On some similarity solutions in magnetohydrodynamics

In this paper we employ similarity considerations to investigate the flow field produced by an electric discharge (mathematically a current source) and a jet of momentum emerging from the same hole of a plane wall bounding a viscous, incompressible conducting fluid, which extends to infinity. We also use similarity solutions in considering the axisymmetric configuration of a problem that has recently received some attention in connexion with field line reconnexion in conducting fluids. We derive the similarity equations for an incompressible, viscous conducting fluid, and discuss the solutions for the case when the fluid is perfectly conducting. When the electrical conductivity of the fluid is finite, we could not construct solutions, satisfying the appropriate boundary conditions.