Eulerian Ornithology

Nikhil, totally excited: "Macha, you should have been there at Tressider this afty. Babes, babes and more babes everywhere da! The babe density was so high that if you saw a babe at a location, you didn't need to move your eyes to follow her. You could be certain that an equally hot babe would be at the same spot in the next instant!"


When you're analyzing motion of a fluid, you have two approaches. The first, called the Eulerian, is to look at one small region in space and see what happens in time at that region. You'd do this if, say, you were measuring the rate of flow of a river at some place.

The second option is to tag a little drop of fluid and follow the drop as it moves. You could do this by putting a small drop of ink that doesn't mix with the flow, for example. You'd do this if you were interested in designing a wing so that the flow over it is smooth.

One of the first things that made me totally fall in love with Feynman many years ago was this example of his that brought out the difference: Consider a liquid going around with uniform velocity in a circular tube with a circular cross section. At any one point in the tube, the velocity of the fluid would not change in time. But if you followed a single particle of water, it's velocity would change direction constantly!

If I ever teach a class on Fluids, I'll give the babe example before I discuss this topic :-)
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