Hydromagnetic Flow due to an Oscillating Plane

A review is given of Stokes' problem concerning the effect of viscosity in modifying the motion of a fluid in contact with vibrating solids. A suggestion was made as to the possibility of measuring the effect of a magnetic field on the propagation of sound in a tube containing mercury. The obvious extension of Stokes' problem was to the case of a conducting fluid in the presence of an impressed uniform magnetic field of strength B/sub 0/ in the z direction. The hydromagnetic flow set up by the plane is governed by the equations of hydrodynamics and continuity, Maxwell's equations (neglecting displacement currents), and Ohm's law for a moving conductor. The boundary conditions necessary to determine the unique solution of these equations are outlined. A discussion is given of a number of limiting cases to the formal solution to the flow problem. The limitations are for low, moderate, and high conductivity ( beta >> 1. beta = 1, beta << 1); in each case the effects of strong and weak magnetic fields are considered. Considerations are given for the rotating and nonrotating states of flow. (B.O.G.)