Scaling laws in axisymmetric magnetohydrodynamic duct flows

We report on a numerical study of axisymmetric flow of liquid metal in a circular duct with a rectangular cross section. The flow is forced through the combination of an axial magnetic field and a radial current. Sweeping a wide range of forcing parameters, we identify the different regimes which characterize the flows and explicate the associate scaling laws. Results from different studies in the literature are interpreted in the light of our numerical simulations.