We performed numerical computations of Taylor vortex flow at small aspect ratio. When the flow developed from its initial state at rest, non-unique flow patterns appeared. This depended on the lengths of the cylinder and the final Reynolds number. In experiment, it is difficult to keep constant conditions because of the imperfection of the apparatus and the small disturbances of the flow field. Therefore, the experimental result may show variations inherit from imperfections. In this study, we focused our attention on the small fluctuations of flows. Two-dimensional numerical analysis is used to estimate the effect on the final modes of Taylor vortex flow. Statistical analysis of the results presents a favorable agreement with our prescribed experimental result.