dc.contributor.author | Berger, MA | |
dc.contributor.author | Hornig, G | |
dc.date.accessioned | 2018-11-16T15:42:13Z | |
dc.date.issued | 2018-11-12 | |
dc.description.abstract | In 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.sponsorship | MB acknowledges STFC grant ST/R000891/1. GH acknowledges support from STFC grant ST/N000714/1. | en_GB |
dc.identifier.citation | Vol. 51, article 495501 | en_GB |
dc.identifier.doi | 10.1088/1751-8121/aaea88 | |
dc.identifier.uri | http://hdl.handle.net/10871/34801 | |
dc.language.iso | en | en_GB |
dc.publisher | IOP Publishing | en_GB |
dc.rights | Open 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.title | A generalized poloidal-toroidal decomposition and an absolute measure of helicity | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2018-11-16T15:42:13Z | |
dc.identifier.issn | 1751-8113 | |
dc.description | This is the final version. Available on open access from IOP Publishing via the DOI in this record | en_GB |
dc.identifier.journal | Journal of Physics A: Mathematical and Theoretical | en_GB |