| The interaction between shear flow and magnetic instabilities plays an important role for the
dynamics of many celestial bodies ranging from galaxies to the dynamo regions of planets.
Several laboratory and numerical experiments have been devoted to studying this
interaction. We have used numerical simulation to explore the flow and dynamo
action in a viscous and electrically conducting fluid between two differentially
rotating spheres, the spherical Couette system. The ration rate of inner and outer
spheres as well as the magnetic Prandtl number were varied in order to understand the
dynamics. The solutions for slowly rotating (Ekman number » 1) and fast rotating
outer spheres (Ekman number « 1) differ significantly with an interesting transition
regime. For slow rotating outer spheres and slow rotating inner spheres viscous
forces dominate and the fluid simply sticks to the inner boundary. This changes
when the inner sphere rotation rate increases. Meridional circulation creates a cusp
of fast rotating material attached to the inner sphere which ultimately becomes
instable and non-axisymmetric flow instabilities arise. These can drive a dynamo for
magnetic Prandtl numbers of 0.5 or larger. For a fast rotating outer sphere and slow
rotating inner sphere the system obeys the axisymmetric Taylor/Stewardson solution
where the fluid sticks to the outer boundary outside the tangent cylinder (TC), an
imaginary surface attached to the inner core equator and aligned with the rotation
axis. Inside the TC the fluid rotates with an rate intermediate between that of the
outer and inner spheres. The Stewardson layer that matches the flow inside and
outside the TC becomes instable when the differential rotation between inner and
outer boundary is increased, once more leading to non-axisymmetric flows. These
instabilities differ for prograde and retrograde rotating inner boundaries unless the
outer boundary rotating is very fast (E-¤ 10-6). The time behavior changes from
drifting to oscillatory and ultimately chaotic if the differential rotation is increased
further. As in the case for slow rotating outer boundaries, the instabilities can drive
dynamos. The lowest magnetic Prandtl number we were able to reach so far is 0.05 at
an Ekman number of E=10-4. Lower values may be possible, but we are limited
by our computer resources here. The results suggests that dynamo experiments
based on this setup may indeed succeed to produce self excited dynamo action. |