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- W1517602657 abstract "We apply Noether's first and second theorems to investigate conservation laws in magnetohydrodynamics (MHD) and gas dynamics.A version of Noether's second theoremusing Lagrange multipliers is used to investigate fluid relabelling symmetries conservation laws. Ertel's theorem, the fluid helicity conservation equation and cross helicity conservation equation for a barotropic gas are obtained using Lagrange multipliers which are used to enforce the fluid relabelling symmetry determining equations. The nonlocal form of the non-magnetized fluid helicity conservation law and the nonlocal cross helicity conservation laws obtained previously are briefly discussed. We obtain a new generalized potential vorticity type conservation equation for MHD which takes into account entropy gradients and the ${bf J}times{bf B}$ force on the plasma due to the current ${bf J}$ and magnetic induction ${bf B}$. This new conservation law for MHD is derived by using Noether's second theorem in conjunction with a class of fluid relabelling symmetries in which the symmetry generator for the Lagrange label transformations is non-parallel to the magnetic field induction in Lagrange label space. This is associated with an Abelian Lie pseudo algebra and a foliated phase space in Lagrange label space. It contains as a special case Ertel's theorem in ideal fluid mechanics. An independent derivation shows that the new conservation law is also valid for more general physical situations." @default.
- W1517602657 created "2016-06-24" @default.
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- W1517602657 date "2014-03-12" @default.
- W1517602657 modified "2023-09-27" @default.
- W1517602657 title "Noether's Theorems and Fluid Relabelling Symmetries in Magnetohydrodynamics and Gas Dynamics" @default.
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