The study aims at showing how the dynamics of tracer gradient accounts for the stirring mechanism produced by a periodically forced flow relevant to practical mixing operation. The numerical simulation uses the equations for the orientation and norm of the tracer gradient and an analytic model for velocity. To a large extent, the micromixer properties over different ranges of the Strouhal number are explained through the response of the tracer gradient orientation to the tilting of strain principal axes resulting from flow forcing. The analysis also reveals a rich picture of stirring as the Strouhal number is varied.