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dc.contributor.authorBerger, MA
dc.contributor.authorHornig, G
dc.date.accessioned2018-11-16T15:42:13Z
dc.date.issued2018-11-12
dc.description.abstractIn fluid mechanics and magneto-hydrodynamics it is often useful to decompose a vector field into poloidal and toroidal components. In a spherical geometry, the poloidal component contains all of the radial part of the field, while the curl of the toroidal component contains all of the radial current. This paper explores how they work in more general geometries, where space is foliated by nested simply connected surfaces. Vector fields can still be divided into poloidal and toroidal components, but in geometries lacking spherical symmetry it makes sense to further divide the poloidal field into a standard part and a 'shape' term, which in itself behaves like a toroidal field and arises from variations in curvature. The generalised P–T decomposition leads to a simple definition of helicity which does not rely on subtracting the helicity of a potential reference field. Instead, the helicity measures the net linking of the standard poloidal field with the toroidal field as well as the new shape field. This helicity is consistent with the relative helicity in spherical and planar geometries. Its time derivative due to motion of field lines in a surface has a simple and intuitively pleasing form.en_GB
dc.description.sponsorshipMB acknowledges STFC grant ST/R000891/1. GH acknowledges support from STFC grant ST/N000714/1.en_GB
dc.identifier.citationVol. 51, article 495501en_GB
dc.identifier.doi10.1088/1751-8121/aaea88
dc.identifier.urihttp://hdl.handle.net/10871/34801
dc.language.isoenen_GB
dc.publisherIOP Publishingen_GB
dc.rightsOpen access. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence: https://creativecommons.org/licenses/by/3.0/. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.en_GB
dc.titleA generalized poloidal-toroidal decomposition and an absolute measure of helicityen_GB
dc.typeArticleen_GB
dc.date.available2018-11-16T15:42:13Z
dc.identifier.issn1751-8113
dc.descriptionThis is the final version. Available on open access from IOP Publishing via the DOI in this recorden_GB
dc.identifier.journalJournal of Physics A: Mathematical and Theoreticalen_GB


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