Secondary flows in a rotating circular cylinder of incompressible conducting fluid as the result of the sudden turning-on of a transverse magnetic field

We study vortex flows in a rotating circular cylinder of incompressible fluid resulting from the sudden turning-on of a transverse magnetic field. The investigation is performed for the initial stage when secondary flow is determined mainly by Lorentz forces, and the effect of viscosity and the convective transport of vorticity by secondary flow is negligibly small. No restrictions are imposed on the magnetic Reynolds number R_m for the basic rotational motion; the number R_m' calculated from a typical secondary flow speed is assumed small.