Recently, practical use of a pulsatile flow with separation under a moderate Reynolds number condition has been studied for heat and mass transfer enhancement. In the study of pulsatile flow in a plane channel with periodic rectangular grooves, the occurrence of resonant transfer enhancement, the significant transfer enhancement at a narrow range of a forced frequency, was found. However, it was also found that there is a difference in the dependence on forced frequency of the transfer enhancement between the numerical expectation and experimental measurements. The previous study found that the occurrence of resonant transfer enhancement is affected by flow instability, and it suggested that the three-dimensionality expected in the experimental flow is an important factor in the difference between the numerical and experimental results. Moreover, the study for the flow instability in rectangular grooved channels revealed that the occurrence of three-dimensionality is strongly dependent on the flow transition of the 2D flow element. So, in this paper, we want to show the results of 2D numerical simulation for a pulsatile flow in rectangular grooved channels under the moderate Reynolds number condition, and investigate the influence of forced frequency on the process of flow transition by the extension of the groove length. Numerical results for the two sets of channel geometries and flow parameters show that the transition process of a pulsatile  flow follows a Feigenbaum-like period-doubling cascade scenario dependent on the groove length, and that there is some relation between the flow transition regime and the behavior of  transfer enhancement, which can bridge the difference between the numerical and experimental results.