Instabilities of MHD flows driven by traveling magnetic fields

The flow of an electrically conducting fluid driven by a traveling magnetic field imposed at the end caps of a cylindrical annulus is numerically studied. At sufficiently large magnetic Reynolds number, the system undergoes a transition from synchronism with the traveling field to a stalled flow, similar to the one observed in electromagnetic pumps. An unusual type of boundary layer is identified for such electromagnetically driven flows that can be understood as a combination of Hartmann and Shercliff layers generated by the spatiotemporal variations of themagnetic field imposed at the boundaries. An energy budget calculation shows that energy dissipation mostly occurs within these boundary layers and we observe that the ohmic dissipation D-eta always overcomes the viscous dissipation D-nu, suggesting the existence of an upper bound for the efficiency of electromagnetic pumps. Finally, we showthat the destabilization of the flowoccurs when both dissipations are nearly equal, D-nu similar to D-eta.