Stability of an azimuthal flow formed under the influence of a rotating magnetic field

A. B. Kapusta - V. V. Dremov - E. S. Bartoshuk

Abstract
The stability problem is studied for an azimuthal dissipative flow of an incompressible electrically conducting liquid in an infinitely long tube of circular cross section, the flow being formed under the influence of a rotating homogeneous magnetic field of the form H₀ expi(ω−ϕ), whose axis of rotation coincides with the symmetry axis of the tube. The system of magnetohydrodynamic equations, which describes an axisymmetric rotation of the liquid, averaged over ϕ (in the induction-free approximation), is investigated by the method of small perturbations to test the stability of the primary stationary flow. Solution of the system by Galerkin's method yields the critical values of the Hartmann number and the wave number for different values of the dimensionless number Re_ω=ωR₀²/ν. It is shown that a secondary stationary flow is formed as a double vortex layer. The calculated values of Hacr agree well with the experimental results.