Spin-up from rest in a cylinder of an electrically conducting fluid in an axial magnetic field

Spin-up from rest in a vertically-mounted cylinder of aspect ratio unity of an electrically conducting fluid is studied numerically and analytically. A uniformly-distributed vertically-directed magnetic field is imposed. The formulation is given for the fluid dynamic and the electro-magnetic equations. Numerical solutions are obtained to the time-dependent governing equations. The evolutions of the three-component velocity field and electric current density are portrayed. The solutions for an electrically-nonconducting fluid are in accord with the classical model descriptions. The interactions of the Lorentz force and fluid dynamic forces lead to the suppression of the meridional circulation. For large interaction parameter N, where the Hartmann layer dominates, such an MHD spin-up time scale is proportional to Ha(-1) E-1. This implies that the spin-up proceeds faster as Ha and E increase.