Conformal Models of Two-Dimensional Turbulence

TL;DR

This paper applies conformal field theory to develop an infinite hierarchy of solutions for two-dimensional turbulence, addressing both enstrophy and energy flux cascades, and discusses their stability and physical implications.

Contribution

It introduces a novel conformal field theory framework to model two-dimensional turbulence, generating an infinite hierarchy of solutions for different flux cascades.

Findings

Constructed solutions for enstrophy and energy flux cascades.

Proposed an infinite hierarchy of conformal models.

Discussed potential stability and physical relevance.

Abstract

Polyakov recently showed how to use conformal field theory to describe two-dimensional turbulence. Here we construct an infinite hierarchy of solutions, both for the constant enstrophy flux cascade, and the constant energy flux cascade. We conclude with some speculations concerning the stability and physical meaning of these solutions.