A Three Function Variational Principle for Stationary Non-Barotropic Magnetohydrodynamics

TL;DR

This paper introduces a simplified Eulerian variational principle for stationary non-barotropic magnetohydrodynamics, reducing the number of variables needed to derive the core equations and exploring non-ideal flow conditions.

Contribution

It presents a new, simpler variational principle using only three functions for stationary non-barotropic MHD, streamlining the derivation of fundamental equations.

Findings

Derived all relevant equations from the new variational principle.

Reduced variables from eight to three for certain field topologies.

Investigated non-ideal flow along magnetic lines.

Abstract

Variational principles for magnetohydrodynamics (MHD) were in\-troduced 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 stationary magnetohydrodynamics can be derived for certain field topologies. The variational principle is given in terms of three independent functions for stationary non-barotropic flows. This is a smaller number of variables than the eight variables which appear in the standard equations of non-barotropic magnetohydrodynamics which are the magnetic field $\vec B$ the velocity field $\vec v$, the entropy $s$ and the density $\rho$. We further investigate the case in the flow along magnetic lines is not ideal.