1932

Abstract

Since the seminal studies by Osborne Reynolds in the nineteenth century, pipe flow has served as a primary prototype for investigating the transition to turbulence in wall-bounded flows. Despite the apparent simplicity of this flow, various facets of this problem have occupied researchers for more than a century. Here we review insights from three distinct perspectives: () stability and susceptibility of laminar flow, () phase transition and spatiotemporal dynamics, and () dynamical systems analysis of the Navier—Stokes equations. We show how these perspectives have led to a profound understanding of the onset of turbulence in pipe flow. Outstanding open points, applications to flows of complex fluids, and similarities with other wall-bounded flows are discussed.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-120720-025957
2023-01-19
2024-04-16
Loading full text...

Full text loading...

/deliver/fulltext/fluid/55/1/annurev-fluid-120720-025957.html?itemId=/content/journals/10.1146/annurev-fluid-120720-025957&mimeType=html&fmt=ahah

Literature Cited

  1. Agrawal N, Choueiri GH, Hof B. 2019. Transition to turbulence in particle laden flows. Phys. Rev. Lett. 122:11114502
    [Google Scholar]
  2. Avila K, Moxey D, de Lozar A, Avila M, Barkley D, Hof B. 2011. The onset of turbulence in pipe flow. Science 333:6039192–96
    [Google Scholar]
  3. Avila M, Hof B. 2013. Nature of laminar-turbulence intermittency in shear flows. Phys. Rev. E 87:063012
    [Google Scholar]
  4. Avila M, Mellibovsky F, Roland N, Hof B 2013. Streamwise-localized solutions at the onset of turbulence in pipe flow. Phys. Rev. Lett. 110:22224502
    [Google Scholar]
  5. Avila M, Willis AP, Hof B. 2010. On the transient nature of localized pipe flow turbulence. J. Fluid Mech. 646:127–36
    [Google Scholar]
  6. Barkley D. 2011. Simplifying the complexity of pipe flow. Phys. Rev. E 84:1016309
    [Google Scholar]
  7. Barkley D. 2016. Theoretical perspective on the route to turbulence in a pipe. J. Fluid Mech. 803:P1
    [Google Scholar]
  8. Barkley D, Song B, Mukund V, Lemoult G, Avila M, Hof B. 2015. The rise of fully turbulent flow. Nature 526:7574550–53
    [Google Scholar]
  9. Boberg L, Brosa U. 1988. Onset of turbulence in a pipe. Z. Naturforsch. A 43:8–9697–726
    [Google Scholar]
  10. Bottin S, Chaté H. 1998. Statistical analysis of the transition to turbulence in plane Couette flow. Eur. Phys. J. B 6:1143–55
    [Google Scholar]
  11. Bottin S, Daviaud F, Manneville P, Dauchot O. 1998. Discontinuous transition to spatiotemporal intermittency in plane Couette flow. Europhys. Lett. 43:2171–76
    [Google Scholar]
  12. Brandt L. 2014. The lift-up effect: the linear mechanism behind transition and turbulence in shear flows. Eur. J. Mech. B 47:80–96
    [Google Scholar]
  13. Brosa U. 1989. Turbulence without strange attractor. J. Stat. Phys. 55:51303–12
    [Google Scholar]
  14. Budanur NB, Dogra AS, Hof B. 2019. Geometry of transient chaos in streamwise-localized pipe flow turbulence. Phys. Rev. Fluids 4:10102401
    [Google Scholar]
  15. Chantry M, Tuckerman LS, Barkley D. 2017. Universal continuous transition to turbulence in a planar shear flow. J. Fluid Mech. 824:R1
    [Google Scholar]
  16. Chapman SJ. 2002. Subcritical transition in channel flows. J. Fluid Mech. 451:35–97
    [Google Scholar]
  17. Chen K, Xu D, Song B. 2022. Propagation speed of turbulent fronts in pipe flow at high Reynolds numbers. J. Fluid Mech. 935:A11
    [Google Scholar]
  18. Coles D. 1962. Interfaces and intermittency in turbulent shear flow. Méc. Turbul. 108:108229–50
    [Google Scholar]
