ON THE MOTION OF A RIGID CYLINDER IN A ROTATING ELECTRICALLY CONDUCTING FLUID

The flow structures generated and drag experienced by a rigid cylinder moving in an arbitrary direction through a rotating electrically cond ucting fluid in the presence of an applied magnetic field are investig ated, with the aim of understanding better the nature of the small-sca le flow in the core of the Earth which may be responsible for maintain ing the geomagnetic field through dynamo action. Three cases are consi dered in the limit of small Rossby and magnetic Reynolds numbers. In t he case of very weak rotation, the possible flow structures consist of a thin Hartmann layer and a long wake extending in the direction of t he magnetic field, in which Lorentz and viscous forces balance, but on ly the long wake plays a dynamical role. The dominant drag force is ex perienced for motion that cuts magnetic lines of force. Motion of the cylinder parallel to its axis induces a much weaker drag, while that i n the direction of the magnetic field induces none to dominant order. The cylinder also experiences weak lateral forces due to the Coriolis effect. In the case of weak rotation, the balance in the long wake is now magnetostrophic: between Lorentz and Coriolis forces. The drag is qualitatively identical to that in the first case, but the drag induce d by motion parallel to the axis of the cylinder is increased, though still smaller than that for motions cutting magnetic lines of force. I n the case of strong rotation, the flow structures consist of a thin E kman layer and a foreshortened Taylor column extending in the directio n of the rotation axis. In this column, the force balance is again mag netostrophic. Again only the large-scale structure plays a dynamical r ole. Motion of the cylinder perpendicular to its axis induces a larger drag than does motion parallel to its axis. The cylinder also experie nces large lateral Coriolis forces.