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

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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.

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References

  1. Taylor, G.I.: Diffusion by continuous movements. Proc. Lond. Math. Soc. 20, 196–212 (1922)

    Article  MathSciNet  MATH  Google Scholar 

  2. Toschi, F., Bodenschatz, E.: Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375–404 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Yeung, P.K.: Lagrangian investigations of turbulence. Annu. Rev. Fluid Mech. 34, 115–142 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Sawford, B.: Turbulent relative dispersion. Annu. Rev. Fluid Mech. 33, 289–317 (2001)

    Article  MATH  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  6. Pumir, A., Shraiman, B.I., Chertkov, M.: Geometry of Lagrangian dispersion in turbulence. Phys. Rev. Lett. 85, 5324–5327 (2000)

    Article  MATH  Google Scholar 

  7. Xu, H., Pumir, A., Bodenschatz, E.: The pirouette effect in turbulent flows. Nat. Phys. 7, 709–712 (2011)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  9. Pope, S.B.: The evolution of surfaces in turbulence. Int. J. Eng. Sci. 26, 445–469 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  10. Meneveau, C.: Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 43, 219–245 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Chu, Y.-B., Lu, X.-Y.: Topological evolution in compressible turbulent boundary layers. J. Fluid Mech. 733, 414–438 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  13. Sreenivasan, K.R., Schumacher, J.: Lagrangian views on turbulent mixing of passive scalars. Philos. Trans. R. Soc. A 368, 1561–1577 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Warhaft, Z.: Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203–240 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  15. Pope, S.B.: Turbulent premixed flames. Annu. Rev. Fluid Mech. 19, 237–270 (1987)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  17. Haller, G.: Lagrangian coherent structures. Annu. Rev. Fluid Mech. 47, 137–162 (2015)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  19. Yang, Y., Pullin, D.I.: Geometric study of Lagrangian and Eulerian structures in turbulent channel flow. J. Fluid Mech. 674, 67–92 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  20. Tsinober, A.: An Informal Conceptual Introduction to Turbulence, 2nd edn. Springer, Berlin (2009)

    Book  MATH  Google Scholar 

  21. Helmholtz, H.: Über Integrale der hydrodynamischen Gleichungen welche den Wribelbewegungen ensprechen. J. Reine Angew. Math. 55, 25–55 (1858) (in German)

  22. Davidson, P.A.: An Introduction to Magnetohydrodynamicsa. Cambridge University Press, Cambridge (2001)

    Book  Google Scholar 

  23. Kida, S., Takaoka, M.: Vortex reconnection. Annu. Rev. Fluid Mech. 26, 169–189 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  24. Biskamp, D.: Magnetic Reconnections in Plasmas. Cambridge University Press, Cambridge (2000)

    Book  Google Scholar 

  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)

  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)

    Article  MathSciNet  MATH  Google Scholar 

  27. Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces. Springer, New York (2003)

    Book  MATH  Google Scholar 

  28. Peters, N.: Turbulent Combustion. Cambridge University Press, Cambridge (2000)

    Book  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  30. Hamlington, P.E., Poludnenko, A.Y., Oran, E.S.: Interaction between turbulence and flames in premixed reacting flows. Phys. Fluids 23, 125111 (2011)

    Article  Google Scholar 

  31. Robinson, S.K.: Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639 (1991)

    Article  Google Scholar 

  32. Lee, C.B., Wu, J.Z.: Transition in wall-bounded flows. Appl. Mech. Rev. 61, 030802 (2008)

    Article  MATH  Google Scholar 

  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)

  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)

    Article  MathSciNet  Google Scholar 

  35. Jeong, J., Hussain, F.: On the identification of a vortex. J. Fluid Mech. 285, 69–94 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  38. Lorensen, W.E., Cline, H.E.: Marching cubes: A high resolution 3D surface construction algorithm. Comput. Graph. 21, 163–169 (1987)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  41. Pullin, D.I., Yang, Y.: Whither vortex tubes? Fluid Dyn. Res. 46, 0141618 (2014)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  43. He, P., Yang, Y.: Construction of initial vortex-surface fields and Clebsch potentials for flows with high-symmetry using first integrals (under review)

  44. Haller, G.: Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Phys. D 149, 248–277 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  46. Blazevski, D., Haller, G.: Hyperbolic and elliptic transport barriers in three-dimensional unsteady flows. Phys. D 273–274, 46–62 (2014)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  48. Wang, L.: On properties of fluid turbulence along streamlines. J. Fluid Mech. 648, 183–203 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  49. Wang, L.: Analysis of the Lagrangian path structures in fluid turbulence. Phys. Fluids 26, 045104 (2014)

