Fluid motions due to an electric current source

Abstract

A concentrated electric current enters a region of fluid through an interface. It is shown that the magnetic field due to the current in general gives rise to rotational magnetic forces which must cause motions of the fluid. In particular the paper solves the axisymmetric non-linear problem in which a concentrated current enters a semi-infinite region of inviscid conducting fluid of constant density, inducing an inwards flow along the wall and a jet away from the wall opposite the current source. The case treated is the practically realistic one in which the effective magnetic Reynolds number is small and the current flows isotropically from the source. The first-order perturbation of this current distribution by electromagnetic induction is also calculated.An analytical solution is possible because the non-linear equation of motion happens to be a linear equation in the square of the Stokes stream function. The motion is analytically related to viscous jet flows discussed by Slezkin, Landau and Squire.