The flow generated by the rotation of the disk in a stationary cylindrical casing is investigated by the numerical approaches. In the flow around the rotating disk in the cylindrical casing, the normal and anomalous Taylor vortex occurs in the radial gap between the casing and the disk in particular conditions. When the normal vortex appears, jet-flows are exist between a upper cell and a lower cell. The anomalous Taylor vortex appears, beads-like vortices, ring-like vortices and polygonomical vortices are generated along the edge of the casing. The flow with steady Taylor vortices emerges in the radial gap at relatively low Reynolds numbers. At the higher Reynolds numbers, the turbulent Taylor vortices appear in the radial gap. We investigated steady, wavelet and turbulent vortices by the numerical analysis. According to the disk accelerate is increasing, flow instability is changed to more steady with same Reynolds number and same geometrical condition.