Papers on Large-Scale Ocean Circulation

The history of physical oceanography is not as long as that of meteorology, and the list below tends to have more recent papers. Thus, some selections below may turn out not to have lasting value, and may even have been misleading. The selection below is still a bit scattered and is not balanced or representative.


Langmuir, I. 1938. Surface motion of water induced by wind. Science, 87, 119-123.
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What are now called Langmuir cells -- near surface rolls, produced by wind, with scales of order 10 meters -- were first described in this paper. He noted streaks of seaweed aligned with the wind in the Atlantic. The theory, by Craik and Leibovich, came in 1976.

Wind-driven circulation

Stommel, W. H. 1948. The westward intensification of wind-driven ocean currents. Trans. Amer. Geophys. Union, 29, 202-206.
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Much of the theory of wind-driven gyres stems from this paper. Gives the first (AFAIK) essentially correct explanation of gyres and their western intensification.

Munk, W. H. 1950. On the wind-driven ocean circulation. J. Meteorol., 7, 79--93.
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Munk's well known paper on the wind-driven circulation. The Munk model may be thought of as a variant of Stommel's model, using a harmonic viscosity instead of a surface drag. Apart from the model and its solution, the paper is notable for its informative figures.

Munk, W. H. and Palmen, E. 1951. Note on the dynamics of the Antarctic Cirumpolar Current
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One of the first papers on the ACC. Suggests that the wind stress is balanced by stresses at the ocean bottom where thre current flows over topography (topographic form drag).

Abyssal and buoyancy-driven circulation

Sandstrom, J. W. 1908. Dynamische Versuche mit Meerwasser (Dynamical experiments with seawater). Annal. Hydrogr. Marit. Meteorol.,36, 6--23.
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Sandstrom, J. W. 1916. {Meteologische Studien im {S}chwedischen Hochgebirge, (Meteological studies in the Swedish high mountains). Goteborgs Kungl. Vetenskaps-och Vitterhets-Samhalles, Handingar, 27, 1--48.
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Sandstrom's papers purport to show that the heating must be at a higher pressure than the cooling, in order that a steady circulation can be maintained against the dissipative effects of friction. This has unfortunately become known as Sandstrom's `theorem'. Although his argument can be cast as a theorem, the conditions under which it holds are not satisfied in the ocean. Nevertheless, there is an effect, and it is this effect that suggests that mechanical forcing (wind and possibly tides) are important in maintaining the abyssal circulation of the real ocean. We may call this Sandstrom's effect, and it is a real one.

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.

Mesoscale Eddies

Gill, A., Green, J.S.A. and Simmons, A. 1974. Energy partition in the large-scale ocean circulation and the production of mid-ocean eddies
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This is one of the first papers to discuss baroclinic instability and the maintenance of mesoscale eddies in the ocean.

Spin up

Anderson, D. L. T and Gill, A., 1975. Spin up of a stratified ocean, with applications to upwelling. Deep-Sea Research, 22, 583-596.
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Discusses how a stationary, stratified ocean will spin up when a wind is applied. Distinguishes between the barotropic and baroclinic response, and looks at the role of Rossby and Kelvin waves.

The Thermocline

Welander, 1959. An advective model of the ocean thermocline. Tellus, 11, 309-318.
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Robinson, A. and Stommel, H, 1959. The oceanic thermocline and the associated thermohaline circulation. Tellus, 11, 295-308.
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The modern development of the theory of the thermocline began with the above two back-to-back papers in 1959, both in Tellus. Welander suggested an adiabatic model, based on the ideal-fluid thermocline equations (i.e., the planetary-geostrophic equations, with no diffusion terms in the buoyancy equation), whereas Robinson & Stommel proposed a model that is intrinsically diffusive. The diffusive model was further developed by Stommel and Webster (1963), Salmon (1990) and others.
The adiabatic approach was further discussed by:
Veronis, G. 1969, On theoretical models of the thermohaline circulation, Deep-Sea Research 16, 301-323.
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which provides a useful discussion and summary of the problem. (Link not yet working.)

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 properly elucidated.

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