Turbulence, String Theory and Ising Model

TL;DR

This paper links turbulence modeling to string theory and the Ising model by describing vortex cell dynamics as a 3D Ising system interacting with a string theory framework, revealing new insights into turbulence statistics.

Contribution

It introduces a novel approach connecting vortex cell dynamics in turbulence to the 3D Ising model and string theory, advancing the theoretical understanding of turbulence.

Findings

Ising model cells correspond to turbulence phases

Area law emerges for large circulation loops

Exponential tails in turbulence PDF are explained

Abstract

We advance the vortex cell approach to turbulence \cite{TSVS} by elaborating the Clebsch field dynamics on the surface of vortex cells. We argue that resulting statistical system can be described as 3D Ising model interacting with Compactified Bosonic String on the Riemann surface describing phase boundary. The cells come out as $\sigma=1$ phase of the Ising model in strong magnetic field. At large circulation around large loop the dominant Ising configuration correspond to minimal volume cells covering the area inside the loop, which naturally leads to the Area law and exponential PDF tails.