Evolution of non-linear α2-dynamos and Taylor's constraint

Fearn, D.R. and Rahman, M.M. (2004) Evolution of non-linear α2-dynamos and Taylor's constraint. Geophysical and Astrophysical Fluid Dynamics, 98(5), pp. 385-406. (doi: 10.1080/03091920410001724124)

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Publisher's URL: http://dx.doi.org/10.1080/03091920410001724124


A key non-linear mechanism in a strong-field geodynamo is that a finite amplitude magnetic field drives a flow through the Lorentz force in the momentum equation and this flow feeds back on the field-generation process in the magnetic induction equation, equilibrating the field. We make use of a simpler non-linear α<sup>2</sup>-dynamo to investigate this mechanism in a rapidly rotating fluid spherical shell. Neglecting inertia, we use a pseudo-spectral time-stepping procedure to solve the induction equation and the momentum equation with no-slip velocity boundary conditions for a finitely conducting inner core and an insulating mantle. We present calculations for Ekman numbers (E) in the range 2.5times 10<sup>-3</sup> to 5.0times 10<sup>-5</sup>, for α=α 0cos θ sin π (r-ri) (which vanishes on both inner and outer boundaries). Solutions are steady except at lower E and higher values of α0. Then they are periodic with a reversing field and a characteristic rapid increase then equally rapid decrease in magnetic energy. We have investigated the mechanism for this and shown the influence of Taylor's constraint. We comment on the application of our findings to numerical hydrodynamic dynamos.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Fearn, Professor David
Authors: Fearn, D.R., and Rahman, M.M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Geophysical and Astrophysical Fluid Dynamics
ISSN (Online):1029-0419

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