144
Joseph Pedlosky
was listed as a second author, was “Simple theoretical models of the circulation.”
There was no hint that Peter and Bill had been working on thermocline theory and,
in fact, the seminar started with an elementary, although incisive, review of Sverdrup
theory for the midocean. Abruptly, the seminar shifted focus to a rather fundamental
question. If one considers the region of the thermocline as consisting of a sequence of
frictionless, immiscible layers, i.e., an ideal fluid, what would drive into motion any
layer not immediately in contact with the overlying Ekman layer? It would appear
that only the uppermost layer would carry the total Sverdrup transport. Then, if one
constantly increased the number of such layers, it would appear that the Sverdrup
transport would be confined to an increasingly narrow layer near the sea surface
as the resolution of the model increased with correspondingly large velocity. This
reductio ad absurdum emblemizes the fundamental physical problem of thermocline
theory, that is, the mechanism and the scale of penetration of the surface wind forcing.
If the more obvious question to ask is why the surface forcing should be arrested at
a vertical scale short of the full ocean depth, an equally fundamental question, if
more subtle, is how the forcing can penetrate at all to a domain in which frictional
stresses or thermal turbulent diffusion are not important. It was this question that
Rhines and Young addressed and their solution was brilliant and elegant. If each of
the layers used to resolve the region of the thermocline becomes thinner and thinner as
more layers are added to increase the vertical resolution of the model, the uppermost
layer containing all the Sverdrup transport will have large velocities, so large that the
isolines of potential vorticity of the layer beneath, defined as the Coriolis parameter
divided by the layer thickness, f /h, would be grossly distorted from latitude circles
as the upper interface of the layer responds, by the thermal wind balance, to the strong
velocities. If the potential vorticity trajectories distort enough so that they avoid the
eastern boundary, it is possible that a free mode of geostrophic motion can close on
those distorted contours. Even an infinitesimal forcing, say by an eddy flux of potential
vorticity, can then resonate with that free mode and drive an order one motion in the
layer previously considered at rest. That motion in the second layer would alter the
potential vorticity of the layer beneath it and so on, and the motion would burrow
down to a depth that depended on the wind forcing and the layer thicknesses. Under
some rather plausible assumptions of the nature of the potential vorticity flux, Peter
and Bill deduced that the subsurface motion in the layers not in direct contact with the
Ekman pumping would have uniform potential vorticity. At one stroke, this provided
both an explanation of the depth wind-driven motion and a method for its calculation
(Rhines and Young, 1982a,b). Moving to a layered model, rather than a continuous
one, might seem a step backward but the resulting physical insights produced an
enormous advance in our understanding of the physics of the thermocline.
I remember the very strong impression Peter’s seminar made on me. Not only
was the theory itself extremely elegant but the thought that came most forcefully to my
mind was that a sense of physics had been restored to the search for an understanding
of the thermocline. I remember that Hank Stommel, sitting beside me in the lecture,
shared that view as well. And, as most working scientists will appreciate, a sense of
Joseph Pedlosky
was listed as a second author, was “Simple theoretical models of the circulation.”
There was no hint that Peter and Bill had been working on thermocline theory and,
in fact, the seminar started with an elementary, although incisive, review of Sverdrup
theory for the midocean. Abruptly, the seminar shifted focus to a rather fundamental
question. If one considers the region of the thermocline as consisting of a sequence of
frictionless, immiscible layers, i.e., an ideal fluid, what would drive into motion any
layer not immediately in contact with the overlying Ekman layer? It would appear
that only the uppermost layer would carry the total Sverdrup transport. Then, if one
constantly increased the number of such layers, it would appear that the Sverdrup
transport would be confined to an increasingly narrow layer near the sea surface
as the resolution of the model increased with correspondingly large velocity. This
reductio ad absurdum emblemizes the fundamental physical problem of thermocline
theory, that is, the mechanism and the scale of penetration of the surface wind forcing.
If the more obvious question to ask is why the surface forcing should be arrested at
a vertical scale short of the full ocean depth, an equally fundamental question, if
more subtle, is how the forcing can penetrate at all to a domain in which frictional
stresses or thermal turbulent diffusion are not important. It was this question that
Rhines and Young addressed and their solution was brilliant and elegant. If each of
the layers used to resolve the region of the thermocline becomes thinner and thinner as
more layers are added to increase the vertical resolution of the model, the uppermost
layer containing all the Sverdrup transport will have large velocities, so large that the
isolines of potential vorticity of the layer beneath, defined as the Coriolis parameter
divided by the layer thickness, f /h, would be grossly distorted from latitude circles
as the upper interface of the layer responds, by the thermal wind balance, to the strong
velocities. If the potential vorticity trajectories distort enough so that they avoid the
eastern boundary, it is possible that a free mode of geostrophic motion can close on
those distorted contours. Even an infinitesimal forcing, say by an eddy flux of potential
vorticity, can then resonate with that free mode and drive an order one motion in the
layer previously considered at rest. That motion in the second layer would alter the
potential vorticity of the layer beneath it and so on, and the motion would burrow
down to a depth that depended on the wind forcing and the layer thicknesses. Under
some rather plausible assumptions of the nature of the potential vorticity flux, Peter
and Bill deduced that the subsurface motion in the layers not in direct contact with the
Ekman pumping would have uniform potential vorticity. At one stroke, this provided
both an explanation of the depth wind-driven motion and a method for its calculation
(Rhines and Young, 1982a,b). Moving to a layered model, rather than a continuous
one, might seem a step backward but the resulting physical insights produced an
enormous advance in our understanding of the physics of the thermocline.
I remember the very strong impression Peter’s seminar made on me. Not only
was the theory itself extremely elegant but the thought that came most forcefully to my
mind was that a sense of physics had been restored to the search for an understanding
of the thermocline. I remember that Hank Stommel, sitting beside me in the lecture,
shared that view as well. And, as most working scientists will appreciate, a sense of