Predictions on Two-dimensional Turbulence by Conformal Field Theory

TL;DR

This paper develops a conformal field theory-based framework for two-dimensional turbulence, deriving solutions and statistical properties that align with numerical simulations, offering a novel theoretical approach to turbulence modeling.

Contribution

It introduces a conformal field theory approach to 2D turbulence, solving minimal models under extended constraints and deriving explicit relations between key turbulence parameters.

Findings

Derived relations between central charge, anomalous dimension, and energy spectrum.

Predicted statistical properties consistent with numerical simulations.

Identified two categories of solutions within the conformal turbulence models.

Abstract

A generalized theory of two-dimensional isotropic turbulence is developed based on conformal symmetry. A number of minimal models of conformal turbulence are solved under an extended constraint including both the enstrophy cascade by Kraichnan and the discontinuity of vorticity by Saffman. There are an infinite number of solutions which fall into two different categories. An explicit relation is derived in one of the categories between the central charge of Virasoro algebra, the lowest anomalous dimension and the power of the energy spectrum. Some statistical properties such as energy spectrum, skewness, flatness and Casimir invariants are predicted and compared with numerical simulation by the pseudospectral method.