The Theory of Turbulence in Two Dimensions

TL;DR

This paper applies conformal field theory to derive exact solutions for two-dimensional turbulence, proposing conformal invariance in the inertial range and predicting specific correlation behaviors.

Contribution

It introduces a novel approach using conformal field theory to solve fundamental turbulence equations and establishes conformal invariance as a key property.

Findings

Conformal invariance of the inertial range is supported.

Exact solutions for turbulence equations are obtained.

Predictions for correlation functions in the inertial range are provided.

Abstract

The methods of conformal field theory are used to obtain the series of exact solutions of the fundamental equations of the theory of turbulence. The basic conjecture, proved to be self-consistent ,is the conformal invariance of the inertial range. The resulting physical picture is different from the standard one , since the enstrophy transfer is catalyzed by the large scale motions. The theory gives some unambiguous predictions for the correlations in the inertial range.