Simplified Variational Principles for non-Barotropic Magnetohydrodynamics

TL;DR

This paper introduces simplified Eulerian variational principles for non-barotropic magnetohydrodynamics, reducing the number of variables needed to derive the core equations compared to traditional methods.

Contribution

It presents a more straightforward variational framework using five independent functions for non-stationary flows, simplifying the derivation of MHD equations.

Findings

Derivation of MHD equations from simplified variational principles.

Reduction of variables from eight to five in the variational formulation.

Applicable to non-stationary, non-barotropic MHD flows.

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. The variational principle is given in terms of five independent functions for non-stationary barotropic flows. This is less then the eight variables which appear in the standard equations of barotropic magnetohydrodynamics which are the magnetic field $\vec B$ the velocity field $\vec v$, the entropy $s$ and the density $\rho$.