Acta Mechanica Sinica

, Volume 32, Issue 3, pp 351–361 | Cite as

Identification, characterization and evolution of non-local quasi-Lagrangian structures in turbulence

Research Paper

Abstract

The recent progress on non-local Lagrangian and quasi-Lagrangian structures in turbulence is reviewed. The quasi-Lagrangian structures, e.g., vortex surfaces in viscous flow, gas-liquid interfaces in multi-phase flow, and flame fronts in premixed combustion, can show essential Lagrangian following properties, but they are able to have topological changes in the temporal evolution. In addition, they can represent or influence the turbulent flow field. The challenges for the investigation of the non-local structures include their identification, characterization, and evolution. The improving understanding of the quasi-Lagrangian structures is expected to be helpful to elucidate crucial dynamics and develop structure-based predictive models in turbulence.

Keywords

Turbulence Lagrangian study Coherent structure  Multi-scale analysis Vortex dynamics 

References

  1. 1.
    Taylor, G.I.: Diffusion by continuous movements. Proc. Lond. Math. Soc. 20, 196–212 (1922)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Toschi, F., Bodenschatz, E.: Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375–404 (2009)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Yeung, P.K.: Lagrangian investigations of turbulence. Annu. Rev. Fluid Mech. 34, 115–142 (2002)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Sawford, B.: Turbulent relative dispersion. Annu. Rev. Fluid Mech. 33, 289–317 (2001)CrossRefMATHGoogle Scholar
  5. 5.
    Yang, Y., He, G.-W., Wang, L.-P.: Effects of subgrid-scale modeling on Lagrangian statistics in large-eddy simulation. J. Turbul. 9, 8 (2008)MathSciNetMATHGoogle Scholar
  6. 6.
    Pumir, A., Shraiman, B.I., Chertkov, M.: Geometry of Lagrangian dispersion in turbulence. Phys. Rev. Lett. 85, 5324–5327 (2000)CrossRefMATHGoogle Scholar
  7. 7.
    Xu, H., Pumir, A., Bodenschatz, E.: The pirouette effect in turbulent flows. Nat. Phys. 7, 709–712 (2011)CrossRefGoogle Scholar
  8. 8.
    Batchelor, G.K.: Diffusion in a field of homogeneous turbulence. II. The relative motion of particles. Proc. Camb. Philos. Soc. 48, 345–362 (1952)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Pope, S.B.: The evolution of surfaces in turbulence. Int. J. Eng. Sci. 26, 445–469 (1988)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Meneveau, C.: Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 43, 219–245 (2011)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Chu, Y.-B., Lu, X.-Y.: Topological evolution in compressible turbulent boundary layers. J. Fluid Mech. 733, 414–438 (2013)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Wang, L.-P., Maxey, M.R.: Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 27–68 (1993)CrossRefGoogle Scholar
  13. 13.
    Sreenivasan, K.R., Schumacher, J.: Lagrangian views on turbulent mixing of passive scalars. Philos. Trans. R. Soc. A 368, 1561–1577 (2010)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Warhaft, Z.: Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203–240 (2000)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Pope, S.B.: Turbulent premixed flames. Annu. Rev. Fluid Mech. 19, 237–270 (1987)CrossRefGoogle Scholar
  16. 16.
    Peng, J., Dabiri, J.O.: An overview of a Lagrangian method for analysis of animal wake dynamics. J. Exp. Biol. 211, 280–287 (2008)CrossRefGoogle Scholar
  17. 17.
    Haller, G.: Lagrangian coherent structures. Annu. Rev. Fluid Mech. 47, 137–162 (2015)CrossRefGoogle Scholar
  18. 18.
    Yang, Y., Pullin, D.I., Bermejo-Moreno, I.: Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence. J. Fluid Mech. 654, 233–270 (2010)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Yang, Y., Pullin, D.I.: Geometric study of Lagrangian and Eulerian structures in turbulent channel flow. J. Fluid Mech. 674, 67–92 (2011)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Tsinober, A.: An Informal Conceptual Introduction to Turbulence, 2nd edn. Springer, Berlin (2009)CrossRefMATHGoogle Scholar
  21. 21.
    Helmholtz, H.: Über Integrale der hydrodynamischen Gleichungen welche den Wribelbewegungen ensprechen. J. Reine Angew. Math. 55, 25–55 (1858) (in German)Google Scholar
  22. 22.
    Davidson, P.A.: An Introduction to Magnetohydrodynamicsa. Cambridge University Press, Cambridge (2001)CrossRefGoogle Scholar
