String Theory and Turbulence

TL;DR

This paper introduces a string theory framework for turbulence that explains key scaling laws in different dimensions using the AdS/CFT correspondence and Migdal's loop variables.

Contribution

It develops a novel string theory approach to turbulence, connecting it with the AdS/CFT duality and Migdal's loop equations, providing a unified explanation of turbulence scalings.

Findings

Derives Kolmogorov scaling in 3+1 dimensions.

Explains Kraichnan and Kolmogorov scalings in 2+1 dimensions.

Identifies an area law for turbulence in 2+1 dimensions.

Abstract

We propose a string theory of turbulence that explains the Kolmogorov scaling in 3+1 dimensions and the Kraichnan and Kolmogorov scalings in 2+1 dimensions. This string theory of turbulence should be understood in light of the AdS/CFT dictionary. Our argument is crucially based on the use of Migdal's loop variables and the self-consistent solutions of Migdal's loop equations for turbulence. In particular, there is an area law for turbulence in 2+1 dimensions related to the Kraichnan scaling.