The three-dimensional, nonlinear evolution of a shear flow (or Kelvin-Helmholtz (KH)) instability driven by a large-amplitude shear Alfv¿n wave (SAW) in the Earth's magnetosphere is studied by using numerical solutions to the complete set of ideal magnetohydrodynamic equations. An initial setup is chosen to simulate a standing SAW associated with field line resonances (FLRs) in a dipolar magnetosphere. It is shown that KH vortices grow most rapidly in the equatorial plane. In this region, the growth rate is reduced by the ratio of the KH and SAW frequencies when compared to the growth rate predicted by a two-dimensional theory for transient magnetic field lines. For typical parameters of FLRs, this ratio is small. Field-aligned gradients of the KH mode vorticity and azimuthal phase velocity initiate Alfv¿n waves, which carry energy toward the ionosphere. This results in partial restructuring of field-aligned currents with scale size of ~10 km above the ionosphere. After one period of the SAW, energy in the KH mode returns to the SAW flow. This suggests that vortex formation might be largely periodic in evolution, reconfiguring after each period of the FLR. Finally, we show that this restructuring of field-aligned currents does not depend on the initial phase of the SAW. For example, the model predicts that a ground-based observer in the Northern Hemisphere (looking antiparallel to the Earth's magnetic field) will see that the downward current wraps clockwise and the upward current wraps counterclockwise, though the positions of the currents change latitudes for different phases. ¿ 1999 American Geophysical Union