Potential vorticity in magnetohydrodynamics. (January 2015)

• 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: 2015-01
• Subjects: Plasma (Ionized gases) -- Periodicals; 530.4405
• DOI: 10.1017/S0022377814000658
• Languages: English
• ISSNs: 0022-3778

Abstract

<abstract abstract-type="normal"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>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 <bold>J</bold> × <bold>B</bold> force on the plasma due to the current <bold>J</bold> and magnetic induction <bold>B</bold>. 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.</p> </abstract>