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Stability and nonlinear evolution of rotating magnetohydrodynamic flows in the Princeton magnetorotational instability (MRI) experiment are examined using three-dimensional non-axisymmetric simulations. In particular, the effect of axial boundary conductivity on a free Stewartson-Shercliff layer (SSL) is numerically investigated using the spectral finite-element Maxwell and Navier Stokes (SFEMaNS) code. The free SSL is established by a sufficiently strong magnetic field imposed axially across the differentially rotating fluid with two rotating rings enforcing the boundary conditions. Numerical simulations show that the response of the bulk fluid flow is vastly different in the two different cases of insulating and conducting end caps. We find that, for the insulating end caps, there is a transition from stability to instability of a Kelvin-Helmholtz-like mode that saturates at an azimuthal mode number m=1, whereas for the conducting end caps, the reinforced coupling between the magnetic field and the bulk fluid generates a strong radially localized shear in the azimuthal velocity resulting in axisymmetric Rayleigh-like modes even at reduced thresholds for the axial magnetic field. For reference, three-dimensional nonaxisymmetric simulations have also been performed in the MRI unstable regime to compare the modal structures. [ABSTRACT FROM AUTHOR]

The effects of axial boundary conductivity on the formation and stability of a magnetized free Stewartson-Shercliff layer (SSL) in a short Taylor-Couette device are reported. As the axial field increases with insulating endcaps, hydrodynamic Kelvin-Helmholtz-type instabilities set in at the SSLs of the conducting fluid, resulting in a much reduced flow shear. With conducting endcaps, SSLs respond to an axial field weaker by the square root of the conductivity ratio of endcaps to fluid. Flow shear continuously builds up as the axial field increases despite the local violation of the Rayleigh criterion, leading to a large number of hydrodynamically unstable modes. Numerical simulations of both the mean flow and the instabilities are in agreement with the experimental results. [ABSTRACT FROM AUTHOR]