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Stirring up the abyss
Beach
come_to_think
Many years ago I read an article about attempts to explain the vertical stirring of the oceans as determined by various experimental studies. The efficacy of swimming animals was discussed. Whales & sharks, of course, make quite a stir, but there aren't enough of them to accomplish much. It turned out that shrimps had the greatest effect; their huge numbers made up for their modest size. Even they, however, were a couple of orders of magnitude short of the observed stirring. I eventually worked this puzzle into a sentimental poem: Epithalamium.

Today I happened on a snippet in the Caltech house organ Engineering & Science (Fall 2009, p. 8) revealing the present state of this question. It seems oceanographers have discovered boundary-layer theory. A solid body moving with with respect to a fluid drags a layer of fluid with it, and the slower the motion, the thicker the layer. (This was weighed in on me some time ago by my noticing that a light breeze was often suddenly evident on removing a screen from a window, and by copyediting a journal article in which a rocket engineer miserably confessed that he had not realized that the flow around a supported model in a wind tunnel does not approach the free-body flow as the thickness of the supports approaches zero. One time, I happened to sit next to a beautiful bear on a train, who had been driven out of meteorology by the math required, and told him about all this.) Thus, the tiniest (& thus most numerous & slowest) particles, including swimming plankton and sinking detritus, turn out to be the chief mixers.

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I have looked up some of the references, and it's *much* more complicated than I described above. A body carries some fluid with it even in the completely inviscid limit; viscosity increases the effect. I had naively supposed that the viscous boundary layer had a thickness given by the kinematic viscosity divided by the velocity; that is completely wrong. At present I do not understand the situation at all.

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