Skip to main content
SpringerLink
Log in

Statistical properties of coherent fine eddies in wall-bounded turbulent flows by direct numerical simulation

  • Original Article
  • Published:
Theoretical and Computational Fluid Dynamics Aims and scope Submit manuscript

Abstract

The characteristics of coherent fine eddies in wall-bounded turbulent flows are investigated by direct numerical simulation (DNS). The results show that when coherent eddies scaled with Kolmogorov microscale, η and root mean square (rms) of velocity fluctuations, u′rms, it is found that its average diameter is about 10η ∼ 12η and average maximum azimuthal velocity is about 0.5 ∼ 0.6u′rms. Mean azimuthal velocity of coherent eddies follows the profile of Burgers' vortex. Circulations of coherent vortices at different wall locations collapse in similar patterns and show power law behavior. A theoretical description of coherent eddies can be made based on the Burgers' vortex approximation. The diameter and maximum azimuthal velocity of coherent eddies are well approximated at different circulations of Burgers' vortices. It is observed that coherent eddies, those having an average diameter about 10η ∼ 12η, possess maximum azimuthal velocity and intensity ranges as far as 3u′rms. It is shown that the diameter and velocity of coherent eddies are strongly correlated. The simulation results may provide important insight into better understanding of the behaviors of coherent eddies in wall-bounded turbulent flows.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Sreenivasan, K.R., Antonia, R.A.: The phenomenology of small-scale turbulence. Ann. Rev. Fluid Mech. 29, 435–472 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  2. Kline, S.J., Reynolds, W.C., Schraub, F.A., Rundstadler, P.W.: The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773 (1967)

    Article  ADS  Google Scholar 

  3. Corino, E.R., Brodkey, R.S.: A visual investigation of the wall region in turbulent flow. J. Fluid Mech. 37, 1 (1969)

    Google Scholar 

  4. Willmarth, W.W., Yu, S.S.: Structure of the Reynolds stress near the wall. J. Fluid Mech. 55, 65 (1972)

    Google Scholar 

  5. Blackwelder, R.F., Kaplan, R.E.: On the wall structure of the turbulent boundary layer. J. Fluid Mech. 76, 89 (1976)

    Google Scholar 

  6. Blackwelder, R.F., Eckelmann, H.: Streamwise vortices associated with the bursting phenomenon. J. Fluid Mech. 94, 577–594 (1979)

    Article  ADS  Google Scholar 

  7. Batchelor, G.K., Townsend, A.A.: Proc. Roy. Soc. Lond. Ser. A 199, 238 (1949)

    Article  MATH  ADS  Google Scholar 

  8. Burgers, J.M.: A mathematical model illustrating the theory of turbulence. Advances in Applied Mechanics 1, 171–196 (1948).

    Article  MathSciNet  Google Scholar 

  9. Townsend, A.A.: The Structure of Turbulent Shear Flows, 2nd edn. Cambridge University Press, Cambridge (1976)

    Google Scholar 

  10. Corrsin, S., Kistler, A.L.: Free-stream boundaries of turbulent flows. Nat. Advis. Comm. Aeronaut. Rep. 1244, 1044 (1955)

    Google Scholar 

  11. Corrsin, S.: Turbulent dissipation fluctuations. Phys. Fluids 5(10), 1301–1302 (1962)

    Article  MATH  ADS  Google Scholar 

  12. Tennekes, H.: Simple model for the small-scale structure of turbulence. Phys. Fluids 11(3), 669–671 (1968)

    Article  ADS  Google Scholar 

  13. Townsend, A.A.: On the fine-scale structure of turbulence. Proc. R. Soc. Lond. A208, 534–542 (1951)

    ADS  Google Scholar 

  14. Kuo, A.Y.S., Corrsin, S.: Experiment on the geometry of the fine-structure regions in fully turbulent fluid. J. Fluid Mech. 56, 447–479 (1972)

    Article  ADS  Google Scholar 

  15. Lundgren, T.S.: Strained spiral vortex model for turbulent fine structure. Phys. Fluids 25(12), 2193–2203 (1982)

    Article  MATH  ADS  Google Scholar 

  16. Gomez, T., Politano, H., Pouquet, A., Larcheveque, M.: Spiral vortices in compressible turbulent flows. Phys. Fluids 13(7), 2065–2075 (2001)

    Article  ADS  Google Scholar 

  17. Pullin, D.I., Saffman, P.G.: On the Lundgren-Townsend model of turbulent fine scales. Phys. Fluids A5(1), 126–145 (1993)

    ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  19. Hatakeyama, N., Kambe, T.: Statistical laws of random strained vortices in turbulence. Phys. Rev. Lett. 79, 1257–1260 (1997)

    Article  ADS  Google Scholar 

  20. Douady, S., Couder, Y., Brachet, M.E.: Direct observation of the intermittency of intense vorticity filaments in turbulence. Phys. Rev. Lett. 67, 983–986 (1991)

    Article  PubMed  ADS  Google Scholar 

  21. Jeong, J., Hussain, F., Schoppa, W., Kim, J.: Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185–214 (1997)

    MATH  ADS  Google Scholar 

  22. Siggia, E.D.: Numerical study of small-scale intermittency in three-dimensional turbulence. J. Fluid Mech. 107, 375–406 (1981)

