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Flow patterns in inclined-layer turbulent convection

  • Wei QiangEmail author
  • Hui Cao
Regular Article

Abstract

We study the flow patterns of turbulent convection in an inclined layer with a large aspect ratio Γ and moderately high Rayleigh numbers ranging from 9 × 104 to 2 × 107 based on three-dimensional numerical simulations. The Prandtl number is fixed at σ = 0.7 and the angles of inclination are varied between 5° ≤ θ ≤ 60°. The initial quiescent fluid layer is observed to firstly evolve into a quasi-periodical flow pattern before the turbulent convection is fully developed. The transient flow at earlier times, though elongated along the slope and anisotropic in the directions parallel to the top and bottom plates, becomes isotropic in the final statistically steady state, provided that the Rayleigh number is high (R ≃ 2 × 107) and the angle of inclination is small (θ ≤ 17°). The effect of inclination on the large-scale flow is different from that on individual plumes, which exhibits isotropy and is independent of the angles of inclination for Rayleigh numbers above 5 × 106. The regions near the upper and lower sidewalls of the enclosure, considered as extensions of the thermal boundary layer, shrink with increasing Rayleigh numbers and the scaling exponent is about 2/7.

Graphical abstract

Keywords

Flowing Matter: Liquids and Complex Fluids 

Supplementary material

Supplementary material, approximately 29.3 MB.

Supplementary material, approximately 29.3 MB.

