A Non-Unitary Conformal Field Theory Approach to Two-Dimensional Turbulence

TL;DR

This paper introduces a novel non-unitary conformal field theory framework to model two-dimensional turbulence, successfully reproducing key scaling laws and predicting new phenomena for future validation.

Contribution

It proposes a boundary logarithmic conformal field theory for the inverse cascade and a bulk conformal field theory for the direct cascade, linking conformal symmetry to turbulence scaling laws.

Findings

Reproduces Kraichnan-Batchelor $k^{-3}$ scaling for enstrophy cascade.

Derives Kolmogorov-Kraichnan $k^{-5/3}$ scaling for energy cascade.

Provides predictions for numerical and experimental tests.

Abstract

Fluid turbulence is a far-from-equilibrium phenomenon and remains one of the most challenging problems in physics. Two-dimensional, fully developed turbulence may possess the largest possible symmetry, the conformal symmetry. We focus on the steady-state solution of two-dimensional bounded turbulent flow and propose a $c=0$ boundary logarithmic conformal field theory for the inverse energy cascade and another bulk conformal field theory in the classical limit $c\rightarrow -\infty$ for the direct enstrophy cascade. We show that these theories give rise to the Kraichnan-Batchelor scaling $k^{-3}$ and the Kolmogorov-Kraichnan scaling $k^{-5/3}$ for the enstrophy and the energy cascades, respectively, with the expected cascade directions, fluxes, and fractal dimensions. We also made some new predictions for future numerical simulations and experiments to test.