| Abstract: | An electrically conducting viscous fluid-filled spherical shell is permeated by an axisymmetric strong potential magnetic field with large Elssaser number  2  1. We describe analytically the steady flow driven by a slightly faster rotation of the conducting inner boundary of the shell. The main flow is controlled by Ekman-Hartmann boundary layers with a small thickness  /, where 2
is the Ekman number. Asymptotics based on small –1  1 reveal the nature of a free shear layer O((/)1/2) and a super-rotation that allows a part of the fluid to rotate faster than the inner sphere. The free shear is following an imposed field line that is tangent to the inner or outer sphere. Meridional flux is concentrated in the shear and boundary layers. Fluid tends to rotate with the inner sphere and to expel azimuthal magnetic field from an
-region restricted by the free shear in the spherical shell.
For an imposed axial uniform magnetic field, this
-region is outside the cylinder tangent to the inner sphere and rotates with the outer sphere. Weak differential rotation O(/) is inside the cylinder, while almost all difference in rotation rates between spheres is accommodated in the thin O((/)1/2) free shear.
For an imposed dipole magnet, the region
has a shape of a lobe touching the outer equator. Inside
a super-rotation exists; this is the common case for such
when the source of the imposed field is inside. |
