Periodic flows of a conducting liquid in a traveling magnetic field

V. I. Merkulov - V. F. Tkachenko - V. I. Yatsenko

Abstract
Planar periodic flow of a nonviscous liquid in a traveling field (with a tangential component of the induction specified on the boundaries), or in a field that is a superposition of a longitudinal constant field in a traveling field, is investigated numerically by the grid method. The method used for solving the nonlinear system of magnetohydrodynamics equations is based on explicit difference schemes of second-order accuracy. The evolution of the flow under the influence of a traveling field is considered from the initial state of rest in the channel with zero flow. The dependence of the character of motion of the liquid on the dimensional parameters characterizing the channel and the magnetic field (width of channel, phase shift, magnetic-pressure parameter) is investigated. It is shown that the traveling magnetic field produces in the conducting liquid closed circulating (secondary) flows, as the result of which the motion in the infinite channel has a periodic structure. The circulation zones are located in definite places relative to the conductor and lead to an ordering mixing of the liquid. In a purely traveling field, the distances between the circulation regions are equal to the pole pitch. In a longitudinal field, the appearance and development of circulating motions are more intense, and their repetition period is equal to the wavelength of the traveling field (double the pole pitch). When the inductor is connected in phase or in counterphase, the flow is symmetrical relative to the channel axis, and in a constant magnetic field the flow is asymmetrical.