Understanding how PlanetWater "works" requires us to know how great bodies of fluid (oceans and atmosphere) move -- and why they move. The science of fluid mechanics (how and why fluids move) is in fact quite old and very well developed. Yet there is a problem so daunting it remains unsolved: turbulence. More generically the problem is that many disparate scales of motion are excited. Viewed from space, a storm near Calgary is a mere whirl in the planetary flow. Within that storm, winds vary widely. At any place, gusts come and go. A wisp of smoke soon breaks up into millions of tinier wisps. It is like white milk stirred into black tea forming brown liquid. While the example commenced with a storm near Calgary, similar descriptions apply in the ocean interior.

This problem which has defeated classical fluid mechanics (and other branches of science) occurs when aggregate behavior of the whole system depends upon interactions of hugely many parts. Although classical fluid mechanics may describe a small part, it is not well understood how interactions among many many parts govern the whole. In oceans, atmospheres and other environmental fluids this problem is called eddy parameterization as scientists and engineers attempt to approximate the collective effects of many smaller scale flows upon a few larger scale flows. An accompanying lecture (pdf, 28kb) describes challenges for ocean eddy parameterization.

Traditional efforts at ocean eddy parameterization have followed the stirring-milk-into-tea pardigm, supposing that eddies ("stirring") enhance the rate at which the milk diffuses ("mixing" to brown tea). Such ideas are applied to smoke in the atmosphere, to chemical species in the ocean, etc. Similar ideas are applied to the flows themselves, supposing that large flows break up into smaller eddies -- a process that seems like enhanced friction. Unfortunately these approaches are largely empirical. One does not know if they "work" until afterward when one looks at flows to see if one's answer is "right".

A newer approach attempts to replace classical mechanics (in which motion of every part of a system would be exactly determined) with statistical mechanics (in which motions of systems are described by probabilities). Central to statistical mechanics is the idea of entropy.

To open a tutorial on entropy, click here:

 

Efforts to develop statistical fluid mechanics in practical ways for the study of oceans, lakes or duck ponds can be viewed (pdf, 152kb) here:

Oceans, lakes and (most) duck ponds are too big

Also there is a charming poem (the author is not known) which was quoted by E. T. Jaynes and which is reproduced (click here).

 

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