  We present measurements performed in a spherical shell filled with liquid
sodium, where a 74 mm-radius inner sphere is rotated while a 210 mm-radius
outer sphere is at rest. The inner sphere holds a dipolar magnetic field and
acts as a magnetic propeller when rotated. In this experimental set-up called
DTS, direct measurements of the velocity are performed by ultrasonic Doppler
velocimetry. Differences in electric potential and the induced magnetic field
are also measured to characterize the magnetohydrodynamic flow. Rotation
frequencies of the inner sphere are varied between -30 Hz and +30 Hz, the
magnetic Reynolds number based on measured sodium velocities and on the shell
radius reaching to about 33. We have investigated the mean axisymmetric part of
the flow, which consists of differential rotation. Strong super-rotation of the
fluid with respect to the rotating inner sphere is directly measured. It is
found that the organization of the mean flow does not change much throughout
the entire range of parameters covered by our experiment. The direct
measurements of zonal velocity give a nice illustration of Ferraro's law of
isorotation in the vicinity of the inner sphere where magnetic forces dominate
inertial ones. The transition from a Ferraro regime in the interior to a
geostrophic regime, where inertial forces predominate, in the outer regions has
been well documented. It takes place where the local Elsasser number is about
1. A quantitative agreement with non-linear numerical simulations is obtained
when keeping the same Elsasser number. The experiments also reveal a region
that violates Ferraro's law just above the inner sphere.
