Metafluid dynamics as a gauge field theory

TL;DR

This paper reformulates metafluid dynamics, an analog of electromagnetism for turbulence, as a gauge field theory, revealing hidden symmetries and providing new insights into the physics of turbulence.

Contribution

It introduces a gauge field theory approach to metafluid dynamics, uncovering hidden gauge symmetries and offering a geometric interpretation of turbulence.

Findings

Revealed a hidden gauge symmetry in metafluid dynamics.

Provided a geometric interpretation of the gauge symmetries.

Computed the spectrum for 3D turbulence.

Abstract

In this paper, the analog of Maxwell electromagnetism for hydrodynamic turbulence, the metafluid dynamics, is extended in order to reformulate the metafluid dynamics as a gauge field theory. That analogy opens up the possibility to investigate this theory as a constrained system. Having this possibility in mind, we propose a Lagrangian to describe this new theory of turbulence and, subsequently, analyze it from the symplectic point of view. From this analysis, a hidden gauge symmetry is revealed, providing a clear interpretation and meaning of the physics behind the metafluid theory. Further, the geometrical interpretation to the gauge symmetries is discussed and the spectrum for 3D turbulence computed.