Enstrophy without boost symmetry

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.

v2: a few more comments and clarifications

References in corpus (7)

• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Spacetime Symmetries of the Quantum Hall Effect
• Non-relativistic conformal symmetries and Newton-Cartan structures
• Dynamics of Carroll Particles
• Galilean Isometries
• Torsional Newton-Cartan Geometry from the Noether Procedure
• Numerical Measurements of Scaling Relations in Two-Dimensional Conformal Fluid Turbulence

Cited by in corpus (4)

• Stochastic gravity and turbulence
• On black hole supertranslations and hydrodynamic enstrophy
• Unique Carrollian manifolds emerging from Einstein spacetimes
• Relativistic Fluids, Hydrodynamic Frames and their Galilean versus Carrollian Avatars