Introduction. Turbulence transition in pipe flow: 125th anniversary of the publication of reynolds' paper

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 367, Issue 1888, 2009, Pages 449-455

  Eckhardt, Bruno ^a  

^a PHILIPPS UNIVERSITY MARBURG   (Germany)

Author keywords

Pipe flow; Travelling wave; Turbulence

Indexed keywords

DYNAMICAL SYSTEMS; PIPE; PIPE FLOW; WAVE TRANSMISSION;

QUANTITATIVE CHARACTERISTICS; REYNOLDS; TRANSITION TO TURBULENCES; TRAVELLING WAVE; TURBULENCE TRANSITIONS;

TURBULENCE;

EID: 58149139542     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2008.0217     Document Type: Article

References (48)

1. Biau, D. & Bottaro, A. 2009 An optimal path to transition in a duct. Phil. Trans. R. Soc. A 367, 529-544. (doi:10.1098/rsta.2008.0191)
2. Boberg, L. & Brosa, U. 1988 Onset of turbulence in a pipe. Z. Naturforsch. 43a, 697-726.
3. Brosa, U. 1989 Turbulence without strange attractor. J. Stat. Phys. 55, 1303-1321. (doi:10.1007/BF01041090)
4. Cohen, J., Philip, J. & Ben-Dov, G. 2009 Aspects of linear and nonlinear instabilities leading to transition in pipe and channel flows. Phil. Trans. R. Soc. A 367, 509-527. (doi:10.1098/rsta. 2008.0189)
5. Cvitanovic. P. & Eckhardt, B. 1991 Periodic orbit expansion for classical smooth flows. J. Phys. A 24, L237-L241. (doi:10.1088/0305-4470/24/5/005)
6. deLozar, A. & Hof, B. 2009 An experimental study of the decay of turbulent puffs in pipe flow. Phil. Trans. R. Soc. A 367, 589-599. (doi:10.1098/rsta.2008.0199)
7. Duggleby, A., Ball. K. S. & Paul, M. R. 2007 The effect of span wise wall oscillation on turbulent pipe flow structures resulting in drag reduction. Phys. Fluids 19, 125 107. (doi:10.1063/1.2825428)
8. Duggleby, A. K., Kenneth, B. & Schwacncn, M. 2009 Structure and dynamics of low Reynolds number turbulent pipe flow. Phil. Trans. R. Soc. A 367, 473-488. (doi:10.1098/rsta.2008.0241)
9. Duguet, Y., Willis, A. P. & Kerswell. R. R. 2008 Transition in pipe flow: the saddle structure on the boundary of turbulence. J. Fluid Mech. 613, 255-274. (doi:10.1017/S0022112008003248)
10. Eckhardt, B. 2008 Turbulence transition in pipe flow: some open questions. Nonlinearity 21, Tl-Tll. (doi:10.1088/0951-7715/21/l/ T01)
11. Eckhardt, B., Schneider, T. M., Hof, B. & Westerweel, J. 2007 Turbulence transition in pipe flow. Annu. Rev. Fluid Mech. 39, 447-468. (doi:10.1146/annurcv.fluid.39.050905.110308)
12. Eckhardt, B., Faisst, H., Schmiegel, A. & Schneider, T. M. 2008 Dynamical systems and the transition to turbulence in linearly stable shear flows. Phil. Trans. R. Soc. A 366, 1297-1315. (doi:10.1098/rsta. 2007.2132)
13. Faisst, H. & Eckhardt, B. 2003 Traveling waves in pipe flow. Phys. Rev. Lett. 91, 224-502. (doi:10. 1103/PhysRevLett.91.224502)
14. Faisst, H. & Eckhardt, B. 2004 Sensitive dependence on initial conditions in transition to turbulence in pipe flow. J. Fluid Mech. 504, 343-352. (doi:10.1017/S0022112004008134)
15. Gebhardt, T. & Grossmann, S. 1994 Chaos transition despite linear stability. Phys. Rev. E 50, 3705-3711. (doi:10.1103/PhysRevE.50. 3705)
16. Hof, B., Juel, A. & Mullin, T. 2003 Scaling of the turbulence transition threshold in a pipe. Phys. Rev. Lett. 94, 244-502. (doi:10.1103/PhysRevLett.91.244502)
17. Hof, B., van Doorne, C. W. H., Westerveel, J., Nieuwstadt, F. T. M., Faisst, H., Eckhardt, B., Wedin, H., Kerswell, R. R. & Waleffe, F. 2004 Experimental observation of nonlinear travelling waves in turbulent pipe flow. Science 305, 1594-1598. (doi:10.1126/scicncc. 1100393)
18. Hof, B., Wcstcrwecl, J., Schneider, T. M. & Eckhardt, B. 2006 Finite lifetime of turbulence in shear flows. Nature. 443, 5962. (doi:10.1038/nature05089)
19. Jackson, D. & Launder, B. 2007 Osborne Reynolds and the publication of his papers on turbulent flow. Annu. Rev. Fluid Mech. 39, 19-35. (doi:10.1146/anmirev.fluid.39.050905.110241)
20. Kerswell, R. R. & Tutty, O. R. 2007 Recurrence of travelling waves in transitional pipe flow. J. Fluid Mech. 584, 69-102. (doi:10.1017/S0022112007006301)
21. Mellibovsky, F. & Meseguer, A. 2009 Critical threshold in pipe flow transition. Phil. Trans. R. Soc. A 367. 545-560. (doi:10.1098/rsta.2008.0165)
