Enstrophy without boost symmetry

TL;DR

This paper constructs an approximately conserved enstrophy-like current for 2+1D non boost-invariant fluids, connecting it to known conserved quantities under various symmetry enhancements like Galilean, Lorentzian, Carrollian, and Lifshitz.

Contribution

It introduces a new conserved current in non boost-invariant fluids and explores its relation to known symmetries and conserved quantities in fluid dynamics.

Findings

Current matches enstrophy in Galilean limit

Extends to Lorentzian, Carrollian, Lifshitz symmetries

Provides a framework for non boost-invariant fluid conservation laws

Abstract

We construct an approximately conserved current for $2+1$ dimensional, Aristotelian (non boost invariant), fluid flow. When Aristotelian symmetry is enhanced to Galilean symmetry, this current matches the enstrophy current responsible for the inverse cascade in incompressible fluids. Other enhancements of Aristotelian symmetry discussed in this work include Lorentzian, Carrollian and Lifshitz scale symmetry.