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 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. [1,2]. 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.

[1] Webb et al. 2014a, J. Phys. A, Math. and theoret., Vol. 47, (2014), 095501 (33pp)

[2] Webb et al. 2014b: J. Phys A, Math. and theoret. Vol. 47, (2014), 095502 (31 pp).

[3] Asher Yahalom “Simplified Variational Principles for non-Barotropic Magnetohydrodynamics”. (arXiv: 1510.00637 [Plasma Physics]) J. Plasma Phys. (2016), vol. 82, 905820204 © Cambridge University Press 2016 doi:10.1017/S0022377816000222.

[4] Asher Yahalom “Non-Barotropic Magnetohydrodynamics as a Five Function Field Theory”. International Journal of Geometric Methods in Modern Physics, No. 10 (November 2016). Vol. 13 1650130 (13 pages) © World Scientific Publishing Company, DOI: 10.1142/S0219887816501309.

[5] Asher Yahalom “Simplified Variational Principles for Stationary non-Barotropic Magnetohydrodynamics” International Journal of Mechanics, Volume 10, 2016, p. 336-341. ISSN: 1998-4448.