Loop Equation and Area Law in Turbulence
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 (Γ) which allows the scaling solutions in inertial range of spatial scales. The pdf decays as exponential of some power of Γ3/A 2 where A is the minimal area inside the loop.
KeywordsMinimal Surface Wilson Loop Loop Space Energy Dissipation Rate Inertial Range
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