Saturday, September 27, 2014

Turbulence Theory Through Feynman Diagrams

Surfing Through Space

Are you a fluid mechanics type wanting to break into high energy physics? A high energy physics type looking to work in Fluid Mechanics? A dandy guy in space? Well, this one is aimed at the first three. Huge audience, really pandering.

R Kraichnan

Robert Kraichnan is a famous turbulence theorist, famous for developing the Direct Interaction Approximation, which leads to the Kraichnan Spectrum (which has been an enormous empirical success) and his work in two dimensional turbulence that has been so important in modeling global weather systems (technically, 2D turbulence had been worked on by Onsager. Characteristically, nobody understood him until they were required to as to pass their classes...). It's not as widely known that he got his start in high energy physics! As an undergrad at MIT, Kraichnan was required to turn in a sort of thesis project. An overachiever, Kraichnan founded the modern theory of the "graviton", a hypothetical particle whose existence would imply a geometry equivalent to General Relativity.

thanks a lot internet
Anyway, Kraichnan never stopped being a high energy physicist in many ways. He actually used Feynman diagrams and such techniques to obtain many of his results, the reworked them with techniques his contemporaries were more comfortable with. As a result, many of his papers are very cryptic (deriving this stuff twice must have been exhausting). His talk "Interpretation of a Dynamical Approximation for Isotropic Turbulence" actually reveals a lot more of his method than his later, more obscure papers. I learned about this paper from this talk from Uriel Frisch. Frisch gives a good description of what the paper is about, as long as you already know what it is about. In particular, the three lines on page 6 represent the subscripts in Frisch's equation. Once you realize that, the others are a lot easier to read. One nice thing about this approach is that cross-correlations, so important in turbulence theory even as far back as GI Taylor (one could say fairly that there was no turbulence theory until Taylor started looking at cross correlations...), come right out of the theory.

Anyway this is a really nice paper, but it is too late in the evening for me to attempt a real explanation. Just read it!

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