A conserved local cross helicity for non-barotropic MHD

Cross helicity is not conserved in non-barotropic magnetohydro-dynamics (MHD) (as opposed to barotropic or incompressible MHD). Here we show that variational analysis suggests a new kind of local cross helicity which is conserved in the non-barotropic case. This local cross helicity can be integrated to a global non-barotropic cross helicity which was suggested in the work of Webb et al. (2014a,b). The non-barotropic cross helicity reduces to the standard cross helicity under barotropic assumptions. The new local cross helicity is conserved even for topologies for which the variational principle does not apply.