Mathematicians Prove Universal Law of Turbulence (quantamagazine.org) 21
By exploiting randomness, three mathematicians have proved an elegant law that underlies the chaotic motion of turbulent systems. From a report: Picture a calm river. Now picture a torrent of white water. What is the difference between the two? To mathematicians and physicists it's this: The smooth river flows in one direction, while the torrent flows in many different directions at once. Physical systems with this kind of haphazard motion are called turbulent. The fact that their motion unfolds in so many different ways at once makes them difficult to study mathematically. Generations of mathematicians will likely come and go before researchers are able to describe a roaring river in exact mathematical statements. But a new proof finds that while certain turbulent systems appear unruly, they actually conform to a simple universal law. The work is one of the most rigorous descriptions of turbulence ever to emerge from mathematics. And it arises from a novel set of methods that are themselves changing how researchers study this heretofore untamable phenomenon.
"It may well be the most promising approach to turbulence," said Vladimir Sverak, a mathematician at the University of Minnesota and an expert in the study of turbulence. The new work provides a way of describing patterns in moving liquids. These patterns are evident in the rapid temperature variations between nearby points in the ocean and the frenetic, stylized way that white and black paint mix together. In 1959, an Australian mathematician named George Batchelor predicted that these patterns follow an exact, regimented order. The new proof validates the truth of "Batchelor's law," as the prediction came to be known. "We see Batchelor's law all over the place," said Jacob Bedrossian, a mathematician at the University of Maryland, College Park and co-author of the proof with Alex Blumenthal and Samuel Punshon-Smith. "By proving this law, we get a better understanding of just how universal it is."
"It may well be the most promising approach to turbulence," said Vladimir Sverak, a mathematician at the University of Minnesota and an expert in the study of turbulence. The new work provides a way of describing patterns in moving liquids. These patterns are evident in the rapid temperature variations between nearby points in the ocean and the frenetic, stylized way that white and black paint mix together. In 1959, an Australian mathematician named George Batchelor predicted that these patterns follow an exact, regimented order. The new proof validates the truth of "Batchelor's law," as the prediction came to be known. "We see Batchelor's law all over the place," said Jacob Bedrossian, a mathematician at the University of Maryland, College Park and co-author of the proof with Alex Blumenthal and Samuel Punshon-Smith. "By proving this law, we get a better understanding of just how universal it is."
The next Math Conference will be Turbulent (Score:2, Offtopic)
I guess.
This is Slashdot! (Score:4, Insightful)
Re:This is Slashdot! (Score:4, Funny)
Yeah, who here isn't familiar with the 2D and 3D Navier Stokes equations in both hyper and non-hypervicious forms? You would think they would at least have mentioned it in passing!
Re: This is Slashdot! (Score:5, Funny)
Yeh. I remember the times when all the comments here were peer reviewed articles.
Sadly, those days of excellence are long gone.
Re: (Score:2)
I am.
Re:This is Slashdot! (Score:4, Interesting)
Yeah, who here isn't familiar with the 2D and 3D Navier Stokes equations in both hyper and non-hypervicious forms? You would think they would at least have mentioned it in passing!
"Viscous", not "vicious". Looking back, there has been some nice discussions about the Navier-Stokes equations in the past - including this one [slashdot.org]. There were quite a few on topic post, before the discussion degenerated into discussions about the Riemann hypothesis [wikipedia.org], Godel's incompleteness theorem [wikipedia.org], Zermelo-Fraenkel set theory [wikipedia.org], the finite element method, and Courvoisier.
Now, get off my lawn while reminisce of the good old days before September.
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Yeah memories, I too remember the great cognac flamewar of summer '05, was truly viscous. Many /.ers supporting Remy Martin fell in that battle.
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Isn't this news for nerds? It's okay to say things like Navier Stokes and not elicit panic. What kind of milktoast summary is this?
An article on turbulence that doesn't mention Navier–Stokes or Reynolds numbers is just crazy.
Re:This is Slashdot! (Score:5, Funny)
Oh you can say it. Just don't say it in Unicode.
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Jet noise (Score:2)
Hopefully this will explain 1) why jet noise is so damn loud, and 2) how to make them quiet.
Re:Jet noise (Score:4)
Damn, I was thinking it would help explain 1) why politicians are so loud, and 2) how to make them quiet.
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I would like to know why some politicians are so dumb and why people vote for them. But that probably has more to do with chaos theory.
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The original article on arxiv deals with turbulence at much lower fluid speeds.
It is interesting, but not interesting enough. Wake me up when the physicists finally start using differential inclusions instead of equations to describe it (I do not envy anyone trying to solve this numerically though).
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There are a lot of people that have serious trouble dealing with uncertainty of any kind. Hence religion, excessive amounts of laws and regulations, etc.
"Chaos", by James Gleick (Score:2)
This would actually be the final piece of all the work that is described in that book.
Related papers (Score:3, Informative)
As shown here [umd.edu], "The proof of Batchelor’s law comprises four papers presented in scientific talks at the Society for Industrial and Applied Mathematics Conference on Analysis of Partial Differential Equations (PD19) on December 12, 2019. The papers are:"
Clay Math Institute prize (Score:2)