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Potential vorticity in magnetohydrodynamics

Published online by Cambridge University Press:  05 September 2014

G. M. Webb  and
R. L. Mace
G. M. Webb*
Affiliation:
Center for Space Plasma and Aeronomic Research, The University of Alabama in Huntsville, Huntsville AL 35805, USA
R. L. Mace
Affiliation:
School of Chemistry and Physics, The University of KwaZulu-Natal, Durban Westville, Durban, Natal 4000, South Africa
*
†Email address for correspondence: gmw0002@uah.edu
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Abstract

A version of Noether's second theorem using Lagrange multipliers is used to investigate fluid relabelling symmetries conservation laws in magnetohydrodynamics (MHD). We obtain a new generalized potential vorticity type conservation equation for MHD which takes into account entropy gradients and the J × B force on the plasma due to the current J and magnetic induction B. This new conservation law for MHD is derived by using Noether's second theorem in conjunction with a class of fluid relabelling symmetries in which the symmetry generator for the Lagrange label transformations is non-parallel to the magnetic field induction in Lagrange label space. This is associated with an Abelian Lie pseudo algebra and a foliated phase space in Lagrange label space. It contains as a special case Ertel's theorem in ideal fluid mechanics. An independent derivation shows that the new conservation law is also valid for more general physical situations.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 1 , January 2015 , 905810115
Copyright
Copyright © Cambridge University Press 2014 

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