  19. Darbyshire A, Mullin T. 1995. Transition to turbulence in constant-mass-flux pipe flow. J. Fluid Mech. 289:83–114
    [Google Scholar]
  20. De Lozar A, Mellibovsky F, Avila M, Hof B. 2012. Edge state in pipe flow experiments. Phys. Rev. Lett. 108:21214502
    [Google Scholar]
  21. Draad A, Nieuwstadt F. 1998. The earth's rotation and laminar pipe flow. J. Fluid Mech. 361:297–308
    [Google Scholar]
  22. Drazin PG, Reid WH. 2004. Hydrodynamic Stability Cambridge, UK: Cambridge Univ. Press
  23. Duguet Y, Monokrousos A, Brandt L, Henningson DS. 2013. Minimal transition thresholds in plane Couette flow. Phys. Fluids 25:8084103
    [Google Scholar]
  24. Duguet Y, Pringle CC, Kerswell RR. 2008a. Relative periodic orbits in transitional pipe flow. Phys. Fluids 20:11114102
    [Google Scholar]
  25. Duguet Y, Willis AP, Kerswell RR. 2008b. Transition in pipe flow: the saddle structure on the boundary of turbulence.. J. Fluid Mech. 613:255–74
    [Google Scholar]
  26. Duguet Y, Willis AP, Kerswell RR. 2010. Slug genesis in cylindrical pipe flow. J. Fluid Mech. 663:180–208
    [Google Scholar]
  27. Durst F, Ünsal B. 2006. Forced laminar-to-turbulent transition of pipe flows. J. Fluid Mech. 560:449–64
    [Google Scholar]
  28. Eckert M. 2010. The troublesome birth of hydrodynamic stability theory: Sommerfeld and the turbulence problem. Eur. Phys. J. H 35:129–51
    [Google Scholar]
  29. Eckert M. 2015. Fluid mechanics in Sommerfeld's school. Annu. Rev. Fluid Mech. 47:1–20
    [Google Scholar]
  30. Eckhardt B, Schneider TM, Hof B, Westerweel J. 2007. Turbulence transition in pipe flow.. Annu. Rev. Fluid Mech. 39:447–68
    [Google Scholar]
  31. Faisst H, Eckhardt B. 2003. Traveling waves in pipe flow. Phys. Rev. Lett. 91:22224502
    [Google Scholar]
  32. Faisst H, Eckhardt B. 2004. Sensitive dependence on initial conditions in transition to turbulence in pipe flow. J. Fluid Mech. 504:343–52
    [Google Scholar]
  33. Feynman RP, Leighton RB, Sands ML. 1963. The Feynman Lectures on Physics Reading, MA: Addison-Wesley
  34. Gibson JF, Halcrow J, Cvitanović P. 2008. Visualizing the geometry of state space in plane Couette flow. J. Fluid Mech. 611:107–30
    [Google Scholar]
  35. Goldenfeld N, Guttenberg N, Gioia G. 2010. Extreme fluctuations and the finite lifetime of the turbulent state. Phys. Rev. E 81:3035304(R)
    [Google Scholar]
  36. Gomé S, Tuckerman LS, Barkley D. 2022. Extreme events in transitional turbulence. Philos. Trans. R. Soc. A 380:20210036
    [Google Scholar]
  37. Graham MD, Floryan D. 2021. Exact coherent states and the nonlinear dynamics of wall-bounded turbulent flows. Annu. Rev. Fluid Mech. 53:227–53
    [Google Scholar]
  38. Grebogi C, Ott E, Yorke JA. 1982. Chaotic attractors in crisis. Phys. Rev. Lett. 48:221507–10
    [Google Scholar]
  39. Guckenheimer J, Holmes P. 2002. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Applied Mathematical Sciences, No. 42) New York: Springer. , 7th ed..
  40. Hinrichsen H. 2000. Non-equilibrium critical phenomena and phase transitions into absorbing states. Adv. Phys. 49:7815–958
    [Google Scholar]
  41. Hof B, De Lozar A, Avila M, Tu X, Schneider TM. 2010. Eliminating turbulence in spatially intermittent flows. Science 327:59721491–94
    [Google Scholar]
  42. Hof B, De Lozar A, Kuik DJ, Westerweel J. 2008. Repeller or attractor? Selecting the dynamical model for the onset of turbulence in pipe flow. Phys. Rev. Lett. 101:21214501
    [Google Scholar]
  43. Hof B, Juel A, Mullin T. 2003. Scaling of the turbulence transition threshold in a pipe. Phys. Rev. Lett. 91:24244502
    [Google Scholar]
