The MHD flow driven by a travelling magnetic field (TMF) in an annular channel is investigated numerically. Laminar and turbulent regimes of the flow are studied, using both axisymmetric and 3D simulations. At low hydrodynamical Reynolds numbers Re, it is seen that for sufficiently large magnetic Reynolds number Rm, or if a large enough pressure gradient is externally applied, the system undergoes an instability in which the flow rate in the channel dramatically drops from synchronism with the wave to much smaller velocities. This transition takes the form of a saddle- node bifurcation for the time-averaged quantities. We characterize the bifurcation, and study the stability of the flow as a function of several parameters. We show that the bifurcation of the flow involves a bistability between Poiseuille-like and Hartman-like regimes, and relies on magnetic flux expulsion. Based on this observation, new predictions are made for the occurrence of this stalling instability. For large Re, and with more realistic boundary conditions, we show that the instability takes the form of a large axisymmetric vortex flow in the (r; z)-plane, in which the fluid is locally pumped in the direction opposite to the one of the magnetic field. Close to the marginal stability of this vortex flow, a low-frequency pulsation is generated. For 3D simulations, it is shown that the strong shear produced by the local stalling of the flow leads to a 3D destabilization in the azimuthal direction, characterized by the growth of nonaxisymmetric modes of the velocity field. Finally, these results are compared to theoretical predictions and are discussed within the framework of experimental annular linear induction electromagnetic pumps.