A Conserved Cross Helicity for Non-Barotropic MHD

Abstract

Cross helicity is not conserved in non-barotropic magnetohydrodynamics (MHD) (as opposed to barotropic or incompressible MHD). Here we show that variational analysis suggests a new kind of cross helicity which is conserved in the non barotropic case. The non barotropic cross helicity reduces to the standard cross helicity under barotropic assumptions. The new cross helicity is conserved even for topologies for which the variational principle does not apply.