The nonlinear evolution of magnetic instabilities in a rapidly rotating annulus

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Abstract
A numerical investigation of the stability of an axisymmetric magnetic field is discussed. The magnetic field permeates a finitely conducting fluid contained within a rapidly rotating cylindrical annulus. The fluid is incompressible and viscid. The evolution of a non-axisymmetric perturbation to the axisymmetric magnetic field is governed by the momentum and induction equations which are integrated using a spectral timestep method. We follow the growth of the perturbation to finite amplitude and find that the character of the solution is dominated by the most unstable axially dependent mode found from the linear theory.

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