  23. 23.
    Kida, S., Takaoka, M.: Vortex reconnection. Annu. Rev. Fluid Mech. 26, 169–189 (1994)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Biskamp, D.: Magnetic Reconnections in Plasmas. Cambridge University Press, Cambridge (2000)CrossRefGoogle Scholar
  25. 25.
    Luo, K., Shao, C.X., Yang, Y., et al.: Direct numerical simulation of droplet breakup in homogeneous isotropic turbulence using level set method: The effects of Weber number and volume fraction (under review)Google Scholar
  26. 26.
    Yang, Y., Pullin, D.I.: On Lagrangian and vortex-surface fields for flows with Taylor–Green and Kida–Pelz initial conditions. J. Fluid Mech. 661, 446–481 (2010)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces. Springer, New York (2003)CrossRefMATHGoogle Scholar
  28. 28.
    Peters, N.: Turbulent Combustion. Cambridge University Press, Cambridge (2000)CrossRefMATHGoogle Scholar
  29. 29.
    Yang, Y., Pullin, D.I.: Evolution of vortex-surface fields in viscous Taylor–Green and Kida–Pelz flows. J. Fluid Mech. 685, 146–164 (2011)MathSciNetCrossRefMATHGoogle Scholar
  30. 30.
    Hamlington, P.E., Poludnenko, A.Y., Oran, E.S.: Interaction between turbulence and flames in premixed reacting flows. Phys. Fluids 23, 125111 (2011)CrossRefGoogle Scholar
  31. 31.
    Robinson, S.K.: Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639 (1991)CrossRefGoogle Scholar
  32. 32.
    Lee, C.B., Wu, J.Z.: Transition in wall-bounded flows. Appl. Mech. Rev. 61, 030802 (2008)CrossRefMATHGoogle Scholar
  33. 33.
    Hunt, J.C.R., Wray, A.A., Moin, P.: Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research Report CTR-S88, 193–208 (1988)Google Scholar
  34. 34.
    Chong, M.S., Perry, A.E., Cantwell, B.J.: A general classification of three-dimensional flow fields. Phys. Fluids A 2, 765–777 (1990)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Jeong, J., Hussain, F.: On the identification of a vortex. J. Fluid Mech. 285, 69–94 (1995)MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    Zhou, J., Adrian, R.J., Balachandar, S., et al.: Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396 (1999)MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    LeHew, J.A., Guala, M., MeKeon, B.J.: Time-resolved measurements of coherent structures in the turbulent boundary layer. Exp. Fluids 54, 1508 (2013)CrossRefGoogle Scholar
  38. 38.
    Lorensen, W.E., Cline, H.E.: Marching cubes: A high resolution 3D surface construction algorithm. Comput. Graph. 21, 163–169 (1987)CrossRefGoogle Scholar
  39. 39.
    Van der Pijl, S.P., Segal, A., Vuik, C., et al.: A mass-conserving level-set method for modeling of multi-phase flows. Int. J. Numer. Meth. Fluids 47, 339–361 (2005)CrossRefMATHGoogle Scholar
  40. 40.
    Luo, K., Shao, C.X., Yang, Y., et al.: A mass conserving level set method for detailed numerical simulation of liquid atomization. J. Comput. Phys. 298, 495–519 (2015)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Pullin, D.I., Yang, Y.: Whither vortex tubes? Fluid Dyn. Res. 46, 0141618 (2014)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Krauskopf, B., Osinga, H.M., Doedel, E.J., et al.: A survey of methods for computing (un)stable manifold of vector fields. Int. J. Bifurcat. Chaos 15, 763–791 (2005)MathSciNetCrossRefMATHGoogle Scholar
  43. 43.
    He, P., Yang, Y.: Construction of initial vortex-surface fields and Clebsch potentials for flows with high-symmetry using first integrals (under review)Google Scholar
  44. 44.
    Haller, G.: Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Phys. D 149, 248–277 (2001)MathSciNetCrossRefMATHGoogle Scholar
  45. 45.
    Green, M.A., Rowley, C.W., Haller, G.: Detection of Lagrangian coherent structures in three-dimensional turbulence. J. Fluid Mech. 572, 111–120 (2007)MathSciNetCrossRefMATHGoogle Scholar
  46. 46.
    Blazevski, D., Haller, G.: Hyperbolic and elliptic transport barriers in three-dimensional unsteady flows. Phys. D 273–274, 46–62 (2014)MathSciNetCrossRefGoogle Scholar
  47. 47.
    Wang, L., Peters, N.: The length-scale distribution function of the distance between extremal points in passive scalar turbulence. J. Fluid Mech. 554, 457–475 (2006)CrossRefMATHGoogle Scholar
  48. 48.
    Wang, L.: On properties of fluid turbulence along streamlines. J. Fluid Mech. 648, 183–203 (2010)MathSciNetCrossRefMATHGoogle Scholar
  49. 49.
