David Fearn ,  University of Glasgow

Studies of the stability of prescribed magnetic fields in rapidly rotating systems have
clearly established the relevance of the mechanism of magnetic field instability to the dynamics of planetary cores.
The present study investigates the nonlinear development of such instabilities and their feedback on the field generation process.
The non-axisymmetric instability of a mean magnetic field $\bar{\mathbf B}$ generated by
 a prescribed $\alpha$-effect has been investigated in a rapidly rotating fluid spherical shell. The
mean field drives a flow through the Lorentz force in the momentum equation and this flow feeds back on the field-generation process in the magnetic induction equation,
equilibrating the field at some finite amplitude.
This amplitude increases with $\alpha_0$, the strength of $\alpha$. Above some critical
value of $\alpha_0$ the mean field becomes unstable to a non-axisymmetric instability.
We are particularly interested in how the instability affects the mean field generated.
We find that instability can dramatically reduce
the strength of the mean field and significantly constrains the growth of $\bar{\mathbf B}$ with $\alpha_0$.