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Wake Instabilities Behind Bluff Bodies

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Dynamics of Spatio-Temporal Cellular Structures

Part of the book series: Springer Tracts in Modern Physics ((STMP,volume 207))

Abstract

The observation by Bénard of a vortex street in the wake of a circular cylinder has been commonly associated with the stability analysis of the double alternate street proposed by von Kármán. After a short historical review of these studies, we present the main progress in understanding this instability during the last decade. New experiments and the control of two-dimensional flows have clarified the source of different modes as well as the results of three-dimensional numerical simulations. The introduction of new concepts (absolute and convective instabilities) allows us to link the velocity defect in the wake to the mechanism of formation of the vortex street. The dynamics of the wake has been successfully compared to the nonlinear Landau and Ginzburg-Landau models. Besides the configuration of the circular cylinder wake, we describe different kinds of bluff bodies and the diversity of their applications.

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References

  1. V. Strouhal, Uber eine besondere Art der Tonerregung. Wied, Anna. Phys. und Chem. (Leipzig) Series 3, 216–251 (1878).

    Article  Google Scholar 

  2. H. Bénard, Formation de centres de giration à l’arrière d’un obstacle en mouvement, 9 novembre 1908, Compt. Rend. Acad. Sci. Paris 147, 839–842 (1908).

    Google Scholar 

  3. H. Bénard, Étude cinématographique des remous et des rides produits par la translation d’un obstacle, 23 novembre 1908, Compt. Rend. Acad. Sci Paris, 147, 970–972 (1908).

    Google Scholar 

  4. A. Mallock, On the resistance of air, Proc. Roy. Soc. A79, 262–273 (1907).

    Article  ADS  Google Scholar 

  5. H. Bénard, Sur la zone de formation des tourbillons alternés derrière un obstacle, 31 mars 1913, Compt. Rend. Acad. Sci. Paris (1913).

    Google Scholar 

  6. H. Bénard, Sur la marche des tourbillons alternés derrière un obstacle, 21 avril 1913, Compt. Rend. Acad. Sci. Paris (1913).

    Google Scholar 

  7. H. Bénard, Sur les lois de la fréquence des tourbillons alternés détachés derrière un obstacle, 7 juin 1926, Compt. Rend. Acad. Sci. Paris (1926).

    Google Scholar 

  8. H. Bénard, Sur l’inexactitude, pour les liquides réels, des lois théoriques de Kármán relatives à la stabilité des tourbillons alternés, 21 juin 1926, Compt. Rend. Acad. Sci. Paris (1926).

    Google Scholar 

  9. H. Bénard, Sur les écarts des valeurs de la fréquence des tourbillons alternés par rapport à la loi de similitude dynamique, 5 juillet 1927, Compt. Rend. Acad. Sci. Paris (1927).

    Google Scholar 

  10. D. Riabouchinsky, L’Aérophile, 19, 15 (1911).

    Google Scholar 

  11. G. von dem Borne, Zeits. Für Flugtechnik, 3 (1912).

    Google Scholar 

  12. T. von Kármán, The Wind and Beyond: Theodore von Kármán Pionneer in Aviation and Pathfinder in Space, Little Brown, New York (1967).

    Google Scholar 

  13. T. von Kármán, Aerodynamics, Cornell University Press, Ithaca, New York, see also McGraw-Hill paperback (1954).

    MATH  Google Scholar 

  14. T. von Kármán, Uber den Mechanismus den Widerstands, den ein bewegter Korper in einer Flussigkeit erfahrt, Gott. Nachr, part 1: 509–517 (1911).

    Google Scholar 

  15. T. von Kármán, Uber den Mechanismus den Widerstands, den ein bewegter Korper in einer Flussigkeit erfahrt, Gott. Nachr, part 2: 547–556 (1912).

    Google Scholar 

  16. T. von Kármán and H. Rubach, Phys. Z 13, 49–59 (1912).

    Google Scholar 

  17. L. Rayleigh, Theory of Sound, second edition (1896).

    Google Scholar 

  18. L. Rayleigh, Aeolian tones, Phil. Mag. 29, 433 (1915).

    Google Scholar 

  19. E. Berger and R. Wille, Periodic flow phenomena, Ann. Rev. Flluid. Mech. 4, 313 (1972).

    Article  ADS  Google Scholar 

  20. M. Coutanceau and J.-R. Defaye, Circular cylinder wake configurations: a flow visualization survey, Appl. Mech. Rev. 44, 255–305 (1991).

