What Makes Turbulence So Hard

Turbulence – that pestersome, unpredictable, and chaotic state of flow – has been a thorn in the sides of mathematicians, physicists, and engineers for centuries. It is certainly one of – if not the – oldest unsolved problem in physics. Over at Ars Technica, Lee Phillips has a nice overview of the situation, including what makes the problem so difficult:

The Navier-Stokes equation is difficult to solve because it is nonlinear. This word is thrown around quite a bit, but here it means something specific. You can build up a complicated solution to a linear equation by adding up many simple solutions. An example you may be aware of is sound: the equation for sound waves is linear, so you can build up a complex sound by adding together many simple sounds of different frequencies (“harmonics”). Elementary quantum mechanics is also linear; the Schrödinger equation allows you to add together solutions to find a new solution.

But fluid dynamics doesn’t work this way: the nonlinearity of the Navier-Stokes equation means that you can’t build solutions by adding together simpler solutions. This is part of the reason that Heisenberg’s mathematical genius, which served him so well in helping to invent quantum mechanics, was put to such a severe test when it came to turbulence. 

Phillips goes on to describe some of the many methods researchers use to unravel the mysteries of turbulence computationally, experimentally, and theoretically. This is a great introduction for those curious to get a sense of how turbulence, stability theory, and computational fluid dynamics all fit together. (Image credits: L. Da Vinci; NASA; see also: Ars Technica; submitted by Kam Yung-Soh)

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