A History of Thermocline Theory
145
envy was mixed with the admiration because one always regrets missing out on an
idea that seems so obvious but only in retrospect. I recall that in leaving the seminar I
mentioned to Stommel that the theory seemed to me very powerful, indeed it seemed
to explain, and perhaps had been stimulated by, some earlier modeling experiments
Peter had done with Bill Holland (1980), but one feature of the oceanic thermocline
that it lacked was the outcropping of the isopycnal surfaces within the subtropical
gyre. In the Rhines and Young quasi-geostrophic model each layer was perturbed
only slightly from its rest thickness and so in the quasi-geostrophic layer model the
surface density was a constant. This seemed to me the main direction in which the
Rhines–Young theory could be extended further.
At the time I was involved in some other work and did not do anything to
pick up on this suggestion but, if my memory serves correctly, nearly a year later
Stommel came to my office to show me the results of some numerical calculations
he and Jim Luyten were doing for a two-layer model over a resting abyss. The model
had a single outcrop and they were numerically finding the structure of the interface
heights as a function of latitude; the longitudinal dependence could be independently
determined from the Sverdrup relation. Hank had been coming regularly to talk to me
about his ideas during the year since I had arrived at Woods Hole from Chicago. The
discussions were always deeply interesting; Hank, after all, had a prodigiously creative
mind. Usually, I could provide only encouragement or ask for some clarification but
no further collaboration followed. In this case, however, my overall interest in the
problem and the chance to formulate a simple model of a difficult physical process
really appealed to me. After Hank left my office I brushed aside what I had been
working on and took up the analytical formulation of the problem. After working
out the geostrophic pressure fields in terms of the layer thicknesses of the 2
1
2
-layer
model, I confronted the essential issue. The lower layer north of the outcrop line is
directly exposed to Ekman pumping. In the subtropical gyre it is forced southward
according to the Sverdrup relation and when meeting the outcrop line it becomes
shielded from the Ekman pumping by the upper, lighter layer. What would happen to
the fluid in the lower layer next? Clearly it was being pushed beneath the upper layer.
The word “subduction” came immediately to my mind. In Chicago I had worked
with Frank Richter, a student in the Geophysical Sciences Department, and we had
been thinking hard about mantle convection, downgoing slabs, and a model of that
process had formed Frank’s Ph.D. thesis. This seemed an oceanographic equivalent
except that for the subducted water its potential vorticity would be conserved along its
(unknown) streamline path. For this layer the potential vorticity was just f /h 2 where
h 2 is the thickness of the second layer and that quantity would have to be constant
on a streamline that, because of geostrophy, would be along a line of total depth
h = h 1 + h 2 so that f /h 2 = Q(h) where Q is some yet to be determined function.
This, the determination of Q, was the nub of the problem. As a student I had been
tremendously impressed by Charney’s inertial model of the Gulf Stream (Charney,
1955) in which the functional relationship between the sum of the planetary and
relative vorticity to the external Sverdrup streamfunction needed to be determined.
145
envy was mixed with the admiration because one always regrets missing out on an
idea that seems so obvious but only in retrospect. I recall that in leaving the seminar I
mentioned to Stommel that the theory seemed to me very powerful, indeed it seemed
to explain, and perhaps had been stimulated by, some earlier modeling experiments
Peter had done with Bill Holland (1980), but one feature of the oceanic thermocline
that it lacked was the outcropping of the isopycnal surfaces within the subtropical
gyre. In the Rhines and Young quasi-geostrophic model each layer was perturbed
only slightly from its rest thickness and so in the quasi-geostrophic layer model the
surface density was a constant. This seemed to me the main direction in which the
Rhines–Young theory could be extended further.
At the time I was involved in some other work and did not do anything to
pick up on this suggestion but, if my memory serves correctly, nearly a year later
Stommel came to my office to show me the results of some numerical calculations
he and Jim Luyten were doing for a two-layer model over a resting abyss. The model
had a single outcrop and they were numerically finding the structure of the interface
heights as a function of latitude; the longitudinal dependence could be independently
determined from the Sverdrup relation. Hank had been coming regularly to talk to me
about his ideas during the year since I had arrived at Woods Hole from Chicago. The
discussions were always deeply interesting; Hank, after all, had a prodigiously creative
mind. Usually, I could provide only encouragement or ask for some clarification but
no further collaboration followed. In this case, however, my overall interest in the
problem and the chance to formulate a simple model of a difficult physical process
really appealed to me. After Hank left my office I brushed aside what I had been
working on and took up the analytical formulation of the problem. After working
out the geostrophic pressure fields in terms of the layer thicknesses of the 2
1
2
-layer
model, I confronted the essential issue. The lower layer north of the outcrop line is
directly exposed to Ekman pumping. In the subtropical gyre it is forced southward
according to the Sverdrup relation and when meeting the outcrop line it becomes
shielded from the Ekman pumping by the upper, lighter layer. What would happen to
the fluid in the lower layer next? Clearly it was being pushed beneath the upper layer.
The word “subduction” came immediately to my mind. In Chicago I had worked
with Frank Richter, a student in the Geophysical Sciences Department, and we had
been thinking hard about mantle convection, downgoing slabs, and a model of that
process had formed Frank’s Ph.D. thesis. This seemed an oceanographic equivalent
except that for the subducted water its potential vorticity would be conserved along its
(unknown) streamline path. For this layer the potential vorticity was just f /h 2 where
h 2 is the thickness of the second layer and that quantity would have to be constant
on a streamline that, because of geostrophy, would be along a line of total depth
h = h 1 + h 2 so that f /h 2 = Q(h) where Q is some yet to be determined function.
This, the determination of Q, was the nub of the problem. As a student I had been
tremendously impressed by Charney’s inertial model of the Gulf Stream (Charney,
1955) in which the functional relationship between the sum of the planetary and
relative vorticity to the external Sverdrup streamfunction needed to be determined.