    Article  Google Scholar 

  21. C.H. K. Williamson, Vortex Dynamics in the cylinder wake, Ann. Rev. Fluid Mech. 28, 477–539 (1996).

    Article  ADS  Google Scholar 

  22. R.D. Blevins, Flow-Induced Vibrations, New York: Van Nostrand Reinhold (1990).

    Google Scholar 

  23. M. Zdravkovich, Flow Around Circular Cylinders, Oxford University Press, Oxford (2002).

    Google Scholar 

  24. J. Jimenez, On the linear stability of the inviscid Karman vortex street, J. Fluid Mech. 178, 177–194 (1987).

    Article  MATH  ADS  Google Scholar 

  25. P.G. Saffman, Vortex Dynamics, Cambridge University Press (1992).

    Google Scholar 

  26. A. Bers, Space time evolution of plasma instability absolute and convective, in Handbook of Plasma Physics (ed. M.N. Rosenbluth and R.Z. Sagdeev), 1, 451–517 (1983).

    Google Scholar 

  27. P. Huerre and P.A. Monkewitz, Local and global instabilities in spatially developing flows, Ann. Rev. Fluid Mech. 22, 473–537 (1990).

    Article  MathSciNet  ADS  Google Scholar 

  28. E. Hopf, Abzweigung einer periodischen Losung von einer station aren Losung eines Differentialsystems, Ber. Ver h. S achs. Akad. Wiss. Leipzig, Math.-phys. Kl., 94, 1–22 (1942). Translated in The Hopf Bifurcation and Its Applications (eds. J.E. arsden and M. McCracken), Springer, New York, pp. 163–193 (1976).

    Google Scholar 

  29. L.D. Landau, On the problem of turbulence, C. R. Acad. Sci. URSS 44, 311–314 (1944).

    Google Scholar 

  30. L. Kovasznay, Hot wire investigation of the wake behind cylinder at low Reynolds numbers, Proc. Roy. Soc. A, 198, 174–189 (1949).

    Article  ADS  Google Scholar 

  31. A. Roshko, On the development of turbulent wakes from vortex streets, NACA Report 1191, National Advisory Committee for Aeronautics, Washington, DC (1954).

    Google Scholar 

  32. V.K. Horváth, J Cressman, W.I. Goldburg, and X.L. Wu, Hysteretic transition from laminar ro vortex shedding flow in soap films, Advances in Turbulence VIII European Turbulence Conference (Dopazo et al. eds.), (CIMNE, Barcelona 2000).

    Google Scholar 

  33. T. Leweke and M. Provansal, The flow behind rings: bluff body wakes without end effects, J. Fluid Mech. 288, 265–310 (1995).

    Article  ADS  Google Scholar 

  34. G.J. Sheard, M.C. Thompson, and K. Hourigan, A coupled Landau model describing the Strouhal-Reynolds number profile on a three-dimensional circular cylinder wake, Phys. Fluids 15(9), 68–71 (2003).

    Article  ADS  Google Scholar 

  35. G.J. Sheard, M.C, Thompson, and K. Hourigan, From spheres to circular cylinders: the stability and flow structures of bluff ring wakes, J. Fluid Mech. 492, 147–180 (2003).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  36. G.J. Sheard, The stability and characteristics of the flow past rings, Ph.D. dissertation Monash University, Australia (2004).

    Google Scholar 

  37. R.B. Green and J.H. Gerrard, An optical interferometric study of the wake of a bluff body, J. Fluid Mech. 226, 219–242 (1991).

    Article  ADS  Google Scholar 

  38. C. Mathis, M. Provansal, and L. Boyer, The Bénard-von Kármán instability: an experimental study near the threshold, J. Physique Lett. 45, L–483-491 (1984).

    Article  Google Scholar 

  39. M. Provansal, C. Mathis, and L. Boyer, Bénard-von Kármán instability: transient and forced regimes, J. Fluid Mech. 182, 1–22 (1987).

    Article  MATH  ADS  Google Scholar 

  40. K.R. Sreenivasan, P.J. Strykowski, and D.J. Olinger, Hopf bifurcation, Landau equation and vortex shedding behind cylinders, in Forum on Unsteady Flow Separation (ed. K.N. Ghia), ASME, New York, FED 52, 1–13 (1986).

    Google Scholar 

  41. H. Oertel, Wakes behind blunt bodies, Ann. Rev. Fluid Mech. 22, 539 (1990).

    Article  MathSciNet  ADS  Google Scholar 

  42. P. Albarède and P. A Monkewitz, A model for the formation of oblique shedding and chevron patterns in cylinder wakes, Phys. Fluids A 4,. 744–756 (1992).

