The Structure of Turbulent Flows

  • Wolfgang KollmannEmail author


Structural properties of turbulent flows are introduced and classified in the present chapter. They have been the subject of experimental and theoretical research for a long time, see the proceedings of the IUTAM symposium in Cambridge U.K. 1989 [1] for the topological and geometric aspects of flow structures.


  1. 1.
    Moffatt, H.K., Tsinober, A. (eds.): Topological Fluid Mechanics. IUTAM Symposium Cambridge, Cambridge University Press, Proc (1989)Google Scholar
  2. 2.
    Wray, A.A., Hunt, J.C.R.: Algorithms for classification of turbulent structures. In: Proceedings of the IUTAM Symposium, pp. 95–104. Cambridge U.K., Cambdridge Univ. Press (1989)Google Scholar
  3. 3.
    Tsinober, A.: An Informal Conceptual Introduction to Turbulence, 2nd edn. Springer, Dordrecht (2009)zbMATHCrossRefGoogle Scholar
  4. 4.
    Marusic, I.: Unraveling turbulence near walls. JFM 630, 1–4 (2009)ADSzbMATHCrossRefGoogle Scholar
  5. 5.
    Adrian, R.J.: Hairpin vortex organization in wall turbulence. Phys. Fluids 19(041301), 1–16 (2007)zbMATHGoogle Scholar
  6. 6.
    Adrian, R.J., Marusic, I.: Coherent structures in flow over hydraulic engineering surfaces. J. Hydraulic Res. 50, 451–464 (2012)CrossRefGoogle Scholar
  7. 7.
    Dallmann, U.: Topological structures of three-dimensional flow separation. DVLR-AVA Bericht no. 221-82 A 07 (1983)Google Scholar
  8. 8.
    Surana, A., Grunberg, O., Haller, G.: Exact theory of three-dimensional flow separation. Part 1. Steady separation. JFM 564, 57–103 (2006)ADSzbMATHCrossRefGoogle Scholar
  9. 9.
    Chong, M.S., Monty, J.P., Chin, C., Marusic, I.: The topolgy of skin friction and surface vorticity fields in wall-bounded flows. J. Turbul. 13, 1–10 (2012)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Ganapathisubramani, B., Hutchins, N., Monty, J.P., Chung, D., Marusic, I.: Amplitude and frequency modulation in wall turbulence. JFM 712, 61–91 (2012)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Lawson, J.M., Dawson, J.R.: On velocity gradient dynamics and tubulent structure. JFM 780, 60–98 (2015)ADSzbMATHCrossRefGoogle Scholar
  12. 12.
    Wilczek, M., Meneveau, C.: Pressure Hessian and viscous contributions to velocity gradient statistics based on Gaussian random fields. JFM 756, 191–225 (2014)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Vlaykov, D.G., Wilczek, M.: On the small-scale structure of turbulence and its impact on the pressure field. JFM 861, 422–446 (2018)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Lozano-Durán, A., Jimenez, J.: Time-resolved evolution of coherent structures in turbulent channels: Characterization of eddies and cascades. JFM 759, 432–471 (2014)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Shekar, A., Graham, M.D.: Exact coherent states with hairpin-like vortex structure in channel flow. JFM 849, 76–89 (2018)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Yang, Y., Pullin, D.I.: Geometric study of Lagrangian and Eulerian structures in turbulent channel flow. JFM 674, 67–92 (2011)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Kollmann, W., Prieto, M.I.: DNS of the collision of co-axial vortex rings. Comput. Fluids 73, 47–64 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Leung, T., Swaminathan, N., Davidson, P.A.: Geometry and interaction of structures in homogeneous isotropic turbulence. JFM 710, 453–481 (2012)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Sahni, V., Sathyaprakash, B., Shandarin, S.F.: Shapefinders: s new shape diagnostic for large-scale structures. Astrophys. J. 495, L1–L4 (1998)ADSCrossRefGoogle Scholar
  20. 20.
    Griffiths, R.A.C., Chen, J.H., Kolla, H., Cant, R.S., Kollmann, W.: Three-dimensional topology of turbulent premixed flame interaction. Proc. Combust. Inst. 35, 1341–1348 (2015)CrossRefGoogle Scholar
  21. 21.
    Fulton, W.: Algebraic Topology. Springer, New York (1995)zbMATHCrossRefGoogle Scholar
  22. 22.
    Hussain, F., Duraisamy, K.: Mechanics of viscous vortex reconnection. Phys. Fluids 23, 021701 (4) (2011)ADSCrossRefGoogle Scholar
  23. 23.
    Ni, Q., Hussain, F., Wang, J., Chen, S.: Analysis of Reynolds number scaling for viscous vortex reconnection. Phys. Fluids 24, 105102 (12) (2012)ADSCrossRefGoogle Scholar
  24. 24.
    van Rees, W.M., Hussain, F., Koumoutsakos, P.: Vortex tube reconnection at Re=\(10^4\). Phys. Fluids 24, 075105 (2012)ADSCrossRefGoogle Scholar
  25. 25.
