Skip to main content

Turbulent spots in channel flow: An experimental study

Large-scale flow, inner structure and low-order model

Abstract

We present new experimental results on the development of turbulent spots in channel flow. The internal structure of a turbulent spot is measured, with Time Resolved Stereoscopic Particle Image Velocimetry. We report the observation of travelling-wave-like structures at the trailing edge of the turbulent spot. Special attention is paid to the large-scale flow surrounding the spot. We show that this large-scale flow is an asymmetric quadrupole centred on the spot. We measure the time evolution of the turbulent fluctuations and the mean flow distortions and compare these with the predictions of a nonlinear reduced order model predicting the main features of subcritical transition to turbulence.

Graphical abstract

This is a preview of subscription content, access via your institution.

References

  1. P. Manneville, Dissipative structures and weak turbulence (Springer, 1995).

  2. H.W. Emmons, J. Aerospace Sci. 18, 490 (1951).

    MATH  MathSciNet  Google Scholar 

  3. J.H.P. Dawes, Philos. Trans. R. Soc. London, Ser. A: Math. Phys. Eng. Sci. 368, 3519 (2010).

    ADS  Article  MATH  MathSciNet  Google Scholar 

  4. E. Knobloch, Nonlinearity 21, T45 (2008).

    ADS  Article  MATH  MathSciNet  Google Scholar 

  5. R. Richter, I.V. Barashenkov, Phys. Rev. Lett. 94, 184503 (2005).

    ADS  Article  Google Scholar 

  6. P.B. Umbanhowar, F. Melo, H.L. Swinney, Nature 382, 793 (1996).

    ADS  Article  Google Scholar 

  7. A.R. Champneys, G.W. Hunt, and J.M.T. Thompson (Editors), Localization and solitary waves in solid mechanics (World Scientific Publishing Company, 1999).

  8. S.A. Orszag, J. Fluid Mech. 50, 689 (1971).

    ADS  Article  MATH  Google Scholar 

  9. T. Tatsumi, T. Yoshimura, J. Fluid Mech. 212, 437 (1990).

    ADS  Article  MATH  Google Scholar 

  10. D.R. Carlson, S.E. Widnall, M.F. Peeters J. Fluid Mech.1211982.

    Article  Google Scholar 

  11. B.G.B. Klingmann, J. Fluid Mech. 240, 167 (1992).

    ADS  Article  Google Scholar 

  12. G. Lemoult, J.L. Aider, J.E. Wesfreid, Phys. Rev. E 85, 025303 (2012).

    ADS  Article  Google Scholar 

  13. F. Alavyoon, D.S. Henningson, P.H. Alfredsson, Phys. Fluids 29, 1328 (1986).

    ADS  Article  Google Scholar 

  14. D. Seki, M. Matsubara, Phys. Fluids 24, 124102 (2012).

    ADS  Article  Google Scholar 

  15. D.S. Henningson, P. Spalart, J. Kim, Phys. Fluids 30, 2914 (1987).

    ADS  Article  Google Scholar 

  16. D.S. Henningson, J. Kim, J. Fluid Mech. 228, 183 (1991).

    ADS  MATH  Google Scholar 

  17. T. Tsukahara, Y. Seki, H. Kawamura, D. Tochio, in Proceedings of the Fourth International Symposium on Turbulence and Shear Flow Phenomena, Williamsburg, VA, USA, June 27-29, 2005, pp. 935-940.

  18. H. Aida, T. Tsukahara, Y. Kawaguchi, in Proceedings of the Seventh International Symposium on Turbulence and Shear Flow Phenomena, Ottawa, Canada, July 28-31, 2011, Paper-ID #8D2P (USB).

  19. K. Takeishi, G. Kawahara, M. Uhlmann, A. Pinelli, S. Goto, in Proceedings of 31st JSST Annual Conference, Port Island, Kobe, Japan, Sept. 27-28, 2012, p. 197.

