In order to understand the fundamental characteristics of the forced flow driven by iso-and counter-rotation of a shallow pool and a disk on the free surface, we conducted a series of unsteady three-dimensional numerical simulations in a shallow pool. The ratio of the disk to pool radius is R s = 0.3 and the aspect ratio of pool is H = 0.06. The results indicated that the forced flow driven by disk and pool rotation is axisymmetric and steady at the small rotation Reynolds number. However, when Reynolds number exceeds a critical value, the flow will undergo a transition to three-dimensional oscillatory flow, which is characterized by the velocity fluctuation waves traveling in the azimuthal direction. The propagating direction and the velocity of the waves depend on the rotation rates and directions of the disk and pool. Besides, the critical conditions for the onset of the oscillatory flow were determined. The details of the flow fields were discussed and the mechanism of the flow pattern transition was also exhibited.