An analytical estimate of the width of the generated chaotic layer in a time-periodically driven stream function model for the motion of passive tracers is discussed. It is based essentially on the method of the separatrix map and the use of the Melnikov theory. Energy-time variables are used to derive lower bounds for the half width of the layer. In order to perform a comparison with numerical simulations, the results are transformed into space variables. The analytic results of the layer thickness in both parallel and perpendicular directions to the shear flow are compared with numerical computations and some systematic deviations are discussed.