    Article  ADS  Google Scholar 

  43. M. Schumm, E. Berger, and P.A. Monkewitz, Self-excited oscillations in the wake of two-dimensional bluff bodies and their control, J. Fluid Mech. 271, 17–53 (1994).

    Article  ADS  Google Scholar 

  44. M. Gaster, Vortex shedding from slender cones at low Reynolds numbers, J. Fluid Mech. 38, 565–576 (1969).

    Article  ADS  Google Scholar 

  45. B.R. Noack, F. Ohle, and H. Eckelmann, On cell formation in vortex streets, J. Fluid Mech. 227, 293–308 (1991).

    Article  MATH  ADS  Google Scholar 

  46. P. Albarède and M. Provansal, Quasi-periodic cylinder wakes and the Ginzburg-Landau model, J. Fluid Mech. 291, 191–222 (1995).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  47. Y. Pomeau, Remarks on the bifurcations with symmetry, Chaos, Solitons and Fractals 5 (9) 1755–1761 (1995).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  48. E. Villermaux, On the Strouhal-Reynolds dependence in the Bénard.-Kármán problem, IUTAM Symposium on Bluff Body Wakes and Vortex-Induced Vibrations 2, Marseille (2000).

    Google Scholar 

  49. M. Provansal and D. Ormières, Bifurcation from steady to periodic flow in the wake of a sphere, C. R. Acad. Sci. Paris (1998).

    Google Scholar 

  50. B. Ghidersa and J. Dusek, Breaking of axisymmetry and onset of unsteadiness in the wake of a sphere, J. Fluid Mech. 423, 33–69 (2000).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  51. M.C. Thompson, T. Leweke, and M. Provansal, Kinematics and dynamics of sphere wake transition, J. Fluids. Struct. 15, 575–585 (2001).

    Article  ADS  Google Scholar 

  52. M.C. Thompson, T. Leweke, and C.H.K. Williamson, The physical mechanism of transition in bluff body wakes, J. Fluids. Struct. 15, 607–616 (2001).

    Article  ADS  Google Scholar 

  53. A.G. Tomboulides and S.A. Orszag, Numerical investigation of transitional and weak turbulent flow past a sphere, J. Fluid Mech. 416, 45–73 (2000).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  54. S.E. Ramberg, The effects of yaw and finite length upon the vortex wakes of stationary and vibrating cylinders, J. Fluid Mech. 128, 81 (1983).

    Article  ADS  Google Scholar 

  55. D. Gerich and H. Eckelmann, Influence of end plates and free ends on the shedding frequency of circular cylinder, J. Fluid Mech. 122, 109 (1982).

    Article  ADS  Google Scholar 

  56. C.H.K. Williamson, Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers, J. Fluid Mech. 206, 579–627 (1989).

    Article  ADS  Google Scholar 

  57. J.H. Gerrard, The wakes of cylindrical bluff bodies at low Reynolds number, Phil. Trans. R. Soc. London Ser A, 288, 351 (1978).

    Article  ADS  Google Scholar 

  58. D.J. Tritton, Experiments on the flow past a circular cylinder at low Reynolds numbers, J. Fluid Mech. 6, 547 (1959).

    Article  MATH  ADS  Google Scholar 

  59. D.J Tritton, A note on vortex streets behind circular cylinders at low Reynolds numbers, J. Fluid Mech. 45, 203 (1971).

    Article  ADS  Google Scholar 

  60. M. Gaster, Vortex shedding from circular cylinders at low Reynolds numbers, J. Fluid Mech. 46, 565 (1971).

    Article  Google Scholar 

  61. C.H.K. Williamson, Defining a universal and continuous Strouhal-Reynolds number relationship for the laminar vortex shedding of a circular cylinder, Phys. Fluids 31, 2742 (1988).

    Article  ADS  Google Scholar 

  62. H. Eisenlhor and H. Eckelmann, Vortex splitting and its consequences in the vortex street wake of cylinders at low Reynolds numbers, Phys. Fluids A 1, 189 (1989).

    Article  ADS  Google Scholar 

  63. H. Eckelmann, J.M.R. Graham, P. Huerre, and P.A. Monkewitz (eds), Proc. I.U.T.A.M. Conference Bluff Body Wake Instabilities, Berlin, Springer-Verlag (1992).

    Google Scholar 

  64. M. König, H. Eisenlohr, and H. Eckelmann, The fine structure in the Strouhal-Reynolds number relationship of the laminar wake of a circular cylinder, Phys. Fluids A2, 1607–1614 (1990).

    ADS  Google Scholar 

  65. M. Hammache and M. Gharib, An experimental study of the parallel and oblique vortex shedding from circular cylinders, J. Fluid Mech. 232, 567 (1991).

