NONLINEAR STABILITY OF THE GEOMAGNETIC-FIELD

By subjecting a model axisymmetric magnetic field to a nonaxisymmetric perturbation, or instability, linear stability analyses can provide a n 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 or der of 50 Gauss. We have constructed a model of the Earth's core to in vestigate how magnetic field instabilities evolve nonlinearly and find that at reasonably low viscosities, the instability evolves to a fini te amplitude and rotates rigidly, as predicted from the theory of bifu rcations in rotating systems. As the field strength is increased the s olution adopts a completely different spatial configuration and has a different characteristic frequency to the branch found at the lower fi eld strength. The primary Hopf bifurcation is thought to be of a subcr itical 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 str engths lower than the strength at the point of marginal stability.