Noether Currents for Eulerian Variational Principles in Non Barotropic Magnetohydrodynamics and Topological Conservations Laws

TL;DR

This paper derives a Noether current for non-barotropic magnetohydrodynamics (MHD) using an Eulerian variational principle, revealing topological conservation laws and symmetries that deepen understanding of MHD's mathematical structure.

Contribution

It introduces a novel Noether current for non-barotropic MHD and connects symmetries to topological invariants, expanding theoretical insights into MHD conservation laws.

Findings

Derived a Noether current for non-barotropic MHD.

Identified topological constants of motion from flow symmetries.

Discussed implications for MHD topological conservation laws.

Abstract

We derive a Noether current for the Eulerian variational principle of ideal non-barotropic magnetohydrodynamics (MHD). It was shown previously that ideal non-barotropic MHD is mathematically equivalent to a five function field theory with an induced geometrical structure in the case that field lines cover surfaces and this theory can be described using a variational principle. Here we use various symmetries of the flow to derive topological constants of motion through the derived Noether current and discuss their implication for non-barotropic MHD.