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Complexity of localised coherent structures in a boundary-layer flow

  • Taras Khapko
  • Yohann Duguet
  • Tobias Kreilos
  • Philipp Schlatter
  • Bruno Eckhardt
  • Dan S. Henningson
Regular Article
Part of the following topical collections:
  1. Irreversible Dynamics: A topical issue dedicated to Paul Manneville

Abstract

We study numerically transitional coherent structures in a boundary-layer flow with homogeneous suction at the wall (the so-called asymptotic suction boundary layer ASBL). The dynamics restricted to the laminar-turbulent separatrix is investigated in a spanwise-extended domain that allows for robust localisation of all edge states. We work at fixed Reynolds number and study the edge states as a function of the streamwise period. We demonstrate the complex spatio-temporal dynamics of these localised states, which exhibits multistability and undergoes complex bifurcations leading from periodic to chaotic regimes. It is argued that in all regimes the dynamics restricted to the edge is essentially low-dimensional and non-extensive.

Graphical abstract

Keywords

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

References

  1. 1.
    P.J. Schmid, D.S. Henningson, Stability and Transition in Shear Flows (Springer, New York, 2001).Google Scholar
  2. 2.
    T. Herbert, Annu. Rev. Fluid Mech. 20, 487 (1988).ADSCrossRefGoogle Scholar
  3. 3.
    H. Schlichting, Boundary-Layer Theory, 7th edn. (McGraw-Hill, New York, 1987).Google Scholar
  4. 4.
    L.M. Hocking, Q. J. Mech. Appl. Math. 28, 341 (1975).CrossRefMATHGoogle Scholar
  5. 5.
    O. Dauchot, P. Manneville, J. Phys. II 21, 371 (1997).Google Scholar
  6. 6.
    P. Manneville, in IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions, edited by T. Mullin, R. Kerswell, Vol. 77 of Fluid Mechanics and its Applications (Springer, The Netherlands, 2005), pp. 1--33.Google Scholar
  7. 7.
    O. Levin, D.S. Henningson, J. Fluid Mech. 584, 397 (2007).ADSCrossRefMATHGoogle Scholar
  8. 8.
    B. Eckhardt, T.M. Schneider, B. Hof, J. Westerweel, Annu. Rev. Fluid Mech. 39, 447 (2007).ADSCrossRefMathSciNetGoogle Scholar
  9. 9.
    J.D. Skufca, J.A. Yorke, B. Eckhardt, Phys. Rev. Lett. 96, 174101 (2006).ADSCrossRefGoogle Scholar
  10. 10.
    G. Kawahara, Phys. Fluids 17, 041702 (2005).ADSCrossRefMathSciNetGoogle Scholar
  11. 11.
    F. Mellibovsky, A. Meseguer, T.M. Schneider, B. Eckhardt, Phys. Rev. Lett. 103, 054502 (2009).ADSCrossRefGoogle Scholar
  12. 12.
    Y. Duguet, P. Schlatter, D.S. Henningson, Phys. Fluids 21, 111701 (2009).ADSCrossRefGoogle Scholar
  13. 13.
    T.M. Schneider, D. Marinc, B. Eckhardt, J. Fluid Mech. 646, 441 (2010).ADSCrossRefMATHGoogle Scholar
  14. 14.
    Y. Duguet, A.P. Willis, R.R. Kerswell, J. Fluid Mech. 663, 180 (2010).ADSCrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Y. Duguet, P. Schlatter, D.S. Henningson, B. Eckhardt, Phys. Rev. Lett. 108, 044501 (2012).ADSCrossRefGoogle Scholar
  16. 16.
    E. Knobloch, Nonlinearity 21, T45 (2008).ADSCrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    T.M. Schneider, J.F. Gibson, J. Burke, Phys. Rev. Lett. 104, 104501 (2010).ADSCrossRefGoogle Scholar
  18. 18.
    Y. Duguet, O. Le Maitre, P. Schlatter, Phys. Rev. E 84, 066315 (2011).ADSCrossRefGoogle Scholar
  19. 19.
    F. Mellibovsky, B. Eckhardt, J. Fluid Mech. 709, 149 (2012).ADSCrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    T. Kreilos, B. Eckhardt, Chaos 22, 047505 (2012).ADSCrossRefGoogle Scholar
  21. 21.
    M. Avila, F. Mellibovsky, N. Roland, B. Hof, Phys. Rev. Lett. 110, 224502 (2013).ADSCrossRefGoogle Scholar
  22. 22.
    P. Manneville, Phys. Rev. E 79, 025301 (2009).ADSCrossRefGoogle Scholar
  23. 23.
    K. Avila, D. Moxey, A.D. Lozar, M. Avila, D. Barkley, B. Hof, Science 333, 192 (2011).ADSCrossRefGoogle Scholar
  24. 24.
