Investigation of MHD phenomena in the flow of a viscous conducting fluid in a traveling magnetic field

V. F. Tkachenko

Abstract
The flow of a viscous incompressible conducting fluid induced bya magnetic field is investigated. Two problems are solved. In the first, the fluid occupies a half-space and is subjected to a magnetic field which is the superposition of two fields - a constant longitudinal field and a traveling field with a tangential induction component given on the boundary. In the second problem, the flow is investigated in a plane channel in the field of a bilateral inductor. The solution of the nonlinear system of magnetohydrodynamic (MHD) equations, written in terms of the stream function, the vorticity, and the magnetic-field vector potential, is obtained by the method of successive approximations. The method takes specific features of the problem into account and is based on the expansion of the solution in a series of harmonic components which are multiples of the fundamental harmonic of the given traveling field. The principal terms of the expansions are determined for all harmonics in the first problem. The expressions derived for the velocity components indicate that the flow of an electrically conducting fluid is unstable, and the background of the laminar plane-parallel flow contains velocity fluctuations whose frequency equals the frequency of the traveling field and whose magnitude is proportional to the ratio of the constant field to the amplitude of the traveling field. In the second problem, the zero-order approximation for the zeroth harmonic gives the velocity profile of the laminar plane-parallel flow investigated earlier.