Lid-driven cavity flows have been one of the most interesting and challenging flow models. Their geometries are commonly found in polymer mixing, food processing applications, and microfluidic channels. In this study, the effect of a longitudinal periodic length on mixing in a cavity disturbed by a single discontinuous baffle mounted in the middle of its bottom was investigated numerically. The finite volume method (FVM) was used to solve the three-dimensional flow field of a purely viscous, non-Newtonian fluid obeying the Power-law model. Particle tracking was done using a self-developed fourth-order Runge-Kutta scheme. Using a cavity channel with a continuous baffle as an integral system, we proposed a new formula under the action-angle-angle framework of perturbation theory mapping schemes to analyze frequency ratio distribution along the different invariant action surfaces. The perturbation theory provided a good prediction of period tori for small perturbation cases. Three-dimensional geometry patterns of high-period islands were constructed in the reconstructed phase space to intuitively show where the regularity flow predominated mixing in the flow domain. When the perturbation strength increased to 0.5, mixing was sensitive to the chosen periodic lengths. A single discontinuous baffle succeeded in achieving excellent mixing when the periodic length was selected correctly. Poincare sections and the stretching of fluid filaments revealed that a periodic length of 12 mm achieved the best mixing in cases where the KAM cylinders disappeared and only three tiny period-3 tori wound around the top region of the cavity. It was also found that the larger the power law index, the better the mixing.