Three-dimensional instability and patterns of an axisymmetric flow of electrically conducting liquid in a cylindrical enclosure driven by an axial traveling magnetic field (TMF) is studied. The attention is focused on the TMF of a large axial wavenumber or large frequency, which leads to a formation of the skin layer near the sidewall. It is shown that the flow intensity grows with the increase of the TMF wavenumber from small to a moderate value and decreases with further increase of the wavenumber. Similar dependence of the flow intensity on the growing TMF frequency is observed. The critical amplitude of the electromagnetic forcing, which corresponds to a transition from axisymmetric to three-dimensional flow state, sharply decreases with the increase of the TMF wavenumber or frequency from a small value. After reaching a minimum it slowly increases with the further increase of the wavenumber or frequency. (c) 2005 Elsevier B.V. All rights reserved.