this
region might result in homogenized potential vorticity.
An earlier issue that arose in conversations with Hank was to what part of the
subtropical gyre the model should be thought to apply. Hank’s suggestion was that
we should think about a so-called “mid-ocean gyre” one that had a rather artificial
distribution of Ekman pumping whose integral in longitude vanishes at each latitude
so that as much fluid downwelled as upwelled on each latitude circle. This would allow
a circulation that would close without the need of western boundary currents that were
not in our model. We talked a great deal about the advantages of this type of model but
I believed strongly that the effect of our theory on the community would be greater
if we just boldly presented it as a theory for the entire subtropical gyre and accepted
that some undetermined, western part of the solution would be “contaminated” by
effects from an active western boundary layer not considered in our model. We also
attempted to extend the solution into the subpolar region but it was clear to us that
our solution was an arbitrary one, deficient physically even if formally correct.
147
A key feature of this first model was that all layer thicknesses vanished on
the eastern boundary to satisfy the no-normal flow condition there. This particularly
troubled Hank and he insisted that there ought to be some way to save a finite layer
thickness on the eastern boundary. Why couldn’t the subducted layer just be motionless near the eastern boundary? It was a good question like all of Hank’s were and
due to his insistence I was moved to try to find a solution that could accomplish that.
I settled on knitting together two solutions, one in which, for a two-layer model, the
second layer was first arbitrarily at rest near the eastern wall and one in which the
lower layer was in motion due to the subduction from the outcrop line and then sought
to satisfy the compatibility condition that the layer thicknesses be continuous at the
joining line between them. Of course it turned out that the joining line was just the
trajectory of the easternmost path issuing from the outcrop line on the eastern boundary so that the total solution had a natural but non-self-similar form. This trajectory
defined what we called the Shadow Zone in analogy with optics. If one thought of the
subducted fluid as ventilating the lower thermocline, this was the region not reached
by any ventilated pathway. It remained in the shadow of the eastern boundary and
was not illuminated by “rays” from the outcrop line and so did not carry potential
vorticity information from the outcrop line. At this point the choice of the eastern
region as stagnant was arbitrary and I will return to that point later. Continuing the
solution with the Shadow Zone past the second outcrop line to the south led to a
complex foliation of the solution and an increasing departure from the ideas that the
thermocline could have a self-similar structure. Additional special domains appeared
naturally in the model. An isolated region near the western boundary of the model was
formed by a streamline in the subducted fluid that emanated from the intersection of
the western boundary and the outcrop line. It seemed unlikely to us that such a zone
would be at rest and with the Rhines and Young ideas in mind we entirely arbitrarily
assigned that zone a constant potential vorticity equal to the potential vorticity on the
bounding streamline. The idea was simply that eddy mixing and recirculation in this
region might result in homogenized potential vorticity.
An earlier issue that arose in conversations with Hank was to what part of the
subtropical gyre the model should be thought to apply. Hank’s suggestion was that
we should think about a so-called “mid-ocean gyre” one that had a rather artificial
distribution of Ekman pumping whose integral in longitude vanishes at each latitude
so that as much fluid downwelled as upwelled on each latitude circle. This would allow
a circulation that would close without the need of western boundary currents that were
not in our model. We talked a great deal about the advantages of this type of model but
I believed strongly that the effect of our theory on the community would be greater
if we just boldly presented it as a theory for the entire subtropical gyre and accepted
that some undetermined, western part of the solution would be “contaminated” by
effects from an active western boundary layer not considered in our model. We also
attempted to extend the solution into the subpolar region but it was clear to us that
our solution was an arbitrary one, deficient physically even if formally correct.