Variations in driving torque in Couette-Taylor flow subject to a vertical magnetic field

We numerically investigate variations in the required driving torque for Couette-Taylor flow in an electrically-conducting fluid under the influence of a uniform, vertical magnetic field. The radius ratio of the coaxial cylinders (η = Rin/Rout) is 0.5 and the aspect ratio (A height/gap) is 4. The inner cylinder rotates at a constant speed and the outer cylinder is kept at rest. A uniform magnetic field is applied vertically. Without the magnetic field, the azimuthal Couette-Taylor flow induces a secondary meridional flow when the non-dimensional rotation speed of the inner cylinder exceeds the critical Reynolds number. When a moderate magnetic field is applied, Lorentz forces in the fluid lead to first order changes in the meridional flow mode and the required driving torque is reduced by as much as 25%. However, a stronger imposed magnetic field increases the torque due to the suppression of the azimuthal flow by the Lorentz force