Vortex breakdown in time-dependent electromagnetically driven flow between concentric spheres

Abstract

The electromagnetically driven flow in the wide gap of a concentric sphere system is studied experimentally and numerically in the laminar regime ($Re\le 1540$ ). The azimuthal driving Lorentz force is primarily promoted by the interaction of a direct current and a dipolar magnetic field. The current is injected through two ring-shaped copper electrodes located at the equatorial zone of each sphere, and the magnetic field is produced by a permanent magnet located inside the inner sphere. Velocity profiles for the azimuthal component in the equatorial plane were obtained with particle image velocimetry, and the radial velocity component of the flow was recorded using ultrasonic Doppler velocimetry. Laser-fluorescein technique was used for flow visualization. It was found that for a critical electric current (Re = 1140), an instability occurs and the flow becomes time-dependent. We found, theoretically and experimentally, a vortex breakdown structure at each of the polar zones of the spherical gap, and to the best knowledge of the authors, this is the first time it is reported with electromagnetic forcing. A full three-dimensional numerical simulation reproduces the experimental observations qualitatively and quantitatively.