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This paper presents simulations of the 2d model developed by Poth\'erat at al(\emph{J. Fluid Mech}, 2000) for MHD flows between two planes with a strongtransverse homogeneous and steady magnetic field, accounting for moderateinertial effects in Hartmann layers. We first show analytically how theadditional terms in the equations of motion accounting for inertia, softenvelocity gradients in the horizontal plane, and then we implement the model ona code to carry out numerical simulations to be compared with availableexperimental results. This comparison shows that the new model can give veryaccurate results as long as the Hartmann layer remains laminar. Bothexperimental velocity profiles and global angular momentum measurements areclosely recovered, and local and global Ekman recirculations are shown to altersignificantly the aspect of the flow as well as the global dissipation.

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