A New Diffeomorphism Symmetry Group of Non-Barotropic Magnetohydrodynamics

TL;DR

This paper explores a new symmetry group in non-barotropic magnetohydrodynamics, linking it to conservation laws like non-barotropic cross helicity, expanding understanding of symmetries and invariants in MHD.

Contribution

It introduces a novel diffeomorphism symmetry group specific to non-barotropic MHD and connects it to associated conservation laws, enriching the theoretical framework.

Findings

Identification of a new diffeomorphism symmetry group in non-barotropic MHD

Establishment of conservation laws linked to this symmetry, including non-barotropic cross helicity

Extension of Arnold's labelling symmetry to non-barotropic contexts

Abstract

The theorem of Noether dictates that for every continuous symmetry group of an Action the system must possess a conservation law. In this paper we discuss some subgroups of Arnold's labelling symmetry diffeomorphism related to non-barotropic magnetohydrodynamics (MHD) and the conservations laws associated with them. Those include but are not limited to the metage translation group and the associated topological conservations law of non-barotropic cross helicity.