Magnetohydrodynamic Flow in a Container

A linear theory for steady rotational motions is presented under the assumptions that Rm and ε are much less than E where Rm, ε, and E are the “rotational” magnetic Reynolds, Rossby, and Ekman numbers, respectively. The effect of the “rotational magnetic force coefficient,” N2 ( = σμ2 H02/ρΩ), which is a measure of the relative importance of the magnetic forces (of order σμ2 ΩLH02) and the rotational forces (of order ρΩ2 L) is investigated. Attention is focused on the case when the direction of rotation and applied magnetic field at infinity are parallel, and all boundaries are either perpendicular or parallel to this direction. If N2< < 1, Ekman layer suction and the double structure of the vertical Stewartson layers are dominant, but if N2〉 〈 E−1/3, the magnetic forces dominate and a Hartmann-type boundary layer is present with the double structure of the vertical boundary layer disappearing and being replaced by a single layer. A solution for the complete range of values of N2 is presented.