When a time periodic perturbation is added to a laminar steady flow, fluid mixing effect is sometimes extremely enhanced. In order to clarify the reason, numerical simulations of fluid mixing were conducted for two 2-dimensional and one 3-dimensional flow systems. As a result, it was revealed that for perturbation of constant amplitude the best mixing effect was obtained when the period ratio T-ave/T-p was approximately equal to the golden number (1+ root 5)/2, where T-ave is the mean circulation period of the unperturbed flow and T-p the perturbation period. In addition, the validity of this golden ratio condition for the convective fluid mixing was confirmed in two experiments of the 2-dimensional and the 3-dimensional flows. This phenomenon is due to the fact that the two flows related by the golden period ratio hardly synchronize with each other, and as a result, the streakline acting as the template of fluid mixing distributes uniformly in the fluid mixing region.