We examine the nonlinear evolution of instabilities of toroidal magnetic
fields that are either antisymmetric or symmetric with respect to the equatorial
plane. Strong antisymmetric toroidaI fields will be present in planetary
interiors because of strong differential rotation, and the stability of
such fields will be an important consideration for the overall dynamo mechanism.
An earlier detailed linear stability analysis has provided the foundation
for the calculations, and previous nonlinear stability calculations
of z-independent fields form the basis for our numerical approach.
The magnetic field strength is parameterised by the Elsasser number, L,
such that Lc is the critical field
strength, and we use an Ekman number, e = 10-4.
We find that finite amplitude solutions exist for L
> Lc and that no such solutions exist
for L < Lc
(a weakly nonlinear analysis in the magnetostrophic regime had previously
shown that subcritical finite amplitude solutions do exist). By investigating
the dominant nonlinear effects, we conclude that our solutions are influenced
by the viscosity of the model fluid, and that at e
= 10-4 the solutions are not yet dominated by the geostrophic
flow, as we might expect in the small e limit.