Thursday, April 9, 2009

The Kolomogorov Spectrum

Yeah, maybe yesterday I should have taken a step back there and thought maybe everyone doesn't think a lot about eddies in fluids. An eddy is the rotating swirls you see in a moving river. What happens is these large scale whirls rapidly break down into smaller and smaller whirls. In this manner a fluid can transfer energy from large scales to individual molecules. So watching the vortices in the river yesterday you can watch them getting smaller and well, you get it now, right? The math-y way to describe this is called the Kolomogorov spectrum and is like the Matryoshka (nesting) dolls on the right here: each doll is similar but exists at a smaller and smaller scale.

The famous fluid dynamicist Lewis Fry Richardson summarized all this in a rhyme:

Big whorls have little whorls that feed on their velocity,
and little whorls have lesser whorls and so on to viscosity.

Viscosity is the term for friction in a fluid, in a higher viscosity fluid (like honey) molecules have stronger forces between one another and flow past each other slower than a lower viscosity fluid (like water).

Now you know the rest of the story...

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