Numerical simulations of an effective two-dimensional model for flows with a transverse magnetic field

This paper presents simulations of the two-dimensional model developed by Pothérat et al. (2000) for MHD flows between two planes with a strong transverse homogeneous and steady magnetic field, accounting for moderate inertial effects in Hartmann layers. We first show analytically how the additional terms, in the equations of motion accounting for inertia soften velocity gradients in the horizontal plane, and then we implement the model in a code to carry out numerical simulations to be compared with available experimental results. This comparison shows that the new model can give very accurate results as long as the Hartmann layer remains laminar. Both experimental velocity profiles and global angular momentum measurements are recovered, and local and global Ekman recirculations are shown to alter significantly the shape of the flow as well as the global dissipation.