In this paper, we investigate numerically the flow of an electrically conducting fluid in a
cylindrical Taylor-Couette flow when an axial magnetic field is applied. To minimize Ekman
recirculation due to vertical no-slip boundaries, two independently rotating rings are used at
the vertical endcaps. This configuration reproduces setup used in laboratory experiments
aiming to observe the magnetorotational instability (MRI). Our 3D global simulations show
that the nature of the bifurcation, the non-linear saturation, and the structure of axisymmetric …