    Orlandi, P., Carnevale, G.F.: Nonlinear amplification of vorticity in inviscid interaction of orthogonal Lamb dipoles. Phys. Fluids 19, 057106 (2007)ADSzbMATHCrossRefGoogle Scholar
  26. 26.
    Bogachev, V.I.: Measure Theory, vol. 1. Springer, New York (2006)Google Scholar
  27. 27.
    Federer, H.: Geometric Measure Theory. Springer, Berlin (1969)zbMATHGoogle Scholar
  28. 28.
    Pesin, Y.B.: Dimension Theory in Dynamical Systems, p. 60637. The University of Chicago Press, Chicago (1997)CrossRefGoogle Scholar
  29. 29.
    Barenghi, C.F., Ricca, R.L., Samuels, D.C.: How tangled is a tangle ? Physica D 157, 197–206 (2001)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Hasselblatt, B., Katok, A.: A First Course in Dynamics: With a Panaorama of Recent Developments. Cambridge University Press (2003)Google Scholar
  31. 31.
    Kusnetsov, Y.A.: Elements of Applied Bifurcation Theory. Springer, New York (2004)CrossRefGoogle Scholar
  32. 32.
    Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer, New York (2003)zbMATHGoogle Scholar
  33. 33.
    Wu, J.-Z., Tramel, R.W., Zhu, F.L., Yin, X.Y.: A vorticity dynamics theory of three-dimensional flow separation. Phys. Fluids 12, 1932–1954 (2000)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    Serra, M., Haller, G.: Objective Eulerian coherent structures. Chaos 26, 053110 (2016)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Candel, S.M., Poinsot, T.J.: Flame stretch and the balance equation for the flame area. Combust. Sci. and Tech. 70, 1–15 (1990)CrossRefGoogle Scholar
  36. 36.
    Girimaji, S.S., Pope, S.B.: Propagating surfaces in isotropic turbulence. JFM 234, 247–277 (1992)ADSzbMATHCrossRefGoogle Scholar
  37. 37.
    Wu, J.-Z., Ma, H.-Y., Zhou, M.-D.: Vorticity and Vortex Dynamics. Springer, Berlin (2006)CrossRefGoogle Scholar
  38. 38.
    Federer, H.: Curvature measures. Trans. Am. Math. Soc. 93, 418–491 (1959)MathSciNetzbMATHCrossRefGoogle Scholar
  39. 39.
    Maz’ja, V.G.: Sobolev Spaces. Springer, Berlin (1985)CrossRefGoogle Scholar
  40. 40.
    Kollmann, W., Chen, J.H.: Dynamics of the flame surface area in turbulent non-premixed combustion. Twenty-fifth Symposium (Int.) on Combustion, The Combustion Institute, pp. 1091–1098 (1994)CrossRefGoogle Scholar
  41. 41.
    Farazmand, M., Haller, G.: Computing Lagrangian coherent structures from their variational theory. Chaos 22, 013128 (2012)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  42. 42.
    Wiggins, S.: Coherent structures and chaotic advection in three dimensions. JFM 654, 1–4 (2010)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  43. 43.
    Waleffe, F.: Exact coherent structures in channel flow. JFM 435, 93–102 (2001)ADSzbMATHCrossRefGoogle Scholar
  44. 44.
    Chini, G.P.: Exact coherent structures at extreme Reynolds number. JFM 794, 1–4 (2016)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    Melander, M.V., Hussain, F.: Polarized vorticity dynamics on a vortex column. Phys. Fluids A 5, 1992–2003 (1993)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  46. 46.
    Glezer, A., Coles, D.: An experimental study of a turbulent vortex ring. JFM 211, 243 (1990)ADSCrossRefGoogle Scholar
  47. 47.
    Bergdorf, M., Koumoutsakos, P., Leonard, A.: Direct numerical simulation of vortex rings at \(Re_\gamma =7500\). JFM 581, 495–505 (2007)ADSzbMATHCrossRefGoogle Scholar
  48. 48.
    Borisov, V.I.: Hamiltonian Dynamics, Vortex Structures, Turbulence, vol. 6. Springer, Dordrecht, IUTAM book series (2008)Google Scholar
  49. 49.
    Saffman, P.G.: Vortex Dynamics. Cambridge University Press, Cambridge, U.K. (1992)zbMATHGoogle Scholar
  50. 50.
    Archer, P.J., Thomas, T.G., Coleman, G.N.: Direct numerical simulation of vortex ring evolution from the laminar to the early turbulent regime. JFM 598, 201–226 (2008)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  51. 51.
    Fukumoto, Y., Moffatt, H.K.: Motion and expansion of a viscous vortex ring: elliptical slowing down and diffusive expansion. In: Hunt, J.C.R., Vassilicos, J.C. (eds.) Turbulence Structure and Vortex Dynamics. Cambridge Univ. Press (2000)Google Scholar
  52. 52.
    Kollmann, W.: Simulation of vorticity dominated flows using a hybrid approach: i formulation. Comput. Fluids 36, 1638–1647 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  53. 53.
