Journal of Hydrodynamics

, Volume 31, Issue 2, pp 249–255 | Cite as

Galilean invariance of Omega vortex identification method

  • Jian-ming Liu
  • Yi-qian Wang
  • Yi-sheng Gao
  • Chaoqun LiuEmail author
Special Column for Symposium on Vortex Identification Methods and Applications (Guest Editor Yu-Ning Zhang)


In the new vortex identification method (Liu et al. 2016) to represent the rotation level and capture and visualize the vortices, proposed in our previous study, the independence of the reference frame and the Galilean invariant were not proved. In the present study, the Galilean invariance of the omega vortex identification method is proved and several examples are presented to verify the conclusion.

Key words

Vortex identification Ω method Galilean invariance turbulence visualization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This work was supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 18KJA110001), the Visiting Scholar Scholarship of the China Scholarship Council (Grant No. 201808320079) and the China Post-Doctoral Science Foundation (Grant No. 2017M610876). This work is accomplished by using the code DNSUTA released by Dr. Chaoqun Liu at the University of Texas at Arlington in 2009.


  1. [1]
    Epps B. P. Review of vortex identification methods [C]. 55th AIAA Aerospace Sciences Meeting, Grapevine, Texas, USA, 2017.Google Scholar
  2. [2]
    Liu C., Wang Y. Q., Yang Y. et al. New omega vortex identification method [J]. Science China Physics, Mechanics and Astronomy, 2016, 59(8): 684711.CrossRefGoogle Scholar
  3. [3]
    Hunt J., Wary A., Moin P. Eddies, streams, convergence zones in turbulent flows [C]. Proceedings of the Summer Program 1988 in its Studying Turbulence Using Numerical Simulation Databases, Stanford, California, USA, 1988, 193–208.Google Scholar
  4. [4]
    Chong M. S., Perry A. E., Cantwell B. J. A general classification of three-dimensional flow fields [J]. Physics of Fluids, 1990, 2(5): 765–777.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Jeong J., Hussain F. On the identification of a vortex [J]. Journal of Fluid Mechanics, 1995, 285: 69–94.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Dong X. R., Wang Y. Q., Chen X. P. et al. Determination of epsilon for omega vortex identification method [J]. Journal of Hydrodynamics, 2018, 30(4): 541–548.CrossRefGoogle Scholar
  7. [7]
    Zhang Y., Liu K., Xian H. et al. A review of methods for vortex identification in hydroturbines [J]. Renewable and Sustainable Energy Reviews, 2018, 81: 1269–1285.CrossRefGoogle Scholar
  8. [8]
    Zhang Y. N., Qiu X., Chen P. F. et al. A selected review of vortex identification methods with applications [J]. Journal of Hydrodynamics, 2018, 30(5): 767–779.CrossRefGoogle Scholar
  9. [9]
    Zhang Y. N., Liu K. H., Li J. W. et al. Analysis of the vortices in the inner flow of reversible pump turbine with the new omega vortex identification method [J]. Journal of Hydrodynamics, 2018, 30(3): 463–469.CrossRefGoogle Scholar
  10. [10]
    Kareem W. A. Anisotropic complex diffusion filtering for comparison of the vortex identification methods in homogeneous turbulence [J]. International Journal of Mechanical Sciences, 2017, 134: 291–305.CrossRefGoogle Scholar
  11. [11]
    Liu C., Gao Y., Dong X. et al. Third generation of vortex identification methods: Omega and Liutex/Rortex based systems [J]. Journal of Hydrodynamics, 2019, Scholar
  12. [12]
    Liu C., Gao Y., Tian S. et al. Rortex a new vortex vector definition and vorticity tensor and vector decompositions [J]. Physics of Fluids, 2018, 30(3): 035103.CrossRefGoogle Scholar
  13. [13]
    Gao Y., Liu C. Rortex and comparison with eigenvaluebased vortex identification criteria [J]. Physics of Fluids, 2018, 30(8): 085107.CrossRefGoogle Scholar
  14. [14]
    Tian S., Gao Y., Dong X. et al. Definitions of vortex vector and vortex [J]. Journal of Fluid Mechanics, 2018, 849: 312–339.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Itskov M. Tensor algebra and tensor analysis for engineers [M]. Berlin, Germany: Springer-Verlag, 2007.zbMATHGoogle Scholar
  16. [16]
    Golub G., Van Loan C. Matrix computations [M]. 4th Edition, Baltimore, Maryland, USA: Johns Hopkins University Press, 2013.zbMATHGoogle Scholar
  17. [17]
    Wang Y., Gao Y., Liu C. Letter: Galilean invariance of Rortex [J]. Physics of Fluids, 2018, 30(11): 111701.CrossRefGoogle Scholar
  18. [18]
    Gallay T., Maekawa Y. Three-dimensional stability of burgers vortices [J]. Communications in Mathematical Physics, 2010, 302(2): 477–511.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    Liu C., Yan Y., Lu P. Physics of turbulence generation and sustenance in a boundary layer [J]. Computers and Fluids, 2014, 102: 353–384.CrossRefGoogle Scholar
  20. [20]
    Dong X., Yan Y., Yang Y. et al. Spectrum study on unsteadiness of shock wave–vortex ring interaction [J]. Physics of Fluids, 2018, 30(5): 056101.CrossRefGoogle Scholar

Copyright information

© China Ship Scientific Research Center 2019

Authors and Affiliations

  • Jian-ming Liu
    • 1
    • 2
  • Yi-qian Wang
    • 3
  • Yi-sheng Gao
    • 2
  • Chaoqun Liu
    • 2
    Email author
  1. 1.School of Mathematics and StatisticsJiangsu Normal UniversityXuzhouChina
  2. 2.Department of MathematicsUniversity of Texas at ArlingtonArlingtonUSA
  3. 3.School of Aerospace EngineeringTsinghua UniversityBeijingChina

Personalised recommendations