Choosing a simple class of flows, with characteristics that may be present in
the Earth's core, we study the ability to generate a magnetic field when the
flow is permitted to oscillate periodically in time. The flow characteristics
are parameterised by D, representing a differential rotation, M, a meridional
circulation, and C, a component characterising convective rolls. Dynamo action
is sensitive to these flow parameters and fails spectacularly for much of the
parameter space where magnetic flux is concentrated into small regions.
Oscillations of the flow are introduced by varying the flow parameters in
time, defining a closed orbit in the space (D,M). Time-dependence appears to
smooth out flux concentrations, often enhancing dynamo action. Dynamo action
can be impaired, however, when flux concentrations of opposite signs occur
close together as smoothing destroys the flux by cancellation.
It is possible to produce geomagnetic-type reversals by making the orbit
stray into a region where the steady flows generate oscillatory fields. In this
case, however, dynamo action was not found to be enhanced by the
time-dependence.
A novel approach is taken to solving the time-dependent eigenvalue problem,
where by combining Floquet theory with a matrix-free Krylov-subspace method we
avoid large memory requirements for storing the matrix required by the standard
approach.Comment: 22 pages, 12 figures. Geophys. Astrophys. Fluid Dynam., as accepted
(2004