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Loop Equation and Area Law in Turbulence
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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.
Forward citations
Cited by 3 Pith papers
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Euler Ensemble as Decaying Turbulence Attractor: Universality, Stability and Parity Classes
Odd-N Euler ensemble polygons are locally Lyapunov-stable attractors of decaying NS turbulence, with universal defect spectrum λ_m=−sec²(πm/N) and leading angular Laplacian.
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Area and Perimeter Rules of Velocity Circulation in Two-Dimensional Turbulence with Large-scale Absolute Equilibrium
In the absolute equilibrium of 2D turbulence, circulation statistics depend only on loop area under enstrophy equipartition and only on loop perimeter under energy equipartition, with a proposed perimeter rule for the...
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Geometric Solution of Turbulence as Diffusion in Loop Space
A review presenting the Euler ensemble—an exact, number-theoretic solution for decaying turbulence—and a claimed geometric solution of Yang–Mills loop equations.
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