Magneto-Stokes Flow in a Shallow Free-Surface Annulus*

We present a magnetohydrodynamic flow inspired by the remarkable kinematic reversibility of viscous Taylor-Couette flows. We retain the cylindrical-annular geometry of the Taylor-Couette cell, but consider "magneto-Stokes" flow of a shallow, free-surface layer of electrolyte driven by applied electromagnetic forces. An analytical solution is presented here and validated with coupled laboratory and numerical experiments. The dominant balance of Lorentz forcing and basal viscous drag reproduces the kinematic reversibility observed by Taylor with precise electromagnetic control. Induced fluid deformation may be undone by simply reversing the polarity of electric current through the system. We illustrate this analogy with theory and experiment, and we draw a further connection to potential flow using the Hele-Shaw approximation. The stability and controllability of the magneto-Stokes system make it an attractive tool for investigating macro-scale shear flows in a variety of settings from industrial to astrophysical. In addition, the simplicity of the set-up and robustness of the flow also make magneto-Stokes flow a good candidate for PIV calibration and for educational demonstrations of magnetohydrodynamics, boundary layers, and flow transition.