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

2020/05/26 by Asher Yahalom, Hong Qin · 1 citation
Physics and Astronomy · #physics.flu-dyn #astro-ph.SR #physics.plasm-ph

paper · pdf · doi:10.1017/jfm.2020.856

34 pages. arXiv admin note: substantial text overlap with arXiv:1510.00637, arXiv:1703.08072, arXiv:1801.06443, arXiv:physics/0603115

arxiv created 2020/05/26 · arxiv updated 2020/12/03

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.

Citations

• Simplified Variational Principles for non-Barotropic Magnetohydrodynamics
• Variational Principles and Applications of Local Topological Constants of Motion for Non-Barotropic Magnetohydrodynamics
• A New Diffeomorphism Symmetry Group of Non-Barotropic Magnetohydrodynamics
• Simplified Variational Principles for Barotropic Magnetohydrodynamics

Cited by

• A Three Function Variational Principle for Stationary Non-Barotropic Magnetohydrodynamics