Potential Vorticity in Magnetohydrodynamics
  A version of Noether's second theorem using Lagrange multipliers is used to investigate fluid relabelling symmetries conservation laws in magnetohydrodynamics (MHD). 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. 
G.M. Webb and R.L. Mace
math-ph math.MP