  The flow of an electrically conducting fluid in a thin disc under the action
of an azimuthal Lorentz force is studied experimentally. At small forcing, the
Lorentz force is balanced by either viscosity or inertia, yielding
quasi-Keplerian velocity profiles. For very large current and moderate magnetic
field, we observe a new regime, fully turbulent, which exhibits large
fluctuations and a Keplerian mean rotation profile $\Omega\sim
\frac{\sqrt{IB}}{r^{3/2}}$. In this turbulent regime, the dynamics is typical
of thin layer turbulence, characterized by a direct cascade of energy towards
the small scales and an inverse cascade to large scale. Finally, at very large
magnetic field, this turbulent flow bifurcates to a quasi-bidimensional
turbulent flow involving the formation of a large scale condensate in the
horizontal plane. These results are well understood as resulting from an
instability of the B\"odewadt-Hartmann layers at large Reynolds number and
discussed in the framework of similar astrophysical flows.
