Linear stability analysis for a rotating cylinder with a rotating magnetic field

This paper treats the first hydrodynamic instability for a uniform-density, electrically conducting liquid in a finite-length cylinder which is rotating about its centerline. There is a uniform, transverse magnetic field which rotates about the cylinder’s centerline and which produces a steady, axisymmetric, azimuthal body force on the liquid. For the initial transition from a steady, axisymmetric flow to a periodic, nonaxisymmetric flow, results for the critical value of the magnetic Taylor number and for the frequency of the critical disturbance are presented as functions of the Reynolds number for the cylinder rotation. Rotations of the cylinder and of the magnetic field in the same azimuthal direction and in opposite directions are considered.