Abstract
Recently, new progress has been made in vortex recognition, and the definition of Liutex (Rortex) based on eigenvectors has established a relation between rotation axis and eigenvectors of velocity gradient tensor. Based on this relation, the mathematical condition of vortex boundary is given: the set of points with multiple roots in the characteristic equation of velocity gradient tensor in a flow field. In this way, the topological structure of critical point theory is applied to vortex boundary. According to whether the velocity gradient tensor can be diagonalized, there are shear boundary and non-shear boundary, while according to the positive, negative and zero of the double root, there would be stable boundary, unstable boundary and degenerate boundary. In order to define and classify the boundary, a mapping method is proposed, and we establish the relation between particle and fluid microelement. Under different decomposition modes, we can analyze the superposition of fluid deformation behavior more clearly by mapping image space, which can be used to compare Helmholtz decomposition with Liutex velocity gradient decomposition. Moreover, considering the simple shear, geometric meaning of Liutex can be explained through geometric relations, and it is believed that the dominant quantity rotation described by Liutex is circular symmetry. (National Science and Technology Major Project (2017-II-0006–0019, 2017-I-0009–0010))
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Li, X., Zheng, Q., Jiang, B. (2021). Mathematical Definition of Vortex Boundary and Boundary Classification Based on Topological Type. In: Skiadas, C.H., Dimotikalis, Y. (eds) 13th Chaotic Modeling and Simulation International Conference. CHAOS 2020. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-70795-8_37
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