A History of Thermocline Theory
143
is given as well as the surface Ekman pumping vertical velocity, what is the resulting
shape of the density surfaces, what determines the depth of the thermocline, and how
is the motion field determined? As a problem in fluid mechanics this is clearly what
is desired rather than finding a fortuitous solution of the differential equations and
asking for the consistent boundary conditions that allow it.
More to the point, the solutions with constant potential vorticity were simply
not able to answer the simple question, “How important is κ for determining the
thermocline structure?” In the similarity solutions constant potential vorticity is a
solution for both the ideal fluid model and the model with dissipation and the only
difference between them is the vertical velocity predicted at the base of the thermocline
and that depends linearly on κ.
Again, in my own opinion, the problem of the thermocline as a problem in
fluid mechanics was stymied by the prospect of dealing with a complex mathematical problem that transformed thermocline theory into a rather abstruse mathematical
search for special solutions to a very difficult differential equation. And yet, also
in my opinion, Welander had in a very thoughtful way outlined a fruitful adiabatic
approach to the problem that was not followed up. It is an interesting question in
my own mind why this is so. As I recall the years of the 1960s as a student and
then a young researcher in the field, the power of boundary layer theory to deal with
fundamental and difficult problems in ocean circulation theory had seemed indisputable. At the same time there was an intuitive feeling that the thermocline was a
thermal boundary layer and it was natural to think of it as an advective/diffusive
one. Once diffusion enters the problem on the same level as advection, and the
three-dimensional character of the dynamics is respected, it becomes almost impossible to make theoretical progress in a way that leads to deeper physical understanding.
One has to admit in retrospect that, as a consequence, progress seems to have stalled
for at least a decade and most people, including me, accepted the similarity solutions
as the closest to a theoretical basis for understanding the thermocline as we were going to get. It is also provocative and natural to ask why numerical models of the
thermocline, not limited by the analytical difficulties described earlier, were not able
to confront the physical issues and elucidate the basic physics of the problem. There
are probably many reasons for this including a desire to deal with other problems, especially the problem of the oceanic eddy field at that time, or to focus on increasingly
complex models that could simulate important oceanographic processes, but the fact
remains that conceptual help in understanding the thermocline came first from simple
analytical models.
LAYER MODELS OF THE THERMOCLINE: ONE STEP BACK,
TWO STEPS FORWARD
In August 1980 Peter Rhines gave a seminar in Woods Hole shortly after his return
from a sabbatical visit in Cambridge. The title of his seminar, in which Bill Young
143
is given as well as the surface Ekman pumping vertical velocity, what is the resulting
shape of the density surfaces, what determines the depth of the thermocline, and how
is the motion field determined? As a problem in fluid mechanics this is clearly what
is desired rather than finding a fortuitous solution of the differential equations and
asking for the consistent boundary conditions that allow it.
More to the point, the solutions with constant potential vorticity were simply
not able to answer the simple question, “How important is κ for determining the
thermocline structure?” In the similarity solutions constant potential vorticity is a
solution for both the ideal fluid model and the model with dissipation and the only
difference between them is the vertical velocity predicted at the base of the thermocline
and that depends linearly on κ.
Again, in my own opinion, the problem of the thermocline as a problem in
fluid mechanics was stymied by the prospect of dealing with a complex mathematical problem that transformed thermocline theory into a rather abstruse mathematical
search for special solutions to a very difficult differential equation. And yet, also
in my opinion, Welander had in a very thoughtful way outlined a fruitful adiabatic
approach to the problem that was not followed up. It is an interesting question in
my own mind why this is so. As I recall the years of the 1960s as a student and
then a young researcher in the field, the power of boundary layer theory to deal with
fundamental and difficult problems in ocean circulation theory had seemed indisputable. At the same time there was an intuitive feeling that the thermocline was a
thermal boundary layer and it was natural to think of it as an advective/diffusive
one. Once diffusion enters the problem on the same level as advection, and the
three-dimensional character of the dynamics is respected, it becomes almost impossible to make theoretical progress in a way that leads to deeper physical understanding.
One has to admit in retrospect that, as a consequence, progress seems to have stalled
for at least a decade and most people, including me, accepted the similarity solutions
as the closest to a theoretical basis for understanding the thermocline as we were going to get. It is also provocative and natural to ask why numerical models of the
thermocline, not limited by the analytical difficulties described earlier, were not able
to confront the physical issues and elucidate the basic physics of the problem. There
are probably many reasons for this including a desire to deal with other problems, especially the problem of the oceanic eddy field at that time, or to focus on increasingly
complex models that could simulate important oceanographic processes, but the fact
remains that conceptual help in understanding the thermocline came first from simple
analytical models.
LAYER MODELS OF THE THERMOCLINE: ONE STEP BACK,
TWO STEPS FORWARD
In August 1980 Peter Rhines gave a seminar in Woods Hole shortly after his return
from a sabbatical visit in Cambridge. The title of his seminar, in which Bill Young