Turbulence and Random Geometry

TL;DR

This paper proposes a field theory model for fluid turbulence that incorporates a dilaton mode to explain anomalous scaling behaviors and relates intermittency to conformal anomalies.

Contribution

It introduces a novel field theory framework with a Nambu-Goldstone mode to describe turbulence scaling and intermittency.

Findings

Derives a KPZ-type formula for anomalous scaling exponents.

Connects intermittency parameter to boundary conformal anomaly.

Provides a theoretical basis for turbulence intermittency modeling.

Abstract

We outline our proposal for a field theory description of steady state incompressible fluid turbulence at the inertial range of scales in a general number of space dimensions. The theory consists of a Kolmogorov linear scaling mean field theory dressed by a Nambu-Goldstone dilaton mode that induces a random measure on the inertial range. We derive a KPZ-type formula for the anomalous scalings of the velocity structure functions, the velocity gradients and the local energy dissipation, and relate the dimensionless intermittency parameter to the boundary conformal anomaly.