Problems in magnetohydrodynamics and in electrohydrostatic stability

The fluid motions induced in a container by electromagnetic forces at high currents are investigated. The nonlinear Navier-Stokes equations governing the problem are formulated in terms of ordinary differential equations which are solved semi-analytically. Taking adequate account of the finiteness of the area through which the current is discharged into the fluid it is shown that a current of up to 600A may be discharged into a steel weld pool without causing any breakdown in the velocity. The development of the flow field for a particular case is discussed, the solution of which is obtained analytically. It is shown that when the flow field is confined into the interior of a hemisphere the time taken to establish the steady state flow is reduced by a factor of ten compared with the situation where the flow takes place in a semi-infinite fluid. The equilibrium and stability of two conducting charged membranes in an axisymmetric configuration are discussed. Our results suggest that when the membranes are charged beyond a certain level there is a breakdown in the equilibrium of the membranes, the mode of breakdown being dependent on the distance between the membranes. In the special case when the membranes are equal and the gap between them is much less than their radii our results are in quantitative agreement with existing solutions and experimental data. (author)