Liutex (vortex) core definition and automatic identification for turbulence vortex structures

  • Hongyi Xu
  • Xiao-shu Cai
  • Chaoqun LiuEmail author


As a milestone research in vortex identification (VI), the physical quantity of Liutex, including its forms of scalar, vector and tensor, was systematically explored and rigorously obtained as the third-generation (3G) of the vortex definition and identification methods distinguished from the first generation (1G) by vorticity and the second generation (2G) by the vortex identification (VI) criteria solely dependent on the velocity gradient tensor eigenvalues. Based on these findings, the vortex-core lines were abstracted from the well-defined Liutex, and for the first time, were automatically generated and massively visualized using computer. The distinctive characteristics of these vortex cores with the intriguing threshold-independency make them be the uniquely appropriate entity to represent and to depict the vortex structures in turbulence. The letter made use of the DNS data for the natural transition in a zero-pressure gradient flat-plate (Type-A turbulent boundary layer (TBL)) and the fully-developed turbulence in a square annular duct (Type-B TBL) to demonstrate the vortex structure represented by the vortex-core lines. The 3G VI approach based on the vortex-core lines is capable of profoundly uncovering the vortex natures. Moreover, the capability of automatically identifying the vortex cores and massively visualizing the large number of vortex-core behaviors in a transient way will enable the fluid-mechanics and other related-science communities to step into a new era to explore the intrinsic natures of the centennial puzzle of turbulence and other vortex-related phenomena in future.

Key words

Direct numerical simulation turbulence structure vortex core vortex identification and automation 


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This work is partially accomplished by using Code DNSUTA which was released by Dr. Chaoqun Liu at University of Texas at Arlington (UTA) in 2009. The work is financially supported by the talent recruiting program at Fudan University. The authors also applied the software of LiutexUTA released to public by Dr. Chaoqun Liu in 2019 and the turbulence database established by Dr. Hong-yi Xu at the Department of Aeronautics and Astronautics, Fudan University. The authors are grateful to Dr. Lian-di Zhou for the helpful discussions with him.


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Copyright information

© China Ship Scientific Research Center 2019

Authors and Affiliations

  1. 1.Aeronautics and Astronautics DepartmentFudan UniversityShanghaiChina
  2. 2.School of Energy and Power EngineeringUniversity of Shanghai for Science and TechnologyShanghaiChina
  3. 3.Department of MathematicsUniversity of Texas at ArlingtonArlingtonUSA

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