A numerical analysis for identification of flow transition in vortex generation in terms of local flow topology

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<p>A numerical analysis, based on a novel physical quantity of the topology, is presented to specify the key flow leading into a vortex. This analysis traces the flow transition into a vortical flow in terms of local flow geometry (topology) specified by the velocity gradient tensor, and specifies the important flow component for the vortex transition. The transition where a non-vortical flow becomes vortical can be identified by swirlity that represents the unidirectionality and intensity of the azimuthal flow in a plane. The swirl plane after the vortex transition can be predicted by an eigenplane of real eigenvalues of the velocity gradient tensor. Then the tensor components are represented associating with the predicted plane, and their relations to the flow topology are clarified. The analysis of their transitions enables to specify the important flow components that lead the flow into a vortical flow. This numerical analysis can be applied to various turbulent flows in order to clarify the mechanism or feature of the vortex transition, or suppress a specific vortex in engineering fields.</p>

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