Liquid metal flow in a finite-length cylinder with a rotating magnetic field

A liquid metal flow induced by a rotating magnetic field in a cylindrical container of finite height was investigated experimentally. It was demonstrated that the flow in a rotating magnetic field is similar to geophysical flows: the fluid rotates uniformly with depth and the Ekman layer exists at the container bottom. Near the vertical wall the flow is depicted in the form of a confined jet whose thickness determines the instability onset in a rotating magnetic field. It was shown that the critical Reynolds number can be found by using the jet velocity u₀ for Re_cr =u²₀/u/r. The effect of frequency of a magnetic field on the fluid flow was also studied. An approximate theoretical model is presented for describing the fluid flow in a uniform rotating magnetic field.List of Symbols U_r, U, U_z radial, azimuthal and vertical velocity components, respectively - B_r, U, B_z radial, azimuthal and vertical magnetic induction components - A vector potential of magnetic field - j induced electric current density - electrical conductivity of fluid - electrical potential - kinematic viscosity - tf electromagnetic volume force - angular velocity of fluid rotation - R container radius - H container height - aspect ratio - E Ekman number - Re_cr critical Reynolds number - r, z radial and axial coordinates