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Dynamically consistent magnetic fields produced by differential rotation

Published online by Cambridge University Press:  21 April 2006

D. R. Fearn  and
M. R. E. Proctor
D. R. Fearn
Affiliation:
Department of Mathematics, University Gardens, Glasgow, G12 8QW, UK
M. R. E. Proctor
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

We investigate the dynamical consequences of an axisymmetric velocity field with a poloidal magnetic field driven by a prescribed e.m.f. E. The problem is motivated by previous investigations of dynamically driven dynamos in the magnetostrophic range. A geostrophic zonal flow field is added to a previously described velocity, and determined by the requirement that Taylor's constraint (Taylor 1963) (guaranteeing dynamical self-consistency of the fields) be satisfied. Several solutions are exhibited, and it is suggested that self-consistent solutions can always be found to this ‘forced’ problem, whereas the usual α-effect dynamo formalism in which E is a linear function of the magnetic field leads to a difficult transcendentally nonlinear characteristic value problem that may not always possess solutions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 178 , May 1987 , pp. 521 - 534
Copyright
© 1987 Cambridge University Press

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