    Kollmann, W.: Fluid Mechanics in Spatial and Material Description. University Readers, San Diego (2011)Google Scholar
  54. 54.
    Maxworthy, T.: The Structure and Stability of Vortex Rings. JFM 51, 15–32 (1972)ADSCrossRefGoogle Scholar
  55. 55.
    Dziedzic, M., Leutheusser, H.J.: An experimental study of viscous vortex rings. Exp. Fluids 21, 315–324 (1996)CrossRefGoogle Scholar
  56. 56.
    Leonard, A.: On the motion of thin vortex tubes. Comput. Fluid Dyn, Theor (2009). in pressGoogle Scholar
  57. 57.
    Dazin, A., Dupont, P., Stanislas, M.: Experimental characterisation of the instability of the vortex ring. Part I: Linear phase. Exp. Fluids 40, 383–399 (2006)CrossRefGoogle Scholar
  58. 58.
    Dazin, A., Dupont, P., Stanislas, M.: Experimental characterisation of the instability of the vortex ring. Part II: Non-linear phase. Exp. Fluids 41, 401–419 (2006)CrossRefGoogle Scholar
  59. 59.
    Leweke, T., Williamson, C.H.K.: Three-dimensional Instabilities of a Counterrotating Vortex Pair. In: Maurel, A., Petitjeans, P. (eds.) LNP, vol. 555, pp. 221–230. Springer (2000)Google Scholar
  60. 60.
    Faddy, J.M., Pullin, D.I.: Evolution of vortex structures in a model of the turbulent trailing vortex. In: Kida, S. (ed.) IUTAM Symposium on Elementary Vortices and Coherent Structures, pp. 259–264. Spinger (2006)Google Scholar
  61. 61.
    Lim, T.T., Nickels, T.B.: Vortex Rings. Fluid Vortices, pp. 95–153. Kluwer Academic (1995)Google Scholar
  62. 62.
    Nickels, T.B.: Turbulent Coflowing Jets and Vortex Ring Collisions. University of Melbourne, Australia (1993). PhD thesisGoogle Scholar
  63. 63.
    Lamb, H.: Hydrodynamics. 3rd ed., Cambridge University Press (1906)Google Scholar
  64. 64.
    Meleshko, V.V., van Heijst, G.J.F.: On Chaplygin’s investigations of two-dimensional vortex structures in an invscid fluid. JFM 272, 157–182 (1994)ADSzbMATHCrossRefGoogle Scholar
  65. 65.
    Gibbon, J.D.: The three-dimensional Euler equations: where do we stand? Physica D 237, 1894–1904 (2008)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  66. 66.
    Kerr, R.M.: The role of singularities in turbulence. In: Kida, S. (ed.) Unstable and Turbulent Motion in Fluids, World Scientific Publishing, SingaporeGoogle Scholar
  67. 67.
    Kerr, R.M.: A new role for vorticity and singular dynamics in turbulence. In: Debnath, L. (ed.) Nonlinear Instability Analysis, vol. II, pp. 15–68. WIT Press, Southhampton U.K. (2001)Google Scholar
  68. 68.
    Shelley, M.J., Meiron, D.I., Orszag, S.A.: Dynamical aspects of vortex reconnection in perturbed anti-parallel vortex tubes. JFM 246, 613–652 (1993)ADSzbMATHCrossRefGoogle Scholar
  69. 69.
    Orlandi, P., Pirozzoli, S., Carnevale, G.F.: Vortex events in Euler and Navier-Stokes simulations with smooth initial conditions. JFM 690, 288–320 (2012)ADSzbMATHCrossRefGoogle Scholar
  70. 70.
    Kramer, W., Clercx, H.J.H., van Heijst, G.J.F.: Vorticity dynamics of a dipole colliding with a no-slip wall. Phys. Fluids 19, 126603 (2007)ADSzbMATHCrossRefGoogle Scholar
  71. 71.
    Bragg, S.L., Hawthorne, W.R.: Some exact solutions of the flow through annular cascade discs. J. Aero. Sci. 17, 243–249 (1950)MathSciNetCrossRefGoogle Scholar
  72. 72.
    Derzho, O., Grimshaw, R.: Solitary waves with recirculation zones in axisymmetric rotating flows. J. Fluid Mech. 464, 217–250 (2002)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  73. 73.
    White, F.M.: Fluid Mechanics. McGraw Hill, 6th edn (2008)Google Scholar
  74. 74.
    Mullin, T., Juel, A., Peacock, T.: Sil’nikov chaos in fluid flows. In: Vassilicos, J.C., Hunt, J.C.R., Vassilicos, J.C. (eds.) Intermittency in Turbulent Flows, Cambridge University Press. Cambridge University Press (2001)Google Scholar
  75. 75.
    Shilnikov, L.P., Shilnikov, A.L., Turaev, D.V., Chua, L.O.: Methods of qualitative theory in nonlinear dynamics. vol. I, World Scientific, London (1998)Google Scholar
  76. 76.
    Davidson, P.A.: Turbulence. Oxford University Press, Oxford, U.K. (2004)zbMATHGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of California DavisDavisUSA

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