We present a numerical analysis of free-surface liquid metal flow and its three-dimensional linear stability. The flow is driven by an alternating magnetic field in a spinning cylindrical container. The electromagnetic and hydrodynamic fields are fully coupled via the shape of the liquid free surface. The hydrodynamic equations are solved by a spectral collocation method, and the alternating magnetic field distribution is found by a boundary-integral method. The flow stability is analyzed for various magnetohydrodynamic interaction parameters and Ekman numbers assuming a flat free surface. We find that only a sufficiently fast spinning suppresses and stabilizes the flow, but a moderate spinning can significantly destabilize it.
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