On Magnetohydrodynamics of Rotating Fluids

The influence of rather general electromagnetic forces acting upon steady rotating motions of conducting viscous incompressible fluids over a rotating disk is investigated by means of adjustable local boundary-layer approximations of first order. Numerical results for the most important motions of von Ka´rma´n and Bo¨dewadt are displayed and discussed in full detail. The hypothesis of small variations of the imposed magnetic field assumed in other investigations is found to be justified provided the corresponding Hartmann number and magnetic Reynolds number are of sufficiently small magnitude. Considerable distortions of the rotating motions result from strong electromagnetic forces. When the strength of the imposed electromagnetic forces is increased, the secondary motions may change their stagnation character to wake character, and vice versa. This change may proceed through the development of one-cell and two-cell flows as intermediate stages. The spatial instability of wake-type flows can be decreased or increased depending on the strength and the direction of the applied electromagnetic forces. In addition to critical Reynolds numbers, critical Hartmann numbers and magnetic Reynolds numbers are shown to exist beyond which no simple boundary-layer-type motions are possible. The interpretation of the spatial instability of wake-type flows as a separation phenomenon is supported by the “teacup” experiment photographed.