Turbulence

Somebody recently said that any reasonable theoretical physicist ought to have a good understanding of quantum field theory. No sooner does he say it and it saunters up to his doorstep and kicks his screen in.

Turbulence is the great unsolved problem of classical mechanics. Versions of the following apocryphal story are attributed to Heisenberg, Lamb, and other major figures in fluid mechanics: "when I die, I'm going to ask the Lord to explain two things. Quantum electrodynamics, and turbulence. I expect he will be able to answer the first.

Because turbulence depends exquistely on initial conditions and displays highly random characteristics, we want a statistical theory of turbulence. Unfortunately, when we write down statistical version of the equations of fluid dynamics, we find that the equations for the various statistical quantities are not closed. Each order of correlation depends on higher orders of correlation.

One of the few important constraints we have on the statistics of turbulence are Kolmogorov's scaling laws. It's based on Lewis Richardson's idea of the turbulent energy cascade.

Big whorls have little whorls
That feed on their velocity,
And little whorls have lesser whorls
And so on to viscosity.

-- Lewis F. Richardson

Kolmogorov theory works pretty well for many situations, but the theoretical foundations are a bit shaky.

So much for prolog. This morning, Lumo posted an article linking to a new ArXiv paper on String Theory and Turbulence. The abstract:

We propose a string theory of turbulence that explains the Kolmogorov scaling in 3+1 dimensions and the Kraichnan and Kolmogorov scalings in 2+1 dimensions. This string theory of turbulence should be understood in light of the AdS/CFT dictionary. Our argument is crucially based on the use of Migdal's loop variables and the self-consistent solutions of Migdal's loop equations for turbulence. In particular, there is an area law for turbulence in 2+1 dimensions related to the Kraichnan scaling.

I won't attempt to comment on the success of their program, but probing a bit further showed that their work had important predecessors in papers by Polykov,

The methods of conformal field theory are used to obtain the series of exact solutions of the fundamental equations of the theory of turbulence. ...

and Migdal. Here's Migdal:

The central problem of turbulence is to find the analog of the Gibbs distribution for the
energy cascade.

And it turns out that quantum field theory is the way to look, or so our authors claim.

It's just as I feared.

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