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Turbulence as Statistics of Vortex Cells
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We develop the formulation of turbulence in terms of the functional integral over the phase space configurations of the vortex cells. The phase space consists of Clebsch coordinates at the surface of the vortex cells plus the Lagrange coordinates of this surface plus the conformal metric. Using the Hamiltonian dynamics we find an invariant probability distribution which satisfies the Liouville equation. The violations of the time reversal invariance come from certain topological terms in effective energy of our Gibbs-like distribution. We study the topological aspects of the statistics and use the string theory methods to estimate intermittency.
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Cited by 2 Pith papers
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Topology and the Conformal Invariance of Nodal Lines in Two-Dimensional Active Scalar Turbulence
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Analytic and Numerical Study of Navier-Stokes Loop Equation in Turbulence
A quadratic integral equation determines a vorticity distribution on a minimal surface bounded by a loop, yielding a WKB area-law prediction for circulation PDF tails in turbulence.
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