22. Meseguer, A. & Trefethen, L. N. 2003 Linearized pipe flow to Reynolds number 10,000,000. J. Comp. Phys. 186, 178-197. (doi:10.1016/S0021-9991(03)00029-9)
23. Peixinho, J. & Mullin, T. 2006 Decay of turbulence in pipe flow. Phys. Rev. Lett. 96, 094-501. (doi:10.1103/PhysRevLett.9G.094501)
24. Peixinho, J. & Mullin, T. 2007 Finite-amplitude thresholds for transition in pipe flow. J. Fluid Mech. 582, 169-178. (doi:10.1017/S0022112007006398)
25. Pfenniger, W. 1961 Transition in the inlet length of tubes at high Reynolds numbers. In Boundary layer and flaw control (ed. G. Lachman). pp. 970-980. New York, NY: Pergamon.
26. Prandtl, L. & Tictjens, O. 1931 Hydro - und Aeromechanik. Berlin, Germany: Julius Springer.
27. Pringle, C. & Kerswell, R. R. 2007 Asymmetric, helical and mirror-symmetric travelling waves in pipe flow. Phys. Rev. Lett. 99, 074-502. (doi:10.1103/PhysRevLctt.99.074502)
28. Pringle, C. C, Duguet, Y. & Kerswell, R. R. 2009 Highly-symmetric travelling waves in pipe flow. Phil. Trans. R. Soc. A 367, 457-472. (doi:10.1098/rsta.2008.0236)
29. Reynolds, O. 1883a An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and the law of resistance in parallel channels. Proc. R. Soc. 35, 84-99. (doi:10.1098/rspl. 1883.0018)
30. Reynolds, O. 1883b An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous and the law of resistance in parallel channels. Phil. Trans. R. Soc. 174, 935-982. (doi:10.1098/rstl.1883.0029)
31. Reynolds, O. 1895 On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Phil. Trans. R. Soc. A 186, 123-164. (doi:10.1098/rsta.1895.0004)
32. Rott, N. 1990 A note on the history of the Reynolds number. Annu. Rev. Fluid Mech. 22, 1-11. (doi:10.1146/ammrev.fl.22.010190.000245)
33. Rotta, J. 1956 Experimenteller Beitrag zur Entstehung turbulenter Stromungen im Rohr. Ingenieur. Archiv. 24, 258-281. (doi:10.1007/BF00536526)
34. Salwen. H., Cotton. F. W. & Grosch, C. E. 1980 Linear stability of Poiseuille flow in a circular pipe. J. Fluid Mech. 98, 273-284. (doi:10.1017/S0022112080000146)
35. Schmid, P. J. & Henningson, D. S. 2001 Stability and transition of shear flows. New York, NY: Springer.
36. Schneider, T. M. & Eckhardt, B. 2006 Edge of chaos in pipe flow. Chaos 16, 020-604. (doi:10.1063/1.2390553)
37. Schneider, T. M. & Eckhardt, B. 2009 Edge states intermediate between laminar and turbulent dynamics in pipe flow. Phil. Trans. R. Soc. A 367, 577-587. (doi:10.1098/rsta.2008.0216)
38. Schneider, T. M., Eckhardt, B. & Vollmer, J. 2007a Statistical analysis of coherent structures in transitional pipe flow. Phys. Rev. E 75, 066-313. (doi:10.1103/PhysRevE.75.066313)
39. Schneider, T. M., Eckhardt, B. & Yorkc, J. A. 20076 Turbulence transition and the edge of chaos in pipe flow. Phys. Rev. Lett. 99, 034502. (doi:10.1103/PhysRevLett.99.034502)
40. Skufca, J., Yorke, J. A. & Eckhardt, B. 2006 The edge of chaos in a model for a parallel shear flow. Phys. Rev. Lett. 96, 174 101. (doi:10.1103/PhysRevLett.96.174101)
41. Trefethen. L. N., Trefethen, A. E., Reddy, S. C. & Driscoll. T. A. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578-584. (doi:10.1126/science.261.5121.578)
42. van Doorne, C. W. & Westerweel, J. 2009 The flow structure of a puff. Phil. Trans. R. Soc. A 367, 489-507. (doi:10.1098/rsta.2008.0227)
43. Viswanath, D. 2009 The critical layer in pipe flow at high Reynolds number. Phil. Trans. R. Soc. A 367, 561-576. (doi:10.1098/rsta. 2008.0225)
44. von Kármán, T. 1954 Aerodynamics: selected topics in the light of their historical development. Ithaca, NY: Cornell University Press.
45. Wedin, H. & Kerswell, R. R. 2004 Exact coherent structures in pipe flow: travelling wave solutions. J. Fluid Mech. 508, 333-371. (doi:10.1017/S0022112004009346)
46. Willis, A. P. & Kerswell, R. R. 2007 Critical behavior in the relaminarization of localized turbulence in pipe flow. Phys. Rev. Lett. 98, 014-501. (doi:10.1103/PhysRcvLctt.98.014501)
47. Wygnanski, I. J. & Champagne, F. H. 1973 On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug. J. Fluid Mech. 59, 281-335. (doi:10.1017/S0022112073001576)
48. Wygnanski, I. J., Sokolov, M. & Friedman, D. 1975 On transition in a pipe. Part 2. The equilibrium puff. J. Fluid Mech. 69, 283-304. (doi:10.1017/S0022112075001449)