Numerical simulations of the kinematic induction equation have been carried out in a cylindrical domain that
resembles the configuration of the VKS dynamo experiment. Primary objective are investigations of
non-axisymmetric source terms and their impact on the critical Reynolds number as well as on the structure of
the field geometry.
In case of an axisymmetric velocity distribution the resulting magnetic field is always determined by an
azimuthal m=1-mode which is in contradiction to the experimental realization that is dominated by an
axisymmetric field.
A simple non-axisymmetric contribution can be parameterized by a localized $\alpha$-effect which arises from
the induction action of radially oriented helical outflow between the impeller blades that drive the flow.
However, it turns out, that the amplitude of $\alpha$ which is necessary to obtain an axisymmetric field is far
above realistic values.
Further potential contributions involve a time dependent non-axisymmetric velocity component in form of
azimuthal drifting equatorial vortices as they have been found in water experiments. These structures provide a
coupling between different field modes, but the m=1 mode still remains dominant.
Resonance effects provide a strong increment of the field growthrate if the vortex drift motion proceeds phase
synchronous with a drift of the magnetic field caused by equatorial symmetry braking of the velocity
distribution.
Presumably this phenomenon is not relevant in the experiment, as the drift of the eigenfield is very small so
that resonance would require a much slower vortex drift velocity than it is observed.
So far, non-axisymmetric source terms in the induction equation are not able to explain the dominance of the
m=0 mode, however it remains still possible that a quite exotic dynamo mechanism is operating which is
essentially based on induction terms generated by the azimuthal variation of the permeability introduced by the
ferrous impellers.