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 setup called “Derviche Tourneur Sodium” (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 nonlinear 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.

• Received 14 February 2011

DOI:https://doi.org/10.1103/PhysRevE.83.066310