Loop Equation and Area Law in Turbulence

Details Loop Equation and Area Law in Turbulence Loop Equation and Area Law in Turbulence

1993-10-14

arxiv.org/abs/hep-th/9310088v1

Int.J.Mod.Phys. A9 (1994) 1197-1238

Physics

High Energy Physics

High Energy Physics - Theory

41 pages, 7 figures, LaTeX, PUPT-1426 (the figures uuencoded)

Scientific paper

10.1142/S0217751X94000558

This is the extended version of the preprint \ct{Loop}, based on the lectures given in Cargese Summer School and Chernogolovka Summer School in 93. The incompressible fluid dynamics is reformulated as dynamics of closed loops $C$ in coordinate space. We derive explicit functional equation for the pdf of the circulation $P_C(\Gamma)$ which allows the scaling solutions in inertial range of spatial scales. The pdf decays as exponential of some power of $ \Gamma^3/A^2 $ where $A$ is the minimal area inside the loop.

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