Metage symmetry group of non-barotropic magnetohydrodynamics and the conservation of cross helicity

Abstract

Standard cross helicity is not conserved in non-barotropic magnetohydrodynamics (MHD) (as opposed to barotropic or incompressible MHD). It was shown that a new kind of cross helicity which is conserved in the non barotropic case can be introduced. The non barotropic cross helicity reduces to the standard cross helicity under barotropic assumptions. Here we show that the new cross helicity can be deduced from a variational principle using the Noether’s theorem. The symmetry group associated with the new cross helicity is related to translation in a labelling of the flow elements connected to the magnetic field lines known as magnetic metage.