We performed numerical computations of Taylor vortex flow at small aspect ratio. When the flow develops from its initial state at rest, non-unique flow patterns appear, which depend on the lengths of the cylinders and/or 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 its inherit variations. In this study, we focus our attention on the small fluctuations of flows. Two-dimensional numerical simulation 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.