Enstrophy from symmetry

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.