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Nonlinear stability of the geomagnetic field
Author(s) -
Hutcheson Kenneth A.,
Fearn David R.
Publication year - 1995
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/95gl01429
Subject(s) - instability , earth's magnetic field , field strength , physics , magnetic field , nonlinear system , field (mathematics) , bifurcation theory , bifurcation , mechanics , amplitude , classical mechanics , mathematics , quantum mechanics , pure mathematics
By subjecting a model axisymmetric magnetic field to a nonaxisymmetric perturbation, or instability, linear stability analyses can provide an indirect measure of the toroidal field strength in the Earth's core. It is thought that such field strengths have an upper bound of the order of 50 Gauss. We have constructed a model of the Earth's core to investigate how magnetic field instabilities evolve nonlinearly and find that at reasonably low viscosities, the instability evolves to a finite amplitude and rotates rigidly, as predicted from the theory of bifurcations in rotating systems. As the field strength is increased the solution adopts a completely different spatial configuration and has a different characteristic frequency to the branch found at the lower field strength. The primary Hopf bifurcation is thought to be of a subcritical nature which accords with a previous weakly nonlinear analysis. We conjecture that such an instability could provide the geomagnetic field with a mechanism for evolution to a different state at field strengths lower than the strength at the point of marginal stability.