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Someone described to me the difficulty of numerically simulating turbulence as that as you look at smaller length scales you see more structure like you do in a fractal. Searching on google for 'fractal turbulence' does seem to bring up quite a few hits. But since fractals are self-repeating as you go to smaller and smaller scales, doesn't this mean that we would already know all about the turbulence if we calculate it at one scale, and then add in the all the other scales assuming they are self-similar?

I am not a physicist, so please answer with simple language and not overly mathematical.

Qmechanic
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Ginsberg
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1 Answers1

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The statement that "fluids are fractal" is not quite correct (or at the very least is not precise). Instead what really happens is that energy in fluids transitions to higher and higher frequencies via a recursive formula which looks slightly fractal-like (called the "Selection rule"). This is one of the most famous results in fluid mechanics and is due to Kolmogorov. Here is a slightly mathematical, but very eloquent exposition of this beautiful discovery:

http://www.sjsu.edu/faculty/watkins/kolmo.htm

Note however that this only tells us the approximate structure of a fluid flow; ie its power spectrum. It does not give us enough information to say exactly what any given fluid will do at fine scales, or even if a solution exists! These latter two problems remain unsolved even today and are the subject of one of the famous millennium problems:

http://www.claymath.org/millennium/Navier-Stokes_Equations/

Mikola
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