Journal of Conference Abstracts

Kinematic Dynamo Action in a Sphere: Effects of Differential Rotation and Meridian Circulation

David Gubbins (gubbins@earth.leeds.ac.uk)

School of Earth Sciences, University of Leeds, Leeds, LS2 9JT, U.K.

In the kinematic dynamo the magnetic field is generated by a specified fluid flow which does not have to satisfy the momentum equation. This restriction allows us to investigate dynamo action of a wide range of flows relatively easily. It also gives the relationship between the morphology of the generated field and underlying flow. Kumar & Roberts [1975] found a class of steady flows in a sphere that generate geophysically realistic magnetic fields. Their flows comprise overturning convection, differential rotation (D), and meridian circulation (M). They are here studied to understand the effects of varying D and M, with the following results:

(1) About 20% of the flows generate steady dipole fields. The axial dipole is dominant but smaller in relation to the rest of the field than in the Earth. This is probably because the Earth's field is generated preferentially near the tangent cylinder to the inner core.

(2) About 3% of the flows generate steady quadrupole fields. The flows are all opposite in sign to those generating dipole fields, as expected from the adjoint symmetry of the induction equation.

(3) A very small proportion of the flows generate oscillatory fields. The change from steady to oscillatory solutions takes place with a very small change in flow. Oscillatory solutions are far less common than in the Braginsky limit. In many cases the oscillations take the form of flux migration from equator to pole or vice versa. These oscillations may resemble the geomagnetic field during polarity transition, and it may be possible to construct a geophysically realistic reversal using a time-varying flow.

(4) The remaining flows either generate no field, or generate a field that is too complex to be represented by the numerical scheme. They exhibit a whole menagerie of numerical disasters: some may be resolvable with better numerical methods and a bigger computer but others never will.