Potential vorticity in magnetohydrodynamics. (5th September 2014)

• Record Type: Journal Article
• Authors: Webb, G. M.; Mace, R. L.
• Is Part Of: Journal of plasma physics. Volume 81:Number 1(2015:Feb.)
• Publication Date: 2014-09-05
• Subjects: Plasma (Ionized gases) -- Periodicals; 530.4405
• DOI: 10.1017/S0022377814000658
• Languages: English
• ISSNs: 0022-3778

Abstract

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 theJ ×B force on the plasma due to the currentJ and magnetic inductionB . 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.