Noether Currents for Eulerian Variational Principles in Non Barotropic Magnetohydrodynamics and Topological Conservations Laws
arXiv:2005.14005 · doi:10.1017/jfm.2020.856
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.
arXiv comment34 pages. arXiv admin note: substantial text overlap with arXiv:1510.00637, arXiv:1703.08072, arXiv:1801.06443, arXiv:physics/0603115
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