    Article  ADS  Google Scholar 

  66. T. Leweke and M. Provansal, Determination of the parameters of the Ginzburg-Landau wake model from experiments on a bluff ring, Europhys. Lett. 27, 655–670 (1994).

    Article  ADS  Google Scholar 

  67. C. Norberg, An experimental investigation of the flow around a circular cylinder: influence of aspect ratio, J. Fluid Mech. 258, 287 (1994).

    Article  ADS  Google Scholar 

  68. K. Roussopoulos, Feedback control of vortex shedding at low Reynolds numbers, J.Fluid Mech. 248, 267–296 (1993).

    Article  ADS  Google Scholar 

  69. A. Papangelou, Vortex shedding from slender cones at low Reynolds numbers, J. Fluid Mech. 242, 299–321 (1992).

    Article  ADS  Google Scholar 

  70. D. S. Park and L. G. Redekopp, A model for pattern selection in wake flows, Phys. Fluids A 4, 1697–1706 (1992).

    Article  ADS  Google Scholar 

  71. P.A. Monkewitz, Communication of BBVIV2, Marseille (2000).

    Google Scholar 

  72. M.L. Fachinetti, E.de Langre, and F. Biolley, Vortex shedding modeling using diffusive van der Pol oscillators, Compt.Rend. Acad. Sci. Mécanique Paris (2002).

    Google Scholar 

  73. A. Chiffaudel, Non-linear stability analysis of two-dimensional patterns in the wake of a circular cylinder, Euro-phys. Lett. 18, 589–594 (1992).

    Article  ADS  Google Scholar 

  74. P. A. Monkewitz, C.H.K. Williamson, and G.D. Miller, Phase dynamics of Kármán vortices in cylinder wakes, Phys. Fluids 8, 91–96 (1996).

    Article  MathSciNet  ADS  Google Scholar 

  75. T. Leweke, M. Provansal, G.D. Miller, and C.H.K. Williamson, Cell formation in cylinder wakes at low Reynolds number, Phys. Rev. Lett. 78, 1259–1262 (1997).

    Article  ADS  Google Scholar 

  76. R.D. Henderson, Non linear dynamics and patterns formation in turbulent wake transition, J. Fluid Mech. 352, 65–112 (1997).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  77. S. Bloor, The transition to turbulence in the wake of a circular cylinder, J. Fluid Mech 19, 290 (1964).

    Article  MATH  ADS  Google Scholar 

  78. G. Miller and C.H.K. Williamson, Control of three-dimensional phase dynamics in a cylinder wake, Exp. Fluids. 18, 26 (1994).

    Article  Google Scholar 

  79. D. Barkley and R.D. Henderson, Three-dimensional Floquet analysis of the wake of a circular cylinder, J. Fluid Mech. 322, 215–241 (1996).

    Article  MATH  ADS  Google Scholar 

  80. R.D. Henderson and D. Barkley, Secondary instability in the wake of a circular cylinder, Phys. Fluids 8, 1683–1685 (1996).

    Article  MATH  ADS  Google Scholar 

  81. O. Cadot and S. Kunar, Experimental characterization of viscoelastic effects on two-and three-dimensional shear instabilities, J. Fluid Mech 416, 151–172 (2000).

    Article  MATH  ADS  Google Scholar 

  82. E. Meiburg and J. Lasheras, Experimental and numerical investigation of the three-dimensional transition in plane wakes, J. Fluid Mech. 190, 1 (1988).

    Article  MathSciNet  ADS  Google Scholar 

  83. J. Robichaux, S. Balachandar, and S.P. Vanka, Three-dimensional Floquet instability of the wake of a square cylinder, Phys. Fluids 11, 560–578 (1999).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  84. K. Hourigan, M.C. Thompson, and B.T. Tan, Self-sustained oscillations in flows around long blunt plates, J. Fluids Struct., 15, 387–398 (2001).

    Article  ADS  Google Scholar 

  85. J. Wu, J. Sheridan, M.C. Welsh, K. Hourigan, and M. Thompson, Longitudinal vortex structures in a cylinder wake, Phys. Fluids 6, 2883 (1994).

    Article  ADS  Google Scholar 

  86. M.C. Thompson, K. Hourigan, and J. Sheridan, Three-dimensional instabilities in the wake of a circular cylinder, Exp. Ther. Fluid Sci. 12, 190–196 (1996).

    Article  Google Scholar 

  87. J. Lasheras and E. Meiburg, Three-dimensional vorticity modes in the wake of a flat plate, Phys. Fluids A2, 371 (1990).

