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

Published online by Cambridge University Press:  17 February 2009

G. D. McBain
G. D. McBain
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Australia; e-mail: geordie.mcbain@aeromech.usyd.edu.au.
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Abstract

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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 sum of two-dimensional poloidal fields, and toroidal fields to the sum of unidirectional toroidal fields.

Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 1 , July 2005 , pp. 21 - 38
Copyright
Copyright © Australian Mathematical Society 2005

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