NORMAL MODES OF DECAY OF A MAGNETIC FIELD IN MAGENTOHYDRODYNAMICS

The effect of non-uniform rotation, in which the angular velocity is an increasing function of the distance from the axis, in an infinite circular conducting fluid cylinder, on the normal modes of decay of a magnetic field are studied. It is found that the field is carried round by the fluid. For slow motion, the field in each mode rotates with an angular velocity proportional to the fluid velocity, in the fast decaying modes the angular velocity of the field being one third the angular velocity of the fluid at the boundary. For fast motion, the field in the low modes rotates with the angular velocity of the fluid either near the axis of the cylinder, or near the boundary. Apart from the field in the fundamental mode the shearing motion can increase the time of decay, though in no case is there a substantial increase. © 1969 Oxford University Press.