References

  1. 1.
    G. Ahlers, Physics 2, 74 (2009).CrossRefGoogle Scholar
  2. 2.
    L.P. Kadanoff, Phys. Today 54, 34 (2001).CrossRefGoogle Scholar
  3. 3.
    G. Ahlers, S. Grossmann, D. Lohse, Rev. Mod. Phys. 81, 503 (2009).ADSCrossRefGoogle Scholar
  4. 4.
    F. Chillà, J. Schumacher, Eur. Phys. J. E 35, 58 (2012).CrossRefGoogle Scholar
  5. 5.
    A. Parodi, J. von Hardenberg, G. Passoni, A. Provenzale, E.A. Spiegel, Phys. Rev. Lett. 92, 194503 (2004).ADSCrossRefGoogle Scholar
  6. 6.
    D. Lohse, K.Q. Xia, Annu. Rev. Fluid Mech. 42, 335 (2010).ADSCrossRefGoogle Scholar
  7. 7.
    J.J. Niemela, L. Skrbek, K.R. Sreenivasan, R.J. Donnelly, Nature 404, 837 (2000).ADSCrossRefGoogle Scholar
  8. 8.
    X.L. Qiu, K.Q. Xia, P. Tong, J. Turbulence 6, 30 (2005).ADSCrossRefGoogle Scholar
  9. 9.
    J.C. Tisserand, M. Creyssels, Y. Gasteuil, H. Pabiou, M. Gibert, B. Castaing, F. Chilla, Phys. Fluids 23, 015105 (2011).ADSCrossRefGoogle Scholar
  10. 10.
    A. Namiki, K. Kurita, Phys. Rev. E 65, 056301 (2002).ADSCrossRefGoogle Scholar
  11. 11.
    K.E. Daniels, B.B. Plapp, E. Bodenschatz, Phys. Rev. Lett. 84, 5320 (2000).ADSCrossRefGoogle Scholar
  12. 12.
    E. Bodenschatz, W. Pesch, G. Ahlers, Annu. Rev. Fluid Mech. 32, 709 (2000).ADSCrossRefMathSciNetGoogle Scholar
  13. 13.
    Y.M. Chen, A.J. Pearlstein, J. Fluid Mech. 198, 513 (1989).ADSCrossRefzbMATHGoogle Scholar
  14. 14.
    J.E. Hart, J. Fluid Mech. 47, 547 (1971).ADSCrossRefGoogle Scholar
  15. 15.
    R.M. Clever, F.H. Busse, J. Fluid Mech. 81, 107 (1977).ADSCrossRefzbMATHGoogle Scholar
  16. 16.
    R. Delgado-Buscalioni, Phys. Rev. E 64, 016303 (2001).ADSCrossRefGoogle Scholar
  17. 17.
    F.H. Busse, R.M. Clever, Phys. Fluids 12, 2137 (2000).ADSCrossRefMathSciNetGoogle Scholar
  18. 18.
    K.E. Daniels, E. Bodenschatz, Phys. Rev. Lett. 88, 034501 (2002).ADSCrossRefGoogle Scholar
  19. 19.
    K.E. Daniels, O. Brausch, W. Pesch, E. Bodenschatz, J. Fluid Mech. 597, 261 (2008).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    R. Krishnamurti, L.N. Howard, Proc. Natl. Acad. Sci. U.S.A. 78, 1981 (1981).ADSCrossRefGoogle Scholar
  21. 21.
    T. Hartlep, A. Tilgner, F.H. Busse, Phys. Rev. Lett. 91, 064501 (2003).ADSCrossRefGoogle Scholar
  22. 22.
    T. Hartlep, A. Tilgner, F.H. Busse, J. Fluid Mech. 544, 309 (2005).ADSCrossRefzbMATHGoogle Scholar
  23. 23.
    B. Castaing, G. Gunaratne, L. Kadanoff, A. Libchaber, F. Heslot, J. Fluid. Mech. 204, 1 (1989).ADSCrossRefGoogle Scholar
  24. 24.
    J. Zhang, S. Childress, A. Libchaber, Phys. Fluids 9, 1034 (1997).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  25. 25.
    J. Niemela, L. Skrbek, K. Sreenivasan, R. Donnelly, J. Fluid Mech. 449, 169 (2001).ADSCrossRefzbMATHGoogle Scholar
  26. 26.
    X.L. Qiu, P. Tong, Phys. Rev. E 64, 036304 (2001).ADSCrossRefGoogle Scholar
  27. 27.
    J. Niemela, K. Sreenivasan, Europhys. Lett. 62, 829 (2003).ADSCrossRefGoogle Scholar
  28. 28.
    H.D. Xi, S. Lam, K.Q. Xia, J. Fluid Mech. 503, 47 (2004).ADSCrossRefzbMATHGoogle Scholar
  29. 29.
    J. von Hardenberg, A. Parodi, G. Passoni, A. Provenzale, E.A. Spiegel, Phys. Lett. A 372, 2223 (2008).ADSCrossRefzbMATHGoogle Scholar
  30. 30.
    S. Ciliberto, S. Cioni, C. Laroche, Phys. Rev. E 54, R5901 (1996).ADSCrossRefGoogle Scholar
  31. 31.
    F. Chilla, M. Rastello, S. Chaumat, B. Castaing, Eur. Phys. J. B 40, 223 (2004).ADSCrossRefGoogle Scholar
  32. 32.
    P. Wei, K.Q. Xia, J. Fluid. Mech. 720, 140 (2013).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  33. 33.
    S. Weiss, G. Ahlers, J. Fluid Mech. 715, 314 (2013).ADSCrossRefzbMATHGoogle Scholar
  34. 34.
    P.E. Roche, B. Castaing, B. Chabaud, B. Hébral, Phys. Rev. E 63, 045303 (2001).ADSCrossRefGoogle Scholar
  35. 35.
    K.E. Daniels, C. Beck, E. Bodenschatz, Physica D 193, 208 (2004).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  36. 36.
    P.L. Bhatnagar, E.P. Gross, M. Krook, Phys. Rev. 94, 511 (1954).ADSCrossRefzbMATHGoogle Scholar
  37. 37.
    Y.H. Qian, D. D’Humières, P. Lallemand, Europhys. Lett. 17, 479 (1992).ADSCrossRefzbMATHGoogle Scholar
  38. 38.
