Solitary wave on the surface of a shear stream in crossed electric and magnetic fields: The formation of a single vortex

V. A. Miroshnikov

Institute of Physics, Latvian University, Salaspils-1, LV-2169, Latvia

Abstract
An analytical solution is presented for a long, fast and finite-amplitude solitary wave on the surface of a shear stream of an ideal incompressible electrolyte in crossed nonuniform electric and magnetic fields. The problem is solved using an extension of the Rayleigh method. When the electromagnetic force is potential, the pressure distribution is obtained in an explicit form of the Bernoulli integral for two-dimensional steady-state flows. Both with a potential and a rotational force, a single vortex is formed on the solitary wave crest in a specific Froude number range. The vortex structure of the considered flow is determined by the vorticity of the upstream flow and by rotj x B, both of which are linear functions with respect to the vertical coordinate. Figs 5, Refs 12.