Boris Shraiman, the scientist who made the most important contribution to the field of turbulence in the last 20 years, made an interesting comment to me recently. The study of turbulence is hampered by the knowledge, and blind reverence, of the Navier Stokes equations. Instead of studying the phenomena of turbulence as any other problem of physics, where simple models attempt to capture some set of observed phenomena, the field is obsessed with the governing equations of fluid mechanics. Clearly this is an avenue of research that ought to have been pursued, but after almost a century of this pursuit it is time for new ideas.
I hope to work on turbulence when I grow up. Maybe I can make a name for myself.
5 comments:
What do you think about Goldenfeld's recent stuff? I.e. http://prl.aps.org/abstract/PRL/v96/i4/e044503
This might be useful when attempting to understand critical exponents of flows, and transition to turbulence, in real systems. There is still the question of, in numerical experiments, where the NS equations are modelled to a high degree of precision, why do we see the critical exponents that we do. Furthermore, there is the related problem of passive scalar turbulence, which is one step removed from possible boundary effects.
Although I don't really understand the concept of Widom scaling, I find it interesting that Goldenfeld's scaling of a transition to turbulence in rough pipes is analogous to any concept from statistical mechanics. How else can stat mech inform or otherwise relate to turbulence/NS?
In some sense statistical physics can be viewed as a statement of dominant balance. There is some scale at which some thing is happening, be that the motion of molecules due to them being bombarded in a thermal environment, or the motion of the stock market due to individual trades. At scales larger than this microscale it is reasonable to say there are only certain aspects of this microsrtucture that are relevant. For example, in classical thermal system, you say that the noise is delta correlated. Of course this isn;t true. Its an approximation. In the same way there are similar situations in turbulence where one can do this. I certainly am not an expert on these things, but there are these things called Kraichnan ensembles which was a huge step in understanding parts of passive scalar turbulence. Instead of saying that passive scalars are in a real fluid flow you replace it with a white noise term that advects the particles. It turns out that this is a reasonable model for things. Another limit is when particles are heavy. This work was done by Jeremy Bec at Nice.
Critical points and Widom like scalings is now a natural outcome in any system where there is separation of scales.
I think that made sense. By the way, is this John?
This posting about models is reminiscent of something that Euler says, translated as, "Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena."
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