Angular momentum transport in electrically-conducting fluids

The radial transport of angular momentum is a central quantity in astrophysics, as it is an essential ingredient in the dynamics of many objects, among which the best known are accretion discs or radiative stars. In both cases, the mechanism that generates the turbulence and the amount of angular momentum transported outward remain to be clearly identified. This problem has also attracted a lot of attention on a more fundamental point if view, where it is questionable whether there is a so-called ultimate regime in which the angular momentum flux becomes independant of molecular viscosity. Taylor-Couette setups have long been considered as a powerful tool to study this problem. In this talk, I will briefly review these efforts, and present two recent studies investigating this problem of angular momentum transport from a different perspective: I will first describe a new laboratory experiment in which the Couette flow is driven by an electromagnetic force rather than the rotation of the boundaries, leading to an interesting analogue of astrophysical disks. In a second part, I will describe numerical simulations of stratified spherical Couette flow aiming to model a radiative star. For some parameters, a magnetic field is self- generated by the star and produces a significant angular momentum flux, leading to a drastic spin-down of the inner part of the star