    Article  Google Scholar 

  50. Pullin, D.I., Saffman, P.G.: Vortex dynamics in turbulence. Annu. Rev. Fluid Mech. 30, 31–51 (1998)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  52. Schmid, P.J.: Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  53. Farge, M.: Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech. 24, 395–457 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  54. Bermejo-Moreno, I., Pullin, D.I.: On the non-local geometry of turbulence. J. Fluid Mech. 603, 101–135 (2008)

  55. Candès, E., Demanet, L., Donoho, D., et al.: Fast discrete curvelet transforms. Multiscale Model. Simul. 5, 861–899 (2006)

  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)

    Article  MATH  Google Scholar 

  57. Leung, T., Swaminathan, N., Davidson, P.A.: Geometry and interaction of structures in homogeneous isotropic turbulence. J. Fluid Mech. 710, 453–481 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  58. Mishra, M., Liu, X., Skote, M., et al.: Kolmogorov spectrum consistent optimization for multi-scale flow decomposition. Phys. Fluids 26, 055106 (2014)

    Article  Google Scholar 

  59. Adrian, R.J.: Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301 (2007)

    Article  MATH  Google Scholar 

  60. Zheng, W., Yang, Y., Chen, S.: Evolutionary geometry of Lagrangian structures in a transitional boundary layer (under review)

  61. Townsend, A.A.: The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press, New York (1976)

    MATH  Google Scholar 

  62. Perry, A.E., Chong, M.S.: On the mechanism of wall turbulence. J. Fluid Mech. 119, 173–217 (1982)

    Article  MATH  Google Scholar 

  63. Perry, A.E., Henbest, S., Chong, M.S.: A theoretical and experimental-study of wall turbulence. J. Fluid Mech. 165, 163–199 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  64. Sharma, A.S., McKeon, B.J.: On coherent structure in wall turbulence. J. Fluid Mech. 728, 196–238 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  65. Chung, D., Pullin, D.I.: Large-eddy simulation and wall modelling of turbulent channel flow. J. Fluid Mech. 631, 281–309 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  66. Fung, Y.C.: A First Course in Continuum Mechancis, 3rd edn. Prentice-Hall, Englewood Cliffs (1994)

    Google Scholar 

  67. Goto, S., Kida, S.: Reynolds-number dependence of line and surface stretching in turbulence: folding effects. J. Fluid Mech. 586, 59–81 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  68. Zhang, P.: An analysis of head-on droplet collision with large deformation in gaseous medium. Phys. Fluids 23, 042102 (2011)

    Article  Google Scholar 

  69. Crandall, M.G., Lions, P.L.: Viscosity solutions of Hamilton–Jacobi equations. Trans. Am. Math. Soc. 277, 1–42 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  70. Lundgren, T.S.: Strained spiral vortex model for turbulent fine structure. Phys. Fluid 25, 2193–2203 (1982)

    Article  MATH  Google Scholar 

  71. Zhao, Y., Yang, Y., Chen, S.: Evolution of material surfaces in the temporal transition in channel flow (under review)

  72. Wang, Y., Huang, W., Xu, C.: On hairpin vortex generation from near-wall streamwise vortices. Acta. Mech. Sin. 31, 139–152 (2015)

    Article  MathSciNet  Google Scholar 

  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)

  74. Girimaji, S.S., Pope, S.B.: Material-element deformation in isotropic turbulence. J. Fluid Mech. 220, 427–458 (1990)

    Article  Google Scholar 

  75. Girimaji, S.S., Pope, S.B.: Propagating surfaces in isotropic turbulence. J. Fluid Mech. 234, 247–277 (1992)

    Article  MATH  Google Scholar 

Download references

Acknowledgments

The author thanks Y. Yuan for the visualization in Fig. 3 and Y. Zhao for helpful discussions. This work was supported in part by the National Natural Science Foundation of China (Grants 11342011, 11472015, and 11522215) and the Thousand Young Talents Program of China.

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  1. State Key Laboratory for Turbulence and Complex Systems (LTCS) and Center for Applied Physics and Technology (CAPT), College of Engineering, Peking University, Beijing, 100871, China

    Yue Yang

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  1. Yue Yang
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Yang, Y. Identification, characterization and evolution of non-local quasi-Lagrangian structures in turbulence. Acta Mech. Sin. 32, 351–361 (2016). https://doi.org/10.1007/s10409-015-0555-x

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