    X. Shan, Phys. Rev. E 55, 2780 (1997).ADSCrossRefGoogle Scholar
  39. 39.
    X. He, L.S. Luo, M. Dembo, J. Comput. Phys. 129, 357 (1996).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  40. 40.
    Z. Guo, C. Zheng, B. Shi, Chin. Phys. 11, 366 (2002).ADSCrossRefGoogle Scholar
  41. 41.
    G. Grötzbach, J. Comput. Phys. 49, 241 (1983).ADSCrossRefzbMATHGoogle Scholar
  42. 42.
    X. Chavanne, F. Chilla, B. Chabaud, B. Castaing, B. Hebral, Phys. Fluids 13, 1300 (2001).ADSCrossRefGoogle Scholar
  43. 43.
    X.Z. Wu, A. Libchaber, Phys. Rev. A 45, 842 (1992).ADSCrossRefGoogle Scholar
  44. 44.
    F. Heslot, B. Castaing, A. Libchaber, Phys. Rev. A 36, 5870 (1987).ADSCrossRefGoogle Scholar
  45. 45.
    D.C. Threlfall, J. Fluid. Mech. 67, 17 (1975).ADSCrossRefGoogle Scholar
  46. 46.
    O. Shishkina, R.J.A.M. Stevens, S. Grossmann, D. Lohse, New J. Phys. 12, 075022 (2010).ADSCrossRefGoogle Scholar
  47. 47.
    O. Shishkina, S. Horn, S. Wagner, J. Fluid. Mech. 730, 442 (2013).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  48. 48.
    R.M. Kerr, J. Fluid Mech. 310, 139 (1996).ADSCrossRefzbMATHGoogle Scholar
  49. 49.
    O. Shishkina, C. Wagner, J. Fluid. Mech. 599, 383 (2008).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  50. 50.
    R.J.A.M. Stevens, R. Verzicco, D. Lohse, J. Fluid Mech. 643, 495 (2010).ADSCrossRefzbMATHGoogle Scholar
  51. 51.
    M.S. Emran, J. Schumacher, Eur. Phys. J. E. 35, 108 (2012).CrossRefGoogle Scholar
  52. 52.
    R. Verzicco, R. Camussi, J. Fluid Mech. 477, 19 (2003).ADSCrossRefzbMATHGoogle Scholar
  53. 53.
    R.P.J. Kunnen, H.J.H. Clercx, B.J. Geurts, L.J.A. van Bokhoven, R.A.D. Akkermans, R. Verzicco, Phys. Rev. E 77, 016302 (2008).ADSCrossRefGoogle Scholar
  54. 54.
    S.B. Pope, Turbulent Flows (Cambridge University Press, 2000).Google Scholar
  55. 55.
    A.S. Monin, A.M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. 2 (MIT Press, 1975).Google Scholar
  56. 56.
    J.N. Shadid, R.J. Goldstein, J. Fluid Mech. 215, 61 (1990).ADSCrossRefGoogle Scholar
  57. 57.
    K.E. Daniels, R.J. Wiener, E. Bodenschatz, Phys. Rev. Lett. 91, 114501 (2003).ADSCrossRefGoogle Scholar
  58. 58.
    K.E. Daniels, E. Bodenschatz, Chaos 13, 55 (2003).ADSCrossRefGoogle Scholar
  59. 59.
    F.H. Busse, J. Fluid Mech. 52, 97 (1972).ADSCrossRefzbMATHGoogle Scholar
  60. 60.
    E. Moses, G. Zocchi, A. Libchaberii, J. Fluid Mech. 251, 581 (1993).ADSCrossRefGoogle Scholar
  61. 61.
    E. Kaminski, C. Jaupart, J. Fluid Mech. 478, 287 (2003).ADSCrossRefzbMATHGoogle Scholar
  62. 62.
    X.D. Shang, X.L. Qiu, P. Tong, K.Q. Xia, Phys. Rev. Lett. 90, 074501 (2003).ADSCrossRefGoogle Scholar
  63. 63.
    Q. Zhou, K.Q. Xia, New J. Phys. 12, 075006 (2010).ADSCrossRefGoogle Scholar
  64. 64.
    M. Emran, J. Schumacher, J. Fluid Mech. 611, 13 (2008).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  65. 65.
    M. Kaczorowski, C. Wagner, J. Fluid Mech. 618, 89 (2009).ADSCrossRefzbMATHGoogle Scholar
  66. 66.
    R.M. Kerr, J.R. Herring, J. Fluid Mech. 419, 325 (2000).ADSCrossRefzbMATHGoogle Scholar
  67. 67.
    K. Julien, S. Legg, J. McWilliams, J. Werne, J. Fluid Mech. 391, 151 (1999).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  68. 68.
    S.Q. Zhou, K.Q. Xia, Phys. Rev. Lett. 89, 184502 (2002).ADSCrossRefGoogle Scholar
  69. 69.
    E.S.C. Ching, H. Guo, X.D. Shang, P. Tong, K.Q. Xia, Phys. Rev. Lett. 93, 124501 (2004).ADSCrossRefGoogle Scholar
  70. 70.
    A. Belmonte, A. Libchaber, Phys. Rev. E 53, 4893 (1996).ADSCrossRefGoogle Scholar
  71. 71.
    E.M. Sevick, P.A. Monson, J.M. Ottino, J. Chem. Phys. 88, 1198 (1988).ADSCrossRefGoogle Scholar
  72. 72.
    A. Tilgner, A. Belmonte, A. Libchaber, Phys. Rev. E 47, R2253 (1993).ADSCrossRefGoogle Scholar
  73. 73.
    A. Belmonte, A. Tilgner, A. Libchaber, Phys. Rev. E 51, 5681 (1995).ADSCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.School of Computer ScienceChina University of GeosciencesWuhanChina
  2. 2.Center of Information and LaboratoryChina University of GeosciencesWuhanChina

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