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Multi-symplectic magnetohydrodynamics: II, addendum and erratum

Published online by Cambridge University Press:  09 December 2015

G. M. Webb ,
J. F. McKenzie  and
G. P. Zank
G. M. Webb*
Affiliation:
Center for Space Plasma and Aeronomic Research, The University of Alabama in Huntsville, Huntsville, AL 35805, USA
J. F. McKenzie
Affiliation:
Center for Space Plasma and Aeronomic Research, The University of Alabama in Huntsville, Huntsville, AL 35805, USA Department of Mathematics and Statistics, Durban University of Technology, Steve Biko Campus, Durban, 4001, South Africa School of Mathematical Sciences, University of KwaZulu-Natal, Durban, 4000, South Africa
G. P. Zank
Affiliation:
Center for Space Plasma and Aeronomic Research, The University of Alabama in Huntsville, Huntsville, AL 35805, USA Department of Space Science, The University of Alabama in Huntsville, Huntsville, AL 35805, USA
*
†Email address for correspondence: gmw0002@uah.edu
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Abstract

A recent paper by Webb et al. (J. Plasma Phys., vol. 80, 2014, pp. 707–743) on multi-symplectic magnetohydrodynamics (MHD) using Clebsch variables in an Eulerian action principle with constraints is further extended. We relate a class of symplecticity conservation laws to a vorticity conservation law, and provide a corrected form of the Cartan–Poincaré differential form formulation of the system. We also correct some typographical errors (omissions) in Webb et al. (J. Plasma Phys., vol. 80, 2014, pp. 707–743). We show that the vorticity–symplecticity conservation law, that arises as a compatibility condition on the system, expressed in terms of the Clebsch variables is equivalent to taking the curl of the conservation form of the MHD momentum equation. We use the Cartan–Poincaré form to obtain a class of differential forms that represent the system using Cartan’s geometric theory of partial differential equations

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 6 , December 2015 , 905810610
Copyright
© Cambridge University Press 2015 

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