Azimuthal rotation in the axisymmetric meridional flow due to an electric-current source

Abstract

The steady laminar flow driven by the meridional electromagnetic force due to an electric-current point source on a plane is considered. The previous studies of the problem (Shercliff 1970; Shilova & Shcherbinin 1971) lead to a self-similar solution of the full Navier–Stokes equations analogous to the classic Landau jet. The solution breaks down when a critical electric-current magnitude is exceeded (Sozou 1971). In the present paper the converging meridional flow is shown to be unstable to an axisymmetric azimuthal perturbation when the corresponding critical Reynolds number is exceeded. The flow solution breakdown is eliminated for the coupled converging and rotating flow. The physical process is suggested by the draining-vortex formation. The fluid-flow equations are solved by the Galerkin method, using expansions in Gegenbauer functions. The mechanism sustaining the rotation is examined; the increased angular momentum in the fluid region is maintained by the balance of viscous diffusion upstream and convection to the axis of symmetry. The experimental evidence for vortex formation is considered.