Loop Equation and Area Law in Turbulence

1993/10/14 by Alexander A. Migdal · 1 citation
Physics and Astronomy · #hep-th

paper · pdf · doi:10.1142/s0217751x94000558

published as Int.J.Mod.Phys. A9 (1994) 1197-1238 · 41 pages, 7 figures, LaTeX, PUPT-1426 (the figures uuencoded)

arxiv created 1993/10/14 · arxiv updated 2009/11/30

Abstract

This is the extended version of the preprint \ctLoop, 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(Γ) which allows the scaling solutions in inertial range of spatial scales. The pdf decays as exponential of some power of Γ³/A² where A is the minimal area inside the loop.

Cited by

• Area rule of velocity circulation in two-dimensional instability-driven turbulence beyond the inertial range