| Planetary or stellar dynamos are typically though of as driven by convection.However,
differential rotation offers an alternative mechanism. Being much easier to implement
mechanically it forms the basis for two second generation dynamo experiments in Grenoble
and Maryland. Differential rotation effects may also play a role in planetary or stellar
dynamos.
To explore these possibilities we numerically model the spherical Couette system: a
spherical shell filled with a viscous and electrically conducting fluid where the outer
boundary rotates with Ω and the inner boundary with a slightly slower or faster
rate Ω + δΩ. Performing a large number of simulations at different parameters we
find that larger Ω values (corresponding to low Ekman numbers) allow to decrease
the magnetic Prandtl and Reynolds numbers. Similar to what has been found in
convectively driven dynamo models, the ordering Coriolis force helps dynamo
action.
An extrapolation of our results to the parameters of the Maryland experiment
suggest that this may not work as a dynamo. The predicted critical magnetic Prandtl
number where dynamo action is still possible lies at Pmc -Ã10-3 while the
Prandtl number of liquid sodium used in the experiment is two orders of magnitude
lower.
For super-rotation (δΩ > 0) the produced magnetic field is very similar to recent
Saturn field models: It is highly axisymmetric and strongly concentrated at high
latitudes. When extrapolating our results to Saturn we find that Pmc is around
10-7 which lies below possible Pm values estimated for Saturn. The required
differential rotation is as small as δΩ-Ω - 10-8. Using simple models for the Helium
rain though to happen Saturn’s metallic envelope we try to access whether this
mechanism could maintain this small differential rotation and produce the required power. |