Objective Omega vortex identification method

  • Jian-ming Liu
  • Yi-sheng Gao
  • Yi-qian Wang
  • Chaoqun LiuEmail author


A new vortex identification method.(Liu et al. 2016) was proposed to represent the rotation relative strength and capture and visualize the vortices in our previous study. The basic idea of the Ω method is that a ratio of the vorticity squared over the summation of the vorticity squared and the deformation squared should be used to measure the relative rotation strength. However, the vorticity tensor norm is not objective. Thus, a moving observer will observe different vortex structures in a moving reference frame, which will make people confused with the real vortex structures. In the present study, by the definitions of the net spin tensor and net vorticity vector, an objective omega vortex identification method is presented and the examples are presented to verify the vortex structures will still retain in a moving reference frame.

Key words

Vortex identification the Ω method objectivity turbulence visualization turbulence 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Epps B. P., Alvarado P. V., Youcef–Toumi K., Techet A. H. Swimming Performance of a Biomimetic Compliant Fish–like Robot [J]. Experiments in fluids, 2009, 47(6):927–939CrossRefGoogle Scholar
  2. [2]
    Epps B. P. Review of vortex identification methods [C]. 55th AIAA Aerospace Sciences Meeting, Grapevine, Texas, USA, 2017.Google Scholar
  3. [3]
    Robinson S. K. A review of vortex structures and associated coherent motions in turbulent boundary layers. In Structure of Turbulence and Drag Reduction [M]. Berlin, Germany: Springer, 1990, 23–50.CrossRefGoogle Scholar
  4. [4]
    Robinson S. K., Kline S. J., Spalart P. R. A review of quasi–coherent structures in a numerically simulated turbulent boundary layer [R]. NASA Technical Memorandum, 1989, 102191.Google Scholar
  5. [5]
    Liu C., Cai X. New theory on turbulence generation and structure—DNS and experiment [J]. Science China Physics, Mechanics & Astronomy, 2017, 60(8):084731CrossRefGoogle Scholar
  6. [6]
    Hunt J. C. R., Wray A. A., Moin P. Eddies, streams, and convergence zones in turbulent flows [R]. Proceedings of the Summer Program. Center for Turbulence Research, 1988, 193–208.Google Scholar
  7. [7]
    Chong M. S., Perry A. E., Cantwell B. J. A general classification of three–dimensional flow fields [J]. Physics of Fluids, 1990, 2(5):765–777MathSciNetCrossRefGoogle Scholar
  8. [8]
    Jeong J., Hussain F. On the identification of a vortex [J]. Journal of Fluid Mechanics, 1995, 285: 69–94.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Zhou J., Adrian, R.J., Balachandar S., & Kendall T.M. Mechanisms for generating coherent packets of hairpin vortices in channel flow [J]. Journal of Fluid Mechanics, 1999, 387(5):353–396MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Liu C., Wang Y., Yang Y., et al. New omega vortex identification method [J]. Science China Physics, Mechanics and Astronomy, 2016, 59{(sn8}):684711CrossRefGoogle Scholar
  11. [11]
    Dong X., Wang Y., Chen X., et al. Determination of epsilon for Omega vortex identification method [J]. Journal of Hydrodynamics, 2018, 30{(sn4}):541–548CrossRefGoogle Scholar
  12. [12]
    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}: 1269–1CrossRefGoogle Scholar
  13. [13]
    Zhang Y., Qiu X., Chen P., et al. A selected review of vortex identification methods with applications [J]. Journal of Hydrodynamics, 2018, 30(5):767–779CrossRefGoogle Scholar
  14. [14]
    Zhang Y., Liu K., Li J., 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):463–469CrossRefGoogle Scholar
  15. [15]
    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
  16. [16]
    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,–019–0022–4.Google Scholar
  17. [17]
    Martins R. S., Pereira A. S., Mompean G., Thais L., Thompson R.L. An objective perspective for classic flow classification criteria[J]. Comptes Rendus Mecanique, 2016, 344(1):52–59CrossRefGoogle Scholar
  18. [18]
    Drouot R. Définition d'un transport associé à un modèle de fluide du deuxième ordre. Comparaison de diverses lois de comportement [J]. Comptes rendus de l'Académie des Sciences, Série A, 1976, 282: 923–926.zbMATHGoogle Scholar
  19. [19]
    Wedgewood L. E. An objective rotation tensor applied to non–Newtonian fluid mechanics [J]. Rheologica Acta, 1999, 38(2): 91–99.CrossRefGoogle Scholar
  20. [20]
    Haller G., Hadjighasem A., Farazmand M., Huhn F. Defining coherent vortices objectively from the vorticity [J]. Journal of Fluid Mechanics, 2016, 795: 136–173.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    Wang Y., Liu C. DNS study on bursting and intermittency in late boundary layer transition [J]. Science China Physics, Mechanics & Astronomy, 2017, 60(11):114712CrossRefGoogle Scholar
  22. [22]
    Golub G.H., Van Loan C.F. Matrix computations, 4th Edition [M]. Baltimore, Maryland: The Johns Hopkins University Press, 2013.Google Scholar
  23. [23]
    Gallay T., Maekawa Y. Three–Dimensional Stability of Burgers Vortices [J]. Communications in Mathematical Physics, 2010, 302(2):477–511Google Scholar
  24. [24]
    Haller G. An objective definition of a vortex [J]. Journal of Fluid Mechanics, 2005, 525: 1–26.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    Dong X., Yan Y., Yang Y., et al. Spectrum study on unsteadiness of shock wave–vortex ring interaction [J]. Physics of Fluids, 2018, 30: 056101.CrossRefGoogle Scholar
  26. [26]
    Gan Y., Liu J., Zhao N., et al. A numerical study on a Cartesian–based body–fitted adaptive grid method [J]. International Journal of Computational Fluid Dynamics, 2018, 32(4–5): 186–202.MathSciNetCrossRefGoogle Scholar

Copyright information

© China Ship Scientific Research Center 2019

Authors and Affiliations

  • Jian-ming Liu
    • 1
    • 2
  • Yi-sheng Gao
    • 2
  • Yi-qian Wang
    • 3
  • 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