The response of a flow to which an external control force is applied is of great general interest. The flow studied was a variation of classical circular Taylor-Couette flow in that it was spatially forced by sinusoidal modulations on the inner cylinder, with a forcing wavelength incommensurate with the natural length scale of the Taylor vortices. It was found that this forcing did not affect the conditions for the onset of the vortices, but it did fix the size of the vortices. For the conditions of geometry and flow variations used here, the natural wavelength did not seem to appear in this system. Many of the complex states observed in the unforced case were observed also in the forced case. However, two new types were observed in the present case. They both involved irregularities of the vortices, and they occurred at slow and fast rotation rates, and were named unstable irregularities and temporal irregularities, respectively. The unstable irregularities occurred throughout the entire tank and were constantly changing. The temporal irregularities occurred locally and would appear only for brief periods of time. The azimuthal rotation rate of the irregularities was proportional to the average rotation rate of the cylinders.