    J. Vollmer, T.M. Schneider, B. Eckhardt, New J. Phys. 11, 013040 (2009).ADSCrossRefGoogle Scholar
  25. 25.
    T.M. Schneider, B. Eckhardt, J.A. Yorke, Phys. Rev. Lett. 99, 034502 (2007).ADSCrossRefGoogle Scholar
  26. 26.
    Y. Duguet, A.P. Willis, R.R. Kerswell, J. Fluid Mech. 613, 255 (2008).ADSCrossRefMATHMathSciNetGoogle Scholar
  27. 27.
    T. Khapko, T. Kreilos, P. Schlatter, Y. Duguet, B. Eckhardt, D.S. Henningson, J. Fluid Mech. 717, R6 (2013).ADSCrossRefGoogle Scholar
  28. 28.
    J. Jiménez, G. Kawahara, M.P. Simens, M. Nagata, M. Shiba, Phys. Fluids 17, 015105 (2005).ADSCrossRefGoogle Scholar
  29. 29.
    S. Cherubini, P. De Palma, J.C. Robinet, A. Bottaro, Phys. Fluids 23, 051705 (2011).ADSCrossRefGoogle Scholar
  30. 30.
    D. Biau, Phys. Fluids 24, 034107 (2012).ADSCrossRefGoogle Scholar
  31. 31.
    T. Kreilos, G. Veble, T.M. Schneider, B. Eckhardt, J. Fluid Mech. 726, 100 (2013).ADSCrossRefMATHGoogle Scholar
  32. 32.
    A.P. Kuznetsov, S.P. Kuznetsov, I.R. Sataev, Int. J. Bifurcat. Chaos 3, 139 (1993).CrossRefMATHMathSciNetGoogle Scholar
  33. 33.
    M. Chevalier, P. Schlatter, A. Lundbladh, D.S. Henningson, Tech. Rep. TRITA-MEK 2007:07, KTH Mechanics, Stockholm, Sweden (2007).Google Scholar
  34. 34.
    P. Schlatter, R. Örlü, J. Phys. Conf. Ser. 318, 022020 (2011).ADSCrossRefGoogle Scholar
  35. 35.
    J. Jeong, F. Hussain, J. Fluid Mech. 285, 69 (1995).ADSCrossRefMATHMathSciNetGoogle Scholar
  36. 36.
    A. Schmiegel, B. Eckhardt, Phys. Rev. Lett. 79, 5250 (1997).ADSCrossRefGoogle Scholar
  37. 37.
    K.T. Alligood, T.D. Sauer, J.A. Yorke, Chaos (Springer, New York, 1996).Google Scholar
  38. 38.
    J.M. Hamilton, J. Kim, F. Waleffe, J. Fluid Mech. 287, 317 (1995).ADSCrossRefMATHGoogle Scholar
  39. 39.
    Y. Pomeau, P. Manneville, Commun. Math. Phys. 74, 189 (1980).ADSCrossRefMathSciNetGoogle Scholar
  40. 40.
    A.N. Pisarchik, C. Grebogi, Int. J. Bifurcat. Chaos 18, 1605 (2008).CrossRefGoogle Scholar
  41. 41.
    F. Feudel, N. Seehafer, L.S. Tuckerman, M. Gellert, Phys. Rev. E 87, 023021 (2013).ADSCrossRefGoogle Scholar
  42. 42.
    N. Lebovitz, Nonlinearity 22, 2645 (2009).ADSCrossRefMATHMathSciNetGoogle Scholar
  43. 43.
    H. Faisst, B. Eckhardt, Phys. Rev. Lett. 91, 224502 (2003).ADSCrossRefGoogle Scholar
  44. 44.
    H. Wedin, R.R. Kerswell, J. Fluid Mech. 508, 333 (2004).ADSCrossRefMATHMathSciNetGoogle Scholar
  45. 45.
    J.F. Gibson, J. Halcrow, P. Cvitanović, J. Fluid Mech. 638, 243 (2009).ADSCrossRefMATHGoogle Scholar
  46. 46.
    L. Keefe, P. Moin, J. Kim, J. Fluid Mech. 242, 1 (1992).ADSCrossRefMATHMathSciNetGoogle Scholar
  47. 47.
    J. Jiménez, P. Moin, J. Fluid Mech. 225, 213 (1991).ADSCrossRefMATHGoogle Scholar
  48. 48.
    W. Schoppa, F. Hussain, J. Fluid Mech. 453, 57 (2002).ADSCrossRefMATHMathSciNetGoogle Scholar
  49. 49.
    S. Toh, T. Itano, J. Fluid Mech. 481, 67 (2003).ADSCrossRefMATHMathSciNetGoogle Scholar
  50. 50.
    K. Deguchi, P. Hall, A. Walton, J. Fluid Mech. 721, 58 (2013).ADSCrossRefMATHMathSciNetGoogle Scholar
  51. 51.
    K. Melnikov, T. Kreilos, B. Eckhardt, unpublished, arXiv:1309.6912 (2013).
  52. 52.
    M. Chantry, A.P. Willis, R.R. Kerswell, unpublished, arXiv:1308.6224 (2013).

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Taras Khapko
    • 1
    • 2
  • Yohann Duguet
    • 3
  • Tobias Kreilos
    • 4
    • 5
  • Philipp Schlatter
    • 1
    • 2
  • Bruno Eckhardt
    • 4
    • 6
  • Dan S. Henningson
    • 1
    • 2
  1. 1.KTH MechanicsLinné FLOW CentreStockholmSweden
  2. 2.Swedish e-Science Research Centre (SeRC)StockholmSweden
  3. 3.LIMSI-CNRS, UPR 3251Orsay CedexFrance
  4. 4.Fachbereich PhysikPhilipps-Universität MarburgMarburgGermany
  5. 5.Max Planck Institute for Dynamics and Self-OrganizationGöttingenGermany
  6. 6.J.M. BurgerscentrumDelft University of TechnologyDelftThe Netherlands

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