    Article  MATH  ADS  Google Scholar 

  23. Kerr, R.M.: Higher order derivative correlation and the alignment of small-scale structures in isotropic numerical turbulence. J. Fluid Mech. 153, 31–58 (1985)

    Article  MATH  ADS  Google Scholar 

  24. She, Z.S., Jackson, E., Orszag, S.A.: Intermittent vortex structures in homogeneous isotropic turbulence. Nature 344, 226–228 (1990)

    Article  ADS  Google Scholar 

  25. Vincent, A., Meneguzzi, M.: The spatial and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 1–20 (1991)

    Article  MATH  ADS  Google Scholar 

  26. Jimenez, J., Wray, A.A., Saffman, P.G., Rogallo, R.S.: The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65–90 (1993)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  27. Tanahashi, M., Miyauchi, T., Matsuoka, K.: Coherent fine-scale structure in temporally developing turbulent mixing layers. Turb. Heat Mass Transf. 2, 461–470 (1997)

    Google Scholar 

  28. Tanahashi, M., Miyauchi, T, Ikeda, J.: Scaling law of coherent fine-scale structure in homogeneous isotropic turbulence. Proc. 11th Symp. Turb. Shear Flows 1, 4-17∼4-22 (1997)

  29. Ruetsch, G.R., Maxey, M.R.: The evolution of small-scale structures in homogeneous isotropic turbulence. Phys. Fluids A4, 2747–2760 (1992)

    ADS  Google Scholar 

  30. Metcalfe, R.W., Hussain, F., Menon, S., Hayakawa, M.: Coherent structures in a turbulent mixing layer: a comparison between numerical simulations and experiments. Turb. Shear Flows 5, 110 (1985)

    Google Scholar 

  31. Hunt, J.C.R., Wray, A.A., Moin, P.: Eddies, streams, and convergence zones in turbulent flows. Proc. Summer Program, Center for Turbulence Research, Stanford, USA, 193–207 (1988)

  32. Robinson, S.K., Kline, S.J., Spalart, P.R.: A review of quasi-coherent structures in a numerically simulated turbulent boundary layer. NASA TM-102191 (1989)

  33. Chong, M.S., Perry, A.E., Cantwell, B.J.: A general classification of three-dimensional flow field. Phys. Fluids A2(5) 765–777 (1990)

    Google Scholar 

  34. Tanaka M., Kida S.: Characterization of vortex tubes and sheets. Phys. Fluids A5, 2079–2082 (1993)

    ADS  Google Scholar 

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

    Article  MATH  ADS  MathSciNet  Google Scholar 

  36. Jimenez, J., Wray, A.: On the characteristics of vortex filaments in isotropic turbulence. J. Fluid Mech. 373, 255–285 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  37. Jimenez, J.: Small-scale intermittency in turbulence. In: Euromech Coll. 364, Carry-le-Rouet, FR (1997)

  38. Bradshaw, P.: An Introduction to Turbulence and its Measurement. Pergamon Press, London, UK (1971)

  39. Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods in Fluid Dynamics. Springer, Berlin Heidelberg New York (1988)

  40. Kuroda, A., Kasagi, N.: Establishment of the DNS databases of turbulent transport phenomena. 1990-92 cooperative research (No. 02302043) (1992)

  41. Kim, J., Moin, P., Moser, R.D.: Turbulent statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166 (1987)

    Article  MATH  ADS  Google Scholar 

  42. Das, S.K.: Characteristics of coherent fine-scale eddies in turbulent channel flows at relatively low reynolds numbers. PhD. Dissertation, Department of Mechanical and Aerospace Engineering, Tokyo Institute of Technology, Tokyo, Japan (1999)

  43. Blackburn, H.M., Mansour, N., Cantwell, B.J.: Topology of fine-scale motions in turbulent flows. J. Fluid Mech. 310, 269–292 (1996)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  44. Tanahashi, M., Miyauchi, T., Iwase, S.: Statistics of coherent fine-scale structure in homogeneous isotropic turbulence. Bull Am Phys. Soc. 43(9) (1998)

  45. Tanahashi, M., Kang, S.-J., Miyamoto, T., Shiokawa, S., Miyauchi, T.: Scaling law of fine-scale eddies in turbulent channel flows up to Re τ = 800. Int. J. Heat Fluid Flow 25, 331–340 (2004)

    Article  Google Scholar 

Download references

Author information

Author notes

  1. Susanta K. Das

    Present address: Department of Chemical Engineering, McGill University, 3610 University Street, Montreal, Quebec, H3A 2B2, Canada

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo, 152-8552, Japan

    Susanta K. Das, Mamoru Tanahashi, Kentaro Shoji & Toshio Miyauchi

Authors
  1. Susanta K. Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mamoru Tanahashi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kentaro Shoji
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Toshio Miyauchi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Susanta K. Das.

Additional information

Communicated by P. Sagaut

PACS 47.11.+j · 47.60.+i · 47.27.−i

Rights and permissions

Reprints and permissions

About this article

Cite this article

Das, S.K., Tanahashi, M., Shoji, K. et al. Statistical properties of coherent fine eddies in wall-bounded turbulent flows by direct numerical simulation. Theor. Comput. Fluid Dyn. 20, 55–71 (2006). https://doi.org/10.1007/s00162-006-0008-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00162-006-0008-z

Keywords

Search

Navigation