Magnetohydrodynamics of Conical Flows

Abstract

The effect of diverging or converging electric currents on a stationary, viscous, incompressible, conducting body of fluid, confined in a cone of infinite extent, is investigated. The fluid moves down from upstream infinity near the walls and as it approaches the apex of the cone, it changes its direction in the core of the cone and moves toward upstream infinity near the axis. With increasing currents, the velocity near the axis rises very rapidly. Similar phenomenon have been observed in the laboratory electric arcs and in thermal plasmas of the solar atmosphere. Next, when a fixed amount of fluid is drained from the apex of the cone, the flow divides into two regions far from the apex. The drained fluid reaches the apex only through a narrow region near the walls whereas fluid in the core of the cone executes a secondary motion, similar to the first case of confined flow. There exists a stagnation point on the axis and its location is primarily controlled by current density, fluid drainage rate, and the cone angle of the configuration.