The following paper by Jeffrey's makes some interesting remarks concerning Sandstrom's papers, and their applicability.
Jeffrey, H. 1926. On fluid motions produced by differences of temperature and humidity.
Quart. J. Roy. Meteor. Soc., 51, 347-356.
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Jeffreys notes a logical incompleteness, perhaps a flaw, in Sandstrom's arguments: to reach his conclusions Sandstom must assume that the expansion occurs at the location of the heating, but this is not necessarily the case.
The nice thing about science, as opposed to some other scholarly fields of endeavour, is that we don't feel obliged to study every detail of the original papers with a view to understanding what the authors meant. It seems a little different in philosophy, say, where scholars are still trying to squeeze new meaning from the original articles by Kant. What Sandstrom intended to say is largely irrelevant; we care mainly about whether his argument is correct or not, or leads us to a correct argument. In fact, I think that Sandstrom-like arguments, and their implications for ocean circulation, are now fairly well understood: use of circulation theorems clearly exposes the assumptions in Sandstrom's original work (see for example the book, 'The Ceaseless Wind', by Dutton), and energetic arguments give us the simplest and most robust expression of the Sandstrom effect (as, for example, in Paparella and Young (JFM, 2002)). My own description of the whole matter is to be found
here.
Stommel, H. and Arons, A. B. 1961. On the abyssal circulation of the world ocean- I. Stationary planetary flow patterns on a sphere. Deep-Sea Research, 6, 140-154,
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One of the first dynamical models of the abyssal circulation of the world's oceans. The idea is that the deep circulation is produced by a localized mass source (convection) and more uniform upwelling, constrained by the requirement of potential vorticity conservation on parcels. It is now thought to be, at best, only a partial description of the deep circulation. Its great success was the prediction of deep western boundary currents, observed by Swallow and Worthington (next reference). Observational support for some of its other predictions has been less forthcoming, probably because upwelling is not uniform and through the main thermocline, and because of interhemispheric effects involving wind-driving and the ACC. I will post some alternatives to the Stommel-Arons model soon.
Swallow, J. C. and Worthington, L. V. 1961. An observation of a deep countercurrent in the Western North Atlantic. Deep-Sea Research, 8, 1--19,
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Observations of a deep western boundary current in the Atlantic, in the opposite direction to the Gulf Stream. The observations were motivated by and are consistent with Stommel--Arons theory. The paper heralded the use of neutrally-buoyant 'Swallow' floats, which have become enormously important in our observations of the ocean.
Stommel, H. 1961. Thermohaline convection with two stable regimes of flow. Tellus , 13, 224-230,
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This is Stommel's famous 'two box model'. It is a simple, potentially physically realizable, model of relevance to the ocean circulation. Two boxes communicate with each other by small tubes, with the direction and intensity of the flow governed by the density difference, and so the temperature and salinity difference, between the boxes. For a range of parameters, two solutions are possible, one haline dominated and the other thermally dominated.
Munk, W. H. 1966. Abyssal recipes
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In this paper Munk tries to infer the rates of upwelling and the corresponding isopycnal diffusion. He estimated a value of kappa = 1 cm^2 per sec, which is much higher than subsequent direct measurements in the main thermocline indicated. This lead to notions of 'missing mixing' -- that there must be mixing going on somewhere that we are not aware of -- in order to maintain an overturning circulation. (We need a finite diffusivity to maintain a purely buoyancy-driven overturning because of Sandstrom's effect.) But if we drop the Stommel-Arons picture, and allow for a 'wind-driven' overturning circulation, then an MOC of strength similar to that observed can be maintained with small values of diffusivity (as per Toggweiler and Samuels, 1998, and others). Also, measurements over steep topography do indicate higher values of diffusivity in parts of the ocean. A follow on to Munk (1966) is the paper by Munk and Wunsch (1998) (Abyssal Recipes {II}: energetics of tidal and wind mixing) that I will post later.
The adiabatic approach reached a culmination with:
Luyten, J. R., Pedlosky J. and Stommel, H., 1982. The ventilated thermocline.
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In this paper ('LPS'), a model is proposed for the stratification of the upper ocean, and the associated motion. The model is notable for being wind-driven, inviscid and adiabatic, and satisfying a condition of zero vertical velocity at the thermocline base. The model is based on a layered representation of the ocean, and a calculation presented with three layers. Continuous extensions are provided by Killworth (1987) and Huang (1988, and others).
One paper discussing the dichotomy between the adiabatic and diffusive ideas is:
Welander, P. 1971. The thermocline problem.
In this paper Welander suggests that the thermocline may be 'an ideal fluid regime imbedded between diffusive regimes'. Colin de Verdiere (1989) also noted that diffusion might become important below an adiabatic near-surface layer.
Clearly, the ventilated thermocline cannot be a complete model of the thermocline, because it does not connect smoothly with the abyssal waters beneath. Current thinking (at least by some of us) is that there is an advective-diffusive internal boundary layer, the internal thermocline, below the ventilated thermocline. The main thermocline is composed of the ventilated thermocline plus the internal thermocline. The relative importance of these two components remains the matter of some debate, and the role of mesoscale eddies - and possibly potential vorticity homogenization, beginning with the papers of Rhines and Young - also remains to be resolved. about any of the above.