    ADS  Google Scholar 

  88. D. Barkley, L.S. Tuckermann and M. Golubitzky, Bifurcation theory for three-dimensional flow in the wake of a circular cylinder, Phys. Rev. E. 61, 5247–5252 (2000).

    MathSciNet  ADS  Google Scholar 

  89. T. Leweke and C.H.K. Williamson, J. Fluid Mech. 416, 151–172 (1998).

    MathSciNet  Google Scholar 

  90. H. Persillon and M. Braza, Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier-Stokes simulation, J. Fluid. Mech. 365, 23–89 (1998).

    Article  MATH  ADS  Google Scholar 

  91. R. Mittal and S. Balachandar, Effect of three-dimensionality on the lift and drag of nominally two-dimensional cylinders, Phys. Fluids 7, 1841 (1995).

    Article  ADS  Google Scholar 

  92. Y. Rocard, L’instabilité en Mécanique: Automobiles, Avions, Ponts Suspendus, Masson, Paris (1954).

    Google Scholar 

  93. M. Van Dyke, An Album of Fluid Motion, Parabolic Press, Inc. (1982).

    Google Scholar 

  94. P.W. Bearman, Vortex shedding from oscillating bluff bodies, Ann. Rev. Fluid. Mech. 16, 95 (1984).

    Article  Google Scholar 

  95. P.W. Bearman, K. Hourigan, T. Leweke, and C.H.K. Williamson (eds), Bluff Body Wakes and Vortex Induced Vibrations Conferences, B.B.V.I.V. 1, 2, 3: Proceedings of the Conferences of Washington 1998, Marseille 2000 (cf. J. Fluid and Structures 2001, vol. 15 N o3/4) and Port-Douglas 2002 (to appear in Eur. J. Fl. Mech. 2003).

    Google Scholar 

  96. J.C. Owen, A.A. Szewczyk, and P.W. Bearman, Suppression of Kármán Vortex Shedding, Phys. Fluids 12 (9), S9 (2000).

    Google Scholar 

  97. L. Mathelin, F. Bataille and A. Lallemand, Near wake of a circular cylinder submitted to blowing, Int. J. Heat. Mass Transfer, 44, 3701–3708 (2001).

    Article  Google Scholar 

  98. I. Peschard and P. Le Gal, Coupled wakes of cylinders, Phys. Rev. Lett. 77 (15), 3122 (1996).

    Article  ADS  Google Scholar 

  99. P. Le Gal, I. Peschard, M.P. Chauve, and Y. Takeda, Collective behavior of wakes downstream a row of cylinders, Phys. Fluids 8, 2097 (1996).

    Article  ADS  Google Scholar 

  100. Y. Couder, J.M. Chomaz, and M. Rabaud, On the hydrodynamics of soap films, Physica D37, 384–405 (1989).

    Google Scholar 

  101. M. Gharib and P. Derango, A liquid film (soap film) tunnel to study two-dimensional laminar and turbulent shear flows, Physica D37, 406 (1989).

    Google Scholar 

  102. J. Zhang, S. Childress, A. Libchaber, and M. Shelley, Flexible filaments in a flowing soap film as a model for one-dimensional flags in two-dimensional wind, Nature 408, 835–838 (2000).

    Article  ADS  Google Scholar 

  103. J. Apt, M. Helfert, and J. Wilkinson, Orbit: NASA Astronauts photograph the Earth, National Geographic Society (1996).

    Google Scholar 

  104. T. Mizota, M. Zdravkovich, K.U. Graw, and A. Leder, St Christopher and the vortex, Nature 404, 226 (2000).

    Article  Google Scholar 

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  1. Institut de Recherche sur les Phénomènes Hors Equilibre, U.M.R. 6594 C.N.R.S. Technopôle de Château-Gombert, 49 rue F. Joliot-Curie, B.P. 146 13384, Marseille cedex 13, France

    Michel Provansal

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  1. Laboratoire de Mécanique, Physique et Géosciences, Université du Havre, F-76058, Le Havre Cedex, France

    Innocent Mutabazi

  2. Physique et Mécanique des Milieux Hétérogènes, Ecole Supérieure de Physique et Chimie Industrielles de Paris, F-75231, Paris Cedex 05, France

    José Eduardo Wesfreid  & Etienne Guyon  & 

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Provansal, M. (2006). Wake Instabilities Behind Bluff Bodies. In: Mutabazi, I., Wesfreid, J.E., Guyon, E. (eds) Dynamics of Spatio-Temporal Cellular Structures. Springer Tracts in Modern Physics, vol 207. Springer, New York, NY. https://doi.org/10.1007/978-0-387-25111-0_10

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