Turbulence in electromagnetically-driven Keplerian flows

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.