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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Merrill, R.L., McElhinny, M.W. & McFadden, P.L. (1996) The Magnetic Field of the Earth: Paleomagnetism, the Core, and the Deep Mantle. Academic Press: San Diego.
Gubbins, D. (1999) The distinction between excursions and reversals, Geophys. J. Int. 137 F1–F3
Busse, F.H. (2001) In this volume
Roberts, P.H. (2001) In this volume
Jones, C.A. (2000) Convection-driven geodynamo models, Phil Trans. R. Soc. Lond. A 358 873–897
Bullard, E.C. (1955) The stability of a homopolar dynamo, Proc. Camb. Phil. Soc. 51 744–760
Rikitake, T. (1958) Oscillations in a system of disk dynamos, Proc. Camb. Phil. Soc. 54 89–105
Allan, D.W. (1962) On the behaviour of systems of coupled dynamos, Proc. Camb. Phil. Soc. 58 671–693
Robbins, K.A. (1975) Disk Dynamos and Magnetic Reversal (PhD thesis, M.I.T.)
Chui, A.Y.K. & Moffatt, H.K. (1993) A thermally driven disc dynamo. In Solar and Planetary Dynamos (ed. M.R.E. Proctor, P.C. Matthews & A.M. Rucklidge), pp. 51–58. Cambridge University Press: Cambridge
Hide, R., Skeldon, A.C. & Acheson, D.J. (1996) A study of two novel self-exciting single-disk homopolar dynamos: theory, Proc. R. Soc. Lond. A 452 1369–1395
Moroz, I.M., Hide, R. & Soward, A.M. (1998) On self-exciting coupled Faraday disk homopolar dynamos driving series motors, Physica 117D 128–144
Oprea, I., Chossat, P. & Armbruster, D. (1997) Simulating the kinematic dynamo forced by heteroclinic convective velocity fields, Theor. Comput. Fluid Dyn. 9 293–309
Chossat, P., Guyard, F. Lauterbach, R (1999) Generalized heteroclinic cycles in spherically invariant systems and their perturbations, J. Nonlinear Sci. 9 479–524
Busse, F.H. (1970) Thermal instabilities in rapidly rotating systems, J. Fluid Mech. 44 441–460
Jackson, A., Jonkers, A.R.T. & Walker, M.R. (2000) Four centuries of geomagnetic secular variation from historical records, Phil. Trans. R. Soc. Lond. A 358 957–990
Kumar, S. & Roberts, P.H. (1975) A three-dimensional kinematic dynamo, Proc. R. Soc. Lond. A 344 235–258
Gubbins, D., Barber, C.N., Gibbons, S. & Love, J.J. (2000) Kinematic dynamo action in a sphere. II. Symmetry selection, Proc. R. Soc. Lond. A 456 1669–1683
Proctor, M.R.E. (1977) The role of mean circulation in parity selection by planetary magnetic fields, Geophys. Astrophys. Fluid Dynamics 8 311–324
Krupa, M. & Melbourne, I. (1995) Asymptotic stability of heteroclinic cycles in systems with symmetry, Ergod. Th. & Dynam. Sys. 15 121–147
Melbourne, I. (1989) Intermittency as a codimension three phenomenon, J. Dyn. Diff. Eqns. 1 347–367
Melbourne, L, Proctor, M.R.E. & Rucklidge, A.M. (2001) In preparation
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Melbourne, I., Proctor, M., Rucklidge, A. (2001). A Heteroclinic Model of Geodynamo Reversals and Excursions. In: Chossat, P., Ambruster, D., Oprea, I. (eds) Dynamo and Dynamics, a Mathematical Challenge. NATO Science Series, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0788-7_43
Download citation
DOI: https://doi.org/10.1007/978-94-010-0788-7_43
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-7070-3
Online ISBN: 978-94-010-0788-7
eBook Packages: Springer Book Archive