Magnetohydrodynamic flow due to the discharge of an electric current in a hemispherical container

In this paper the flow field induced in an incompressible viscous conducting fluid in a hemispherical bowl by a symmetric discharge of electric current from a point source at the centre of the plane end of the hemisphere is considered. This plane end is a free surface. An analytic solution for the slow viscous flow and a numerical solution for the nonlinear problem are constructed. The streamlines in an axial cross-section for two sets of closed loops, one on either side of the axis. The computations indicate that, for a given fluid, when the discharged current reaches a certain magnitude the velocity field breaks down. This breakdown probably originates at the vertex of the hemispherical container. (author)