Taylor vortex flow is one of the important vortex flows that have been studied since its classic study made by G. I. Taylor in 1923. State of the flow between inner and outer cylinders of a rotating co-axial cylinder transits from Couette flow to Taylor vortex flow and to wavy Taylor vortex flow as the increase of Reynolds number. This study has identified the critical Reynolds number when the flow changes from Taylor vortex flow to wavy Taylor vortex flow. The numerical analysis making use of the attractor in the chaos theory has been used in this identification of the critical Reynolds number. The calculated critical Reynolds numbers of each flow mode are almost identical to the values obtained by the visualization experiment at small aspect ratios. In the region where the aspect ratio is larger than the ratio at the peak critical Reynolds number, the distribution of the Reynolds number is qualitatively similar between the calculated and experimental values.
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