    Wang, L.: Analysis of the Lagrangian path structures in fluid turbulence. Phys. Fluids 26, 045104 (2014)CrossRefGoogle Scholar
  50. 50.
    Pullin, D.I., Saffman, P.G.: Vortex dynamics in turbulence. Annu. Rev. Fluid Mech. 30, 31–51 (1998)MathSciNetCrossRefGoogle Scholar
  51. 51.
    Berkooz, G., Holmes, P., Lumley, J.L.: The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25, 539–575 (1993)MathSciNetCrossRefGoogle Scholar
  52. 52.
    Schmid, P.J.: Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28 (2010)MathSciNetCrossRefMATHGoogle Scholar
  53. 53.
    Farge, M.: Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech. 24, 395–457 (1992)MathSciNetCrossRefMATHGoogle Scholar
  54. 54.
    Bermejo-Moreno, I., Pullin, D.I.: On the non-local geometry of turbulence. J. Fluid Mech. 603, 101–135 (2008)Google Scholar
  55. 55.
    Candès, E., Demanet, L., Donoho, D., et al.: Fast discrete curvelet transforms. Multiscale Model. Simul. 5, 861–899 (2006)Google Scholar
  56. 56.
    Bermejo-Moreno, I., Pullin, D.I., Horiuti, K.: Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence. J. Fluid Mech. 620, 121–166 (2009)CrossRefMATHGoogle Scholar
  57. 57.
    Leung, T., Swaminathan, N., Davidson, P.A.: Geometry and interaction of structures in homogeneous isotropic turbulence. J. Fluid Mech. 710, 453–481 (2012)MathSciNetCrossRefMATHGoogle Scholar
  58. 58.
    Mishra, M., Liu, X., Skote, M., et al.: Kolmogorov spectrum consistent optimization for multi-scale flow decomposition. Phys. Fluids 26, 055106 (2014)CrossRefGoogle Scholar
  59. 59.
    Adrian, R.J.: Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301 (2007)CrossRefMATHGoogle Scholar
  60. 60.
    Zheng, W., Yang, Y., Chen, S.: Evolutionary geometry of Lagrangian structures in a transitional boundary layer (under review)Google Scholar
  61. 61.
    Townsend, A.A.: The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press, New York (1976)MATHGoogle Scholar
  62. 62.
    Perry, A.E., Chong, M.S.: On the mechanism of wall turbulence. J. Fluid Mech. 119, 173–217 (1982)CrossRefMATHGoogle Scholar
  63. 63.
    Perry, A.E., Henbest, S., Chong, M.S.: A theoretical and experimental-study of wall turbulence. J. Fluid Mech. 165, 163–199 (1986)MathSciNetCrossRefMATHGoogle Scholar
  64. 64.
    Sharma, A.S., McKeon, B.J.: On coherent structure in wall turbulence. J. Fluid Mech. 728, 196–238 (2013)MathSciNetCrossRefMATHGoogle Scholar
  65. 65.
    Chung, D., Pullin, D.I.: Large-eddy simulation and wall modelling of turbulent channel flow. J. Fluid Mech. 631, 281–309 (2009)MathSciNetCrossRefMATHGoogle Scholar
  66. 66.
    Fung, Y.C.: A First Course in Continuum Mechancis, 3rd edn. Prentice-Hall, Englewood Cliffs (1994)Google Scholar
  67. 67.
    Goto, S., Kida, S.: Reynolds-number dependence of line and surface stretching in turbulence: folding effects. J. Fluid Mech. 586, 59–81 (2007)MathSciNetCrossRefMATHGoogle Scholar
  68. 68.
    Zhang, P.: An analysis of head-on droplet collision with large deformation in gaseous medium. Phys. Fluids 23, 042102 (2011)CrossRefGoogle Scholar
  69. 69.
    Crandall, M.G., Lions, P.L.: Viscosity solutions of Hamilton–Jacobi equations. Trans. Am. Math. Soc. 277, 1–42 (1983)MathSciNetCrossRefMATHGoogle Scholar
  70. 70.
    Lundgren, T.S.: Strained spiral vortex model for turbulent fine structure. Phys. Fluid 25, 2193–2203 (1982)CrossRefMATHGoogle Scholar
  71. 71.
    Zhao, Y., Yang, Y., Chen, S.: Evolution of material surfaces in the temporal transition in channel flow (under review)Google Scholar
  72. 72.
    Wang, Y., Huang, W., Xu, C.: On hairpin vortex generation from near-wall streamwise vortices. Acta. Mech. Sin. 31, 139–152 (2015)MathSciNetCrossRefGoogle Scholar
  73. 73.
    Theodorsen, T.: Mechanism of turbulence. In: Proceedings of the Second Midwestern Conference on Fluid Mechanics, March 17–19, 1–18. Ohio State University, Columbus (1952)Google Scholar
  74. 74.
    Girimaji, S.S., Pope, S.B.: Material-element deformation in isotropic turbulence. J. Fluid Mech. 220, 427–458 (1990)CrossRefGoogle Scholar
  75. 75.
    Girimaji, S.S., Pope, S.B.: Propagating surfaces in isotropic turbulence. J. Fluid Mech. 234, 247–277 (1992)CrossRefMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.State Key Laboratory for Turbulence and Complex Systems (LTCS) and Center for Applied Physics and Technology (CAPT), College of EngineeringPeking UniversityBeijingChina

Personalised recommendations