Turbulence as a constrained system

TL;DR

This paper models hydrodynamic turbulence as a gauge theory within a metafluid dynamics framework, proposing a new approach that could facilitate quantization and deepen understanding of turbulence.

Contribution

It introduces a Lagrangian gauge theory approach to turbulence inspired by electromagnetism, providing a novel perspective and tools for analysis.

Findings

Dirac brackets are consistent inside and outside the inertial range

Turbulence can be quantized using this gauge theory framework

New insights into the constrained nature of turbulence

Abstract

Hydrodynamic turbulence is studied as a constrained system from the point of view of metafluid dynamics. We present a Lagrangian description for this new theory of turbulence inspired from the analogy with electromagnetism. Consequently it is a gauge theory. This new approach to the study of turbulence tends to renew the optimism to solve the difficult problem of turbulence. As a constrained system, turbulence is studied in the Dirac and Faddeev-Jackiw formalisms giving the Dirac brackets. An important result is that we show these brackets are the same in and out of the inertial range, giving the way to quantize turbulence.