Super and Sub Critical Bifurcation Found in Flows in Non-uniform Spa es and Identification of Deve aping Process of Disturbances

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We developed a visualization tool that traces the development of vortices in the flows between two rotating cylinders and confirmed its utility. This makes a new way to categorize the formation processes to the non-unique final flow modes and to develop a control method which is used to obtain a prescribed flow mode.Numerical analysis was carried out on the bifurcation phenomena found in the five surface flow between rotating cylinders with vertical axes The critical Reynolds number predicted by the numerical result and the onset Reynolds number of three-dimensional flow give an favorable agreement.The effect of initial flow fields on the final modes was investigated. Two initial fields were used : one is the strict Coutette flow and the other is the homogeneous disturbances in the decaying flows. Both initial fields gave multiple flow modes in the final states. Especially, the homogeneous disturbances well predicted the probability distribution of flow modes founds in the experiment.In the flow around a rotating disk in a cylindrical enclosure, the bifurcation of the centrifugal-force driven flow by the rotating disk and its effect were investigated. New index was introduced to indentify the Hopf bifurcation to the asymmetric and its utility was verified It was bind that the effect of the geometrical structure on the Reynolds number at the onset of the bifurcation was not significant.The bifurcation of modes of flows over an open cavity was investigated. The mechanism of the emerging and decaying of vortices was clarified. A new control method was introduced to suppress the oscillating flow.