Electrically driven vortices in a weak dipolar magnetic field in a shallow electrolytic layer

Steady dipolar vortices continuously driven by electromagnetic forcing in a shallow layer of an electrolytic fluid are studied experimentally and theoretically. The driving Lorentz force is generated by the interaction of a dc uniform electric current injected in the thin layer and the non-uniform magnetic field produced by a small dipolar permanent magnet (0.33 T). Laminar velocity profiles in the neighbourhood of the zone affected by the magnetic field were obtained with particle image velocimetry in planes parallel and normal to the bottom wall. Flow planes at different depths of the layer were explored for injected Currents ranging from 10 to 100 mA. Measurements of the boundary layer attached to the bottom wall reveal that owing to the variation of the field in the normal direction, a slightly flattened developing profile with no shear stresses at the free Surface is formed. A quasi-two-dimensional magnetohydrodynamic numerical model that introduces the non-uniformity of the magnetic field, particularly its decay in the normal direction, was developed. Vertical diffusion produced by the bottom friction was modelled through a linear friction term. The model reproduces the main characteristic behaviour of the electromagnetically forced How.