A History of Thermocline Theory
149
further, that all the higher derivatives forming the Taylor series would also have to be
zero. Hence, any correct solution would be a null one and not at all like ours. After
a few really bad minutes I called Hank and pointed out that the theorem would be
valid in a region near the eastern boundary but only up to the shadow zone boundary
where the first and higher derivatives of the interface thicknesses were not continuous.
The bounding streamline for the Shadow Zone is a characteristic of the hyperbolic
advective system and weak singularities in the derivatives of the variables are natural
and limit the region of validity of the Taylor series . What Killworth’s theorem actually
proved was that our Shadow Zone needed to be truly at rest and so we had chosen
well that solution.
Of course, in spite of our overall satisfaction we also realized that our analysis
in many ways fell short of being a full solution to the thermocline problem. We did
not explain what determined the layer thickness on the eastern boundary (later work
allowed many layers to have such finite thicknesses, e.g., Pedlosky and Robbins,
1991), we still had to find the connection between our model and that of Rhines
and Young (that came later with a joint paper, Pedlosky and Young, 1983), and we
were keenly aware of the very provisional nature of the constant potential vorticity
solution we had desperately employed in the nonventilated western “Pool” region
of our model. Several important theoretical efforts have since been made to discuss
that question, alter our solution, and put that part of the theory on firmer ground, in
particular the recent interesting work of Dewar et al. (2005) and Radko and Marshall
(2005). The biggest lack, still valid in my opinion, is the lack of coupling with
the thermohaline circulation. Some progress along these lines followed the work of
Salmon (1990) and Samelson and Vallis (1997) that carried through the original,
heuristic argument of Welander (1971) and demonstrated the presence of a region of
sharp gradients at the base of the adiabatic thermocline with the associated prediction
of a cross isopycnal velocity that links the thermocline and the abyssal circulation.
Additionally, Huang (1988, 1989) has developed a numerical implementation of a
multilayer model whose limiting form as the layer number increases is equivalent
to a continuously stratified model of the thermocline. Extending the theory into the
equatorial zone also provides a simple model for the Equatorial Undercurrent and the
shape of the equatorial thermocline and emphasizes a link between the midlatitude
and equatorial oceans (e.g., Pedlosky, 1987).
With all its flaws, the ventilated thermocline remains a useful null hypothesis.
We thought of it as an attempt to see just how much of the thermocline could be
understood ignoring all other physical processes than just the simplest adiabatic,
laminar dynamics. Eddy dynamics, micro-scale diffusion, air–sea buoyancy fluxes
were all ignored on aesthetic rather than deductive grounds. At least some of these
have since been proven to have been good guesses (see Ledwell et al., 1993); others
are probably less so. Indeed, it is so simple a solution that perhaps its greatest value
is to serve as a tool for further improvements, alterations, or even, should it prove to
be necessary, a clear basis for considering radical alternatives. After all, the rule is:
what is modern today will seem primitive and dated in the future.
149
further, that all the higher derivatives forming the Taylor series would also have to be
zero. Hence, any correct solution would be a null one and not at all like ours. After
a few really bad minutes I called Hank and pointed out that the theorem would be
valid in a region near the eastern boundary but only up to the shadow zone boundary
where the first and higher derivatives of the interface thicknesses were not continuous.
The bounding streamline for the Shadow Zone is a characteristic of the hyperbolic
advective system and weak singularities in the derivatives of the variables are natural
and limit the region of validity of the Taylor series . What Killworth’s theorem actually
proved was that our Shadow Zone needed to be truly at rest and so we had chosen
well that solution.
Of course, in spite of our overall satisfaction we also realized that our analysis
in many ways fell short of being a full solution to the thermocline problem. We did
not explain what determined the layer thickness on the eastern boundary (later work
allowed many layers to have such finite thicknesses, e.g., Pedlosky and Robbins,
1991), we still had to find the connection between our model and that of Rhines
and Young (that came later with a joint paper, Pedlosky and Young, 1983), and we
were keenly aware of the very provisional nature of the constant potential vorticity
solution we had desperately employed in the nonventilated western “Pool” region
of our model. Several important theoretical efforts have since been made to discuss
that question, alter our solution, and put that part of the theory on firmer ground, in
particular the recent interesting work of Dewar et al. (2005) and Radko and Marshall
(2005). The biggest lack, still valid in my opinion, is the lack of coupling with
the thermohaline circulation. Some progress along these lines followed the work of
Salmon (1990) and Samelson and Vallis (1997) that carried through the original,
heuristic argument of Welander (1971) and demonstrated the presence of a region of
sharp gradients at the base of the adiabatic thermocline with the associated prediction
of a cross isopycnal velocity that links the thermocline and the abyssal circulation.
Additionally, Huang (1988, 1989) has developed a numerical implementation of a
multilayer model whose limiting form as the layer number increases is equivalent
to a continuously stratified model of the thermocline. Extending the theory into the
equatorial zone also provides a simple model for the Equatorial Undercurrent and the
shape of the equatorial thermocline and emphasizes a link between the midlatitude
and equatorial oceans (e.g., Pedlosky, 1987).
With all its flaws, the ventilated thermocline remains a useful null hypothesis.
We thought of it as an attempt to see just how much of the thermocline could be
understood ignoring all other physical processes than just the simplest adiabatic,
laminar dynamics. Eddy dynamics, micro-scale diffusion, air–sea buoyancy fluxes
were all ignored on aesthetic rather than deductive grounds. At least some of these
have since been proven to have been good guesses (see Ledwell et al., 1993); others
are probably less so. Indeed, it is so simple a solution that perhaps its greatest value
is to serve as a tool for further improvements, alterations, or even, should it prove to
be necessary, a clear basis for considering radical alternatives. After all, the rule is:
what is modern today will seem primitive and dated in the future.