Transition to turbulence and transport of angular momentum 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 herein. Quasi-Keplerian velocity profiles occur when the forcing is small so the Lorentz force is balanced by either viscoity or inertia. At large current and moderate magnetic field, a new regime is observed which is characterized by a Keplerian mean rotation profile Ω∼(IB)^1/2r^-3/2.  In this turbulent regime, the dynamics is typical of thin layer turbulence. A direct cascade transports the energy from the vertical integral length scale h towards the small scales and for scales larger than h, an inverse cascade occurs. The transition from the viscous/inertial regime to the fully turbulent state is well understood as resulting from an instability of the B\"odewadt-Hartmann  layers at large Reynolds number. At very large forcing, the experiment then presents a configuration analogous to astrophysical disks, depicted by a fully turbulent flow, a Keplerian rotation rate and a volume injection of angular momentum. The angular momentum is then transported through an ultimate regime Nu∼Ta^1/2 independent of molecular viscosity. It is thus possible to make predictions for the accretion rates of astrophysical  accretion disks.