In Dynamo and Dynamics, a Mathematical Challenge (eds. P. Chossat, D. Armbruster and I. Oprea) Kluwer: Dordrecht (2001) 363-370.

A heteroclinic model of geodynamo reversals and excursions

I. Melbourne,
Department of Mathematics,
University of Houston,
Houston, TX 77204-3476 USA

M.R.E.Proctor and A.M. Rucklidge
Department of Applied Mathematics and Theoretical Physics,
University of Cambridge, Cambridge, CB3 9EW, UK

Abstract. The Earth's magnetic field is by and large a steady dipole, but its history has been punctuated by intermittent excursions and reversals. This is at least superficially similar to the behaviour of differential equations containing structurally stable heteroclinic cycles. We present a model of the geodynamo that is based on the symmetries of velocity fields in a rotating spherical shell, and that contains such a cycle. Patterns of excursions and reversals that resemble the geomagnetic record can be obtained by introducing small symmetry-breaking terms.

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