Enstrophy from symmetry

TL;DR

This paper explores the symmetry principles behind enstrophy conservation in 2+1 dimensional turbulence, linking them to an effective action framework for hydrodynamics, applicable to both relativistic and non-relativistic cases.

Contribution

It identifies an accidental symmetry related to enstrophy current conservation within an effective action approach for hydrodynamics, advancing understanding of turbulence symmetries.

Findings

Identifies symmetry principles associated with enstrophy conservation.

Connects enstrophy symmetry to effective action formulations.

Applies analysis to both relativistic and non-relativistic hydrodynamics.

Abstract

We study symmetry principles associated with the approximately conserved enstrophy current, responsible for the inverse {energy} cascade in non relativistic $2+1$ dimensional turbulence. We do so by identifying the accidental symmetry associated with enstrophy current conservation in a recently realized effective action principle for hydrodynamics. Our analysis deals with both relativistic and non relativistic effective actions and their associated symmetries.