Turbulence as Statistics of Vortex Cells

TL;DR

This paper introduces a novel statistical framework for turbulence based on vortex cell configurations, employing Hamiltonian dynamics and topological methods to analyze intermittency and symmetry violations.

Contribution

It formulates turbulence as a functional integral over vortex cell phase space, incorporating topological effects and string theory techniques for statistical analysis.

Findings

Derived an invariant probability distribution satisfying Liouville's equation.

Identified topological terms responsible for breaking time reversal symmetry.

Applied string theory methods to estimate turbulence intermittency.

Abstract

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.