  20. L.S. Tuckerman, in Proceedings of the 14th European Turbulence Conference, Lyon, France (2013).

  21. A. Lundbladh, A.V. Johansson, J. Fluid Mech. 229, 499 (1991).

    ADS  Article  MATH  Google Scholar 

  22. J. Schumacher, B. Eckhardt, Phys. Rev. E 63, 046307 (2001).

    ADS  Article  Google Scholar 

  23. M. Lagha, P. Manneville, Phys. Fluids 19, 094105 (2007).

    ADS  Article  Google Scholar 

  24. Y. Duguet, P. Schlatter, Phys. Rev. Lett. 110, 034502 (2013).

    ADS  Article  Google Scholar 

  25. C.W.H. van Doorne, J. Westerweel, Philos. Trans. R. Soc. London, Ser. A 367, 489 (2009).

    ADS  Article  MATH  Google Scholar 

  26. G. Lemoult, J.L. Aider, J.E. Wesfreid, J. Fluid Mech. 731, R1 (2013).

    ADS  Article  Google Scholar 

  27. Y. Duguet, O. Le Maître, P. Schlatter, Phys. Rev. E 84, 066315 (2011).

    ADS  Article  Google Scholar 

  28. M. Shimizu, S. Kida, Fluid Dyn. Res. 41, 045501 (2009).

    ADS  Article  Google Scholar 

  29. Y. Duguet, A.P. Willis, R.R. Kerswell, J. Fluid Mech. 663, 180 (2010).

    ADS  Article  MATH  MathSciNet  Google Scholar 

  30. B. Hof, A. de Lozar, M. Avila, X. Tu, T.M. Schneider, Science 327, 1491 (2010).

    ADS  Article  Google Scholar 

  31. A. Prigent, G. Grégoire, H. Chaté, O. Dauchot, Physica D 174, 100 (2003).

    ADS  Article  MATH  Google Scholar 

  32. D. Barkley, L.S. Tuckerman, Phys. Rev. Lett. 94, 014502 (2005).

    ADS  Article  Google Scholar 

  33. P. Manneville, Fluid Dyn. Res. 43, 065501 (2011).

    ADS  Article  MathSciNet  Google Scholar 

  34. L.N. Trefethen, A.E. Trefethen, S.C. Reddy, T.A. Driscoll, Science 261, 578 (1993).

    ADS  Article  MATH  MathSciNet  Google Scholar 

  35. S.C. Reddy, D.S. Henningson, J. Fluid Mech. 252, 209 (1993).

    ADS  Article  MATH  MathSciNet  Google Scholar 

  36. S.C. Reddy, P.J. Schmid, J.S. Baggett, D.S. Henningson, J. Fluid Mech. 365, 269 (1998).

    ADS  Article  MATH  MathSciNet  Google Scholar 

  37. F. Waleffe, Phys. Fluids 9, 883 (1997).

    ADS  Article  Google Scholar 

  38. P. Hall, S. Sherwin, J. Fluid Mech. 661, 178 (2010).

    ADS  Article  MATH  MathSciNet  Google Scholar 

  39. M. Nagata, J. Fluid Mech. 217, 519 (1990).

    ADS  Article  MathSciNet  Google Scholar 

  40. G. Kawahara, M. Uhlmann, L. van Veen, Annu. Rev. Fluid Mech. 44, 203 (2012).

    ADS  Article  Google Scholar 

  41. F. Waleffe, J. Fluid Mech. 435, 93 (2001).

    ADS  Article  MATH  Google Scholar 

  42. T. Itano, S. Toh, J. Phys. Soc. Jpn. 70, 703 (2001).

    ADS  Article  Google Scholar 

  43. M. Nagata, K. Deguchi, J. Fluid Mech. 735, R4 (2013).

    ADS  Article  MathSciNet  Google Scholar 

  44. S. Zammert, B. Eckhardt, private communication (2013).

  45. A. De Lozar, F. Mellibovsky, M. Avila, B. Hof, Phys. Rev. Lett. 108, 214502 (2012).

    ADS  Article  Google Scholar 

  46. Y. Pomeau, Physica D 23, 3 (1986).

    ADS  Article  Google Scholar 

  47. P. Berge, Y. Pomeau, Ch. Vidal, L’espace chaotique Chapt. 4 (Hermann, 1998).

  48. H. Sakaguchi, H.R. Brand, Physica D 97, 274 (1996).

    ADS  Article  Google Scholar 

  49. J.H.P. Dawes, W.J. Giles, Proc. R. Soc. London, Ser. A: Math. Phys. Engin. Sci. 467, 3066 (2011).

    ADS  Article  MATH  MathSciNet  Google Scholar 

  50. P. Manneville, EPL 98, 64001 (2012).

    ADS  Article  Google Scholar 

  51. D. Barkley, Phys. Rev. E 84, 016309 (2011).

    ADS  Article  Google Scholar 

  52. J.F. Gibson, E.W. Brand, preprint arXiv:1304.6323 (2013).

  53. R.S. Laramee, H. Hauser, H. Doleisch, B. Vrolijk, F.H. Post, D. Weiskopf, in Computer Graphics Forum, Vol. 23 (Wiley Online Library, 2004) pp. 203--221.

  54. V. Croquette, P. Le Gal, A. Pocheau, R. Guglielmetti, Europhys. Lett. 1, 393 (1986).

    ADS  Article  Google Scholar 

  55. J.C. Lagarias, J.A. Reeds, M.H. Wright, P.E. Wright, SIAM J. Opt. 9, 112 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  56. D. Barkley, J. Phys. Conf. Ser. 318, 032001 (2011).

    ADS  Article  Google Scholar 

  57. S. Bottin, F. Daviaud, P. Manneville, O. Dauchot, Europhys. Lett. 43, 171 (1998).

    ADS  Article  Google Scholar 

  58. S. Bottin, H. Chate, Eur. Phys. J. B 6, 143 (1998).

    ADS  Article  Google Scholar 

  59. K. Avila, D. Moxey, A. de Lozar, M. Avila, D. Barkley, B. Hof, Science 333, 192 (2011).

    ADS  Article  Google Scholar 

  60. L. Shi, M. Avila, B. Hof, Phys. Rev. Lett. 110, 204502 (2013).

    ADS  Article  Google Scholar 

  61. Y. Duguet, P. Schlatter, D.S. Henningson, J. Fluid Mech. 650, 119 (2010).

    ADS  Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Grégoire Lemoult.

Additional information

Contribution to the Topical Issue “Irreversible Dynamics: A topical issue dedicated to Paul Manneville” edited by Patrice Le Gal and Laurette S. Tuckerman.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lemoult, G., Gumowski, K., Aider, JL. et al. Turbulent spots in channel flow: An experimental study. Eur. Phys. J. E 37, 25 (2014). https://doi.org/10.1140/epje/i2014-14025-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2014-14025-2

Keywords

  • Topical issue: Irreversible Dynamics: A topical issue dedicated to Paul Manneville