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We derive a Noether current for the Eulerian variational principle of idealnon-barotropic magnetohydrodynamics (MHD). It was shown previously that idealnon-barotropic MHD is mathematically equivalent to a five function field theorywith an induced geometrical structure in the case that field lines coversurfaces and this theory can be described using a variational principle. Herewe use various symmetries of the flow to derive topological constants of motionthrough the derived Noether current and discuss their implication fornon-barotropic MHD.

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