New solutions of the kinematic dynamo problem

Stephen Childress

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126 Scopus citations

Abstract

The steady-state kinematic dynamo problem in a homogeneous 3-dimensional core is studied. The existence of a class of smooth solenoidal dynamos, satisfying a no-slip condition on the core boundary, is proved using perturbation theory. The dynamos are of the form q = q(1) + q (2) + q(3), where q(1) is spatially periodic on a sufficiently small scale of length, q(2) is zero except near the core boundary, and q(3) is an arbitrary sufficiently small motion. The term q(1) is also a spatially periodic dynamo in an appropriate sense for an infinite core. The last property allows a simple characterization of the bounded dynamos in terms of the admissible q(1).

Original languageEnglish
Pages (from-to)3063-3076
Number of pages14
JournalJournal of Mathematical Physics
Volume11
Issue number10
DOIs
StatePublished - 1970
Externally publishedYes

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