On Objective and Non-objective Kinematic Flow Classification Criteria

  • Ramon S. MartinsEmail author
  • Anselmo S. Pereira
  • Gilmar Mompean
  • Laurent Thais
  • Roney L. Thompson
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 23)


Turbulent flows present several compact and spatially coherent regions generically known as coherent structures. The understanding of these structures is closely related to the concept of vortex, whose definition is still a subject of controversy within the scientific community. In particular, the role of objectivity in the definition of vortex remains a largely open question. The three most usual criteria for vortex identification (Q, \(\varDelta \) and \(\lambda _2\)) are non-objective since they all depend on the fluid’s rate-of-rotation, which is not invariant to the reference frame. In the present work, we propose an objective definition of these criteria by using the concept of relative rate-of-rotation with respect to the principal directions of the strain rate tensor. We also explore two novel naturally objective flow classification criteria. All the criteria are applied to instantaneous velocity fields obtained by DNS of both Newtonian and viscoelastic turbulent channel flows. The analysis is carried out here for four friction Reynolds numbers from 180 to 1000, emphasizing the difference between objective and non-objective and classification criteria, as well as between Newtonian and non-Newtonian flows. Moreover, we try to obtain from the results of flow classification criteria information related to the polymer drag reduction phenomenon.


Buffer Layer Direct Numerical Simulation Drag Reduction Anisotropic Ratio Strain Rate Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was granted access to the HPC resources of IDRIS under the allocation 2014-i20142b2277 made by GENCI. The authors would also like to express their acknowledgment and gratitude to the Brazilian Scholarship Program Science Without Borders, managed by CNPq (National Council for Scientific and Technological Development), for the partial financial support for this research.


  1. 1.
    R.J. Adrian, Hairpin vortex organization in wall turbulence. Phys. Fluids 19(4), 041301 (2007)CrossRefGoogle Scholar
  2. 2.
    G. Astarita, Objective and generally applicable criteria for flow classification. J. Non-Newton. Fluid 6, 69–76 (1979)CrossRefGoogle Scholar
  3. 3.
    M.S. Chong, A.E. Perry, B.J. Cantwell, A general classification of three-dimensional flow fields. Phys. Fluids A-Fluid 2(5), 765–777 (1990)MathSciNetCrossRefGoogle Scholar
  4. 4.
    C.D. Dimitropoulos, Y. Dubief, E.S.G. Shaqfeh, P. Moin, S.K. Lele, Direct numerical simulation of polymer-induced drag reduction in turbulent boundary layer flow. Phys. Fluids 17, 1–4 (2005)CrossRefGoogle Scholar
  5. 5.
    R. Drouot, Définition d’un transport associé à un modèle de fluide de deuxième ordre. Comparaison de diverses lois de comportement. C. R. Acad. Sci. A Math. 282, 923–926 (1976)Google Scholar
  6. 6.
    R. Drouot, M. Lucius, Approximation du second ordre de la loi de comportement des fluides simples. Lois classiques deduites de l’introduction d’un nouveau tenseur objectif. Arch. Mech. 28(2), 189–198 (1976)Google Scholar
  7. 7.
    F.C. Frank, M.R. Mackley, Localized flow birefringence of polyethylene oxide solutions in a two roll mill. J. Polym. Sci. 14, 69–76 (1976)Google Scholar
  8. 8.
    G. Haller, An objective definition of a vortex. J. Fluid Mech. 525, 1–26 (2005)zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    R. Huilgol, Comments on “Objective and generally applicable criteria for flow classification”, by G. Astarita. J. Non-Newton. Fluid 7(1), 91–95 (1980)Google Scholar
  10. 10.
    J.C.R. Hunt, A.A. Wray, P. Moin, Eddies, stream, and convergence zones in turbulent flows, in Proceedings of Summer Program. Center for Turbulence Research. Report CTR-S88 (1988), pp. 193–208Google Scholar
  11. 11.
    J. Jeong, F. Hussain, On the identification of a vortex. J. Fluid Mech. 285, 69–94 (1995)MathSciNetCrossRefGoogle Scholar
  12. 12.
    K. Kim, C.F. Li, R. Sureshkumar, L. Balachandar, R.J. Adrian, Effects of polymer stresses on eddy structures in drag-reduced turbulent channel flow. J. Fluid Mech. 584, 281–299 (2007)zbMATHCrossRefGoogle Scholar
  13. 13.
    T.S. Luchik, W.G. Tiederman, Turbulent structure in low-concentration drag-reducing channel flows. J. Fluid Mech. 190, 241–263 (1988)CrossRefGoogle Scholar
  14. 14.
    J.L. Lumley, Drag reduction by additives. Annu. Rev. Fluid Mech. 11, 367–384 (1969)CrossRefGoogle Scholar
  15. 15.
    T. Min, J.Y. Yoo, H. Choi, Maximum drag reduction in a turbulent channel flow by polymer additives. J. Fluid Mech. 492, 91–100 (2003)zbMATHCrossRefGoogle Scholar
  16. 16.
    T. Min, J.Y. Yoo, H. Choi, D.D. Joseph, Drag reduction by polymer additives in a turbulent channel flow. J. Fluid Mech. 486, 213–238 (2003)zbMATHCrossRefGoogle Scholar
  17. 17.
    P.R. Schunk, L.E. Scriven, Constitutive equation for modeling mixed extension and shear in polymer solution processing. J. Rheol. 34(7), 1085–1119 (1990)CrossRefGoogle Scholar
  18. 18.
    R. Sureshkumar, A.N. Beris, R.A. Handler, Direct numerical simulation of the turbulent channel flow of a polymer solution. Phys. Fluids 9, 743–755 (1997)zbMATHCrossRefGoogle Scholar
  19. 19.
    M. Tabor, P.G. de Gennes, A cascade theory of drag reduction. Europhys. Lett. 7, 519–522 (1986)CrossRefGoogle Scholar
  20. 20.
    M. Tabor, I. Klapper, Stretching and alignment in chaotic and turbulent flows. Chaos Solitons Fractals 4(6), 1031–1055 (1994)zbMATHCrossRefGoogle Scholar
  21. 21.
    L. Thais, A. Tejada-Martinez, T.B. Gatski, G. Mompean, A massively parallel hybrid scheme for direct numerical simulation of turbulent viscoelastic channel flow. Comput. Fluids 43, 134–142 (2011)zbMATHMathSciNetCrossRefGoogle Scholar
  22. 22.
    R.L. Thompson, Some perspectives on the dynamic history of a material element. Int. J. Eng. Sci. 46, 524–549 (2008)CrossRefGoogle Scholar
  23. 23.
    R.L. Thompson, P.R.S. Mendes, Persistence of straining and flow classification. Int. J. Eng. Sci. 43, 79–105 (2005)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Ramon S. Martins
    • 1
    Email author
  • Anselmo S. Pereira
    • 1
  • Gilmar Mompean
    • 1
  • Laurent Thais
    • 1
  • Roney L. Thompson
    • 2
  1. 1.Laboratoire de Mécanique de Lille (LML), CNRS, UMR 8107, École Polytechnique Universitaire de LilleUniversité Lille Nord de FranceVilleneuve d’ascqFrance
  2. 2.Laboratório de Mecânica Teórica Aplicada (LMTA), Department of Mechanical EngineeringUniversidade Federal FluminenseNiteróiBrazil

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