A new formulation of the near-equilibrium theory of turbulence

Abstract

We present a status report on a discrete approach to the the near-equilibrium statistical theory of three-dimensional turbulence, which generalizes earlier work by no longer requiring that the vorticity field be a union of discrete vortex filaments. The idea is to take a special limit of a dense lattice vortex system, in a way that brings out a connection between turbulence and critical phenomena. The approach produces statistics with basic features of turbulence, in particular intermittency and coherent structures. The numerical calculations have not yet been brought to convergence, and at present the results are only qualitative.