The effect of imposing shear flow on a charge-modulated electroosmotic flow is theoretically investigated. The flow structures exhibit either saddle points or closed streamlines, depending on the relative strength of an imposed shear to the applied electric field. The formation of closed streamlines could be advantageous for trapping nondiffusive particles at desired locations. Different time periodic alternating flows and their corresponding particle trajectories are also examined to assess strategies for creating efficient mixing.