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.

Enstrophy without boost symmetry

“…These currents can be further generalized in the presence of additional conserved U (1) charges, or if the flow is barotropic. See, e.g., [5]. For α = 1 and q = 1 we obtain (1.1).…”

“…Its existence is crucial for the appearance of the inverse energy cascade in two dimensional turbulence [1] and its dynamics is used in modeling turbulent dependent phenomena. While enstrophy is well understood in the context of incompressible fluid flow, barotropic flow and relativistic fluids (see [2][3][4][5]), little is known regarding its existence for more general flows with varying degrees of symmetry. The goal of this work is to study enstrophy conservation for generic fluids in two spatial dimensions with little symmetry.…”

Stochastic gravity and turbulence

“…It may well be that relativistic turbulent flow is not universal [17]. A study of the relativistic entropy current can be found in [8,26,27].…”

Enstrophy without boost symmetry

“…These currents can be further generalized in the presence of additional conserved U(1) charges, or if the flow is barotropic. See, e.g., [5]. For α = 1 and q = 1 we obtain (1).…”

“…Its existence is crucial for the appearance of the inverse energy cascade in two dimensional turbulence [1] and its dynamics is used in modeling turbulent dependent phenomena. While enstrophy is well understood in the context of incompressible fluid flow, barotropic flow and relativistic fluids (see [2][3][4][5]), little is known regarding its existence for more general flows with varying degrees of symmetry.…”