Simplified variational principles for non-barotropic magnetohydrodynamics

Abstract

Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of non-barotropic magnetohydrodynamics can be derived for certain field topologies. The variational principle is given in terms of five independent functions for non-stationary barotropic flows. This is less than the eight variables which appear in the standard equations of barotropic magnetohydrodynamics which are the magnetic field $\boldsymbol{B}$ the velocity field $\boldsymbol{v}$, the entropy $s$ and the density ${\it\rho}$.