Plane poloidal-toroidal decomposition of doubly periodic vector fields. Part 1. Fields with divergence

• Autores: G. D. McBain
• Localización: Anziam journal: The Australian & New Zealand industrial and applied mahtematics journal, ISSN 1446-1811, Vol. 47, Nº 1, 2005, págs. 21-38
• Idioma: inglés
• DOI: 10.1017/s1446181100009743
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• Resumen

  • It is shown how to decompose a three-dimensional field periodic in two Cartesian coordinates into five parts, three of which are identically divergence-free and the other two orthogonal to all divergence-free fields. The three divergence-free parts coincide with the mean, poloidal and toroidal fields of Schmitt and Wahl; the present work, therefore, extends their decomposition from divergence-free fields to fields of arbitrary divergence. For the representation of known and unknown fields, each of the five subspaces is characterised by both a projection and a scalar representation. Use of Fourier components and wave coordinates reduces poloidal fields to the sume of two-dimensional poloidal fields, and toroidal fields to the sum of unidirectional toroidal fields.