Angular Momentum Transport by Keplerian Turbulence in Liquid Metals

Abstract: We report a laboratory study of the transport of angular momentum by a turbulent flow of an electrically conducting fluid confined in a thin disk. When the electromagnetic force applied to the liquid metal is large enough, the corresponding volume injection of angular momentum produces a turbulent flow characterized by a time-averaged Keplerian rotation rate $\bar{\Omega}\sim r^{-3/2}$. Two contributions to the local angular momentum transport are identified: one from the poloidal recirculation induced by the presence of boundaries, and the other from turbulent fluctuations in the bulk. The latter produces efficient angular momentum transport independent of the molecular viscosity of the fluid, and leads to Kraichnan's prediction $\text{Nu}_\Omega\propto\sqrt{\text{Ta}}$. In this so-called ultimate regime, the experiment, therefore, provides a configuration analogous to accretion disks, allowing the prediction of accretion rates induced by Keplerian turbulence.