Loop Equation and Area Law in Turbulence

Abstract

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.

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

References in corpus (2)

• Loop Equation in Turbulence
• Turbulence as Statistics of Vortex Cells

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