Three-dimensional self-sustaining oscillations of the MHD flow of a finite-conductivity liquid trough a circular-cross-section channel in a longitudinal magnetic field

A. M. Sagalakov - A. Yu. Yudintsev

Abstract
The effect of finite conductivity on the branching of the 3D autooscillating regimes of MHD flow in an annular channel with perfectly conducting walls in a longitudinal magnetic field has been studied. Two types of 3D secondary autooscillationary regimes are formed for such flow, axisymmetrical and asymmetrical spiral autooscillations with average rotation. Taking into account the finite conductivity of the fluid, for this fully self-matched problem, one can conclude that along with a nonlinear interaction of velocity disturbances, nonlinear interaction of magnetic field disturbances becomes essential, and because of this, secondary autooscillating regimes not only deform the initial velocity profile but also contain stationary magnetic field components. The exitation of the stationary field is accompanied by the presence of stationary longitudinal and azimuthal currents. In the present paper, the branching of both types of secondary regimes has been calculated and the parameters at which spiral autooscillation with both average rotation and the azimuthal stationary field are stable have been revealed.