A Four Function Variational Principle for Barotropic Magnetohydrodynamics

Abstract

Variational principles for magnetohydrodynamics were introduced by previous authors both in Lagrangian and Eulerian form. In a previous work Yahalom & Lynden-Bell introduced a simpler Eulerian variational principles from which all the relevant equations of magnetohydrodynamics can be derived. The variational principle was given in terms of six independent functions for non-stationary flows and three independent functions for stationary flows. This is less then the seven variables which appear in the standard equations of magnetohydrodynamics which are the magnetic field $\vec{B}$ the velocity field $\vec{v}$ and the density $\rho$. In this work I will improve on the previous results showing that non-stationary magnetohydrodynamics should be described by four functions .

11 pages no figures

References in corpus (1)

• Simplified Variational Principles for Barotropic Magnetohydrodynamics

Cited by in corpus (4)

• A Conserved Cross Helicity for Non-Barotropic MHD
• Simplified Variational Principles for non-Barotropic Magnetohydrodynamics
• Noether Currents for Eulerian Variational Principles in Non Barotropic Magnetohydrodynamics and Topological Conservations Laws
• A New Diffeomorphism Symmetry Group of Non-Barotropic Magnetohydrodynamics