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equilibrium spectrum. In 1963, Hasselmann first pointed out the crucial role played by the nonlinear energy transfer from the short and long components to the energetic central spectrum. The subject has now advanced to a point where wave prediction based on a given (past and future) wind field is routinely used in a wide range of human activities. Now that the wave field can be measured by synthetic aperture radar (SAR) satellites, I predict that the deconvolution of the wave field to provide wind data will become an important future application.


Tides are the earliest application of oceanography to human activities 9 and were a favorite subject of Victorian mathematicians. This field, too, has been revived by the computer revolution. In 1969, Pekeris and Accad solved the Laplace tide equation over a world ocean with realistic topography, using the new GOLEM computer built at the Weizmann Institute.10 There was a need to compare the global computations with measurements in the open sea. Coastal tide gauges have been around for centuries, but the ability to measure deep sea tides did not come until the early 1960s when pressure gauges could be dropped freely to the deep seafloor and subsequently recalled acoustically; about 350 pelagic stations have been occupied (mostly by Cartwright) in the 30-year window before satellite altimetry provided the means of truly global measurements. Tidal dissipation from the principal lunar tide is 2.50 ± .05 Terawatts (TW), very accurately derived from the measured rate of 3.82 cm/s at which the Moon moves away from the Earth. Tidal dissipation may have important implications to ocean mixing (as discussed below).

There are other achievements. We have learned the importance in tidal modeling of allowing for the elastic yield of the solid Earth. A seamark achievement is G. Platzman's expansion into global ocean normal modes. Tidal studies have not been in the oceanographic mainstream; I am one of the very few people who think that lunar studies will become fashionable once more (there is a name for such people).

The Microscale Revolution

At the opposite end of the general circulation scale is the micro-(or dissipation) scale where energy is irreversibly converted into heat. We are talking about millimeters to centimeters, but just because the process scales are small does not mean their importance is small.

It was not always clear that the deep ocean was cold. In the seventeenth century, Boyle argued that the temperature must increase with pressure according to his law PV = NRT (as it does in the Mindanao Deep, from 1.7°C at 5 km to 2.5°C at 10 km). While passing through the tropics on a voyage to the East Indies, Boyle noticed that the cook was lowering some bottles of white wine over the side. "And why should you be doing this?" he asked, to which the cook replied, "Every gentleman knows that white wine must be chilled before serving." Surely this was one of the most decisive oceanographic experiments of all time. 11

At the rate of 25 sverdrups of bottom water formation, the oceans would fill up with ice cold water in 3,000 years, forming a 1-m-thick thermal surface boundary layer controlled by molecular conductivity. Why is it you do not freeze your toes every time you go swimming?

The answer is that turbulent mixing brings warm water downward. A scale depth of 1000 m (roughly as observed) requires 1000 times the molecular diffusivity, or about 10-4 m2/s. Is this in accordance with fact? It has taken 30 years to find out that it is not. Cox, Gregg, and Osborn, among others, have developed the instrumentation with the required vertical resolution and found typical pelagic values of 10-5 m2/s. Ledwell confirmed these values by in situ measurements of the diffusion of a dye patch. Although a discrepancy by a factor of 10 is not large in this context, it appears to be real. A possible interpretation is that most of the ocean mixing takes place in a few regions of rough topography and very high turbulence. Far higher diffusivities have in fact been measured by Schmitt, Toole, and Polzin near rough bottom topography in the South Atlantic Ocean. An ambitious experiment along the Hawaiian ridge is being planned.

Mixing associated with 10-4 m2/s required 2 TW, the pelagic mixing rate of 10-5 m2/s requires 0.2 TW globally. Where does the energy for the mixing come from? Wind is an obvious candidate, tidal dissipation is another (2.5 TW are dissipated by the M2 tide alone, but nearly all of this has been claimed for dissipation in marginal seas).

Getting the mixing right is vital to any realistic modeling of ocean circulation and heat transport. In this connection we need to mention two other important developments. In 1956, Stommel (with Arons and Blanchard) published a paper: "An Oceanographical Curiosity: The Perpetual Salt Fountain."12 In a temperature-stable and salt-unstable stratification, a vertical hose, once primed, will pump up cold, salty (and nutrient-rich) deep water forever. Stern realized that this was associated with a fundamental instability (hose or no hose), and Turner developed this into the discipline of double-diffusive mixing.

The MEDOC (Mediterranean Deep Ocean Convection)


 Cartwright, D.E. 1999. Tides: A Scientific History. Cambridge University Press.


 Supported by the first overseas grant from NSF.


 For a more accurate account, see page 6 in McConnell, A. 1982. No Sea Too Deep. Adam Hilger, Ltd., Bristol.


 Stommel, H., A.B. Arons, and D. Blanchard. 1956. An oceanographical curiosity: The perpetual salt fountain. Deep-Sea Research 3:152-153.

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