  44. Hof B, van Doorne CW, Westerweel J, Nieuwstadt FT. 2005. Turbulence regeneration in pipe flow at moderate Reynolds numbers. Phys. Rev. Lett. 95:21214502
    [Google Scholar]
  45. Hof B, Van Doorne CW, Westerweel J, Nieuwstadt FT, Faisst H et al. 2004. Experimental observation of nonlinear traveling waves in turbulent pipe flow. Science 305:56901594–98
    [Google Scholar]
  46. Hof B, Westerweel J, Schneider TM, Eckhardt B. 2006. Finite lifetime of turbulence in shear flows. Nature 443:710759–62
    [Google Scholar]
  47. Hogendoorn W, Poelma C. 2018. Particle-laden pipe flows at high volume fractions show transition without puffs. Phys. Rev. Lett. 121:19194501
    [Google Scholar]
  48. Hopf E. 1948. A mathematical example displaying features of turbulence. Commun. Pure Appl. Math. 1:4303–22
    [Google Scholar]
  49. Ishida T, Duguet Y, Tsukahara T. 2016. Transitional structures in annular Poiseuille flow depending on radius ratio. J. Fluid Mech. 794:R2
    [Google Scholar]
  50. Ishida T, Duguet Y, Tsukahara T. 2017. Turbulent bifurcations in intermittent shear flows: from puffs to oblique stripes. Phys. Rev. Fluids 2:7073902
    [Google Scholar]
  51. Itano T, Toh S. 2001. The dynamics of bursting process in wall turbulence. J. Phys. Soc. Jpn. 70:3703–16
    [Google Scholar]
  52. Joseph D, Carmi S. 1969. Stability of Poiseuille flow in pipes, annuli, and channels. Q. Appl. Math. 26:4575–99
    [Google Scholar]
  53. Kaneko K. 1985. Spatiotemporal intermittency in coupled map lattices. Prog. Theor. Phys. 74:51033–44
    [Google Scholar]
  54. Kawahara G, Uhlmann M, Van Veen L. 2012. The significance of simple invariant solutions in turbulent flows. Annu. Rev. Fluid Mech. 44:203–25
    [Google Scholar]
  55. Kerswell R. 2018. Nonlinear nonmodal stability theory. Annu. Rev. Fluid Mech. 50:319–45
    [Google Scholar]
  56. Klotz L, Lemoult G, Avila K, Hof B. 2022. Phase transition to turbulence in spatially extended shear flows. Phys. Rev. Lett. 128:1014502
    [Google Scholar]
  57. Kreilos T, Eckhardt B. 2012. Periodic orbits near onset of chaos in plane Couette flow. Chaos 22:4047505
    [Google Scholar]
  58. Kühnen J, Braunshier P, Schwegel M, Kuhlmann H, Hof B. 2015. Subcritical versus supercritical transition to turbulence in curved pipes. J. Fluid Mech. 770:R3
    [Google Scholar]
  59. Kühnen J, Song B, Scarselli D, Budanur NB, Riedl M et al. 2018. Destabilizing turbulence in pipe flow. Nat. Phys. 14:4386–90
    [Google Scholar]
  60. Kuik DJ, Poelma C, Westerweel J. 2010. Quantitative measurement of the lifetime of localized turbulence in pipe flow. J. Fluid Mech. 645:529–39
    [Google Scholar]
  61. Lemoult G, Aider JL, Wesfreid JE. 2012. Experimental scaling law for the subcritical transition to turbulence in plane Poiseuille flow. Phys. Rev. E 85:2025303
    [Google Scholar]
  62. Lemoult G, Shi L, Avila K, Jalikop SV, Avila M, Hof B. 2016. Directed percolation phase transition to sustained turbulence in Couette flow. Nat. Phys. 12:3254–58
    [Google Scholar]
  63. Lindgren ER. 1957. The transition process and other phenomena in viscous flow. Ark. Fys. 12:1–169
    [Google Scholar]
  64. Lindgren ER. 1969. Propagation velocity of turbulent slugs and streaks in transition pipe flow. Phys. Fluids 12:2418–25
    [Google Scholar]
  65. Lübeck S. 2004. Universal scaling behavior of non-equilibrium phase transitions. Int. J. Mod. Phys. B 18:31–323977–4118
    [Google Scholar]
  66. Luchini P, Bottaro A. 2014. Adjoint equations in stability analysis. Annu. Rev. Fluid Mech. 46:493–517
    [Google Scholar]
  67. Lustro JRT, Kawahara G, van Veen L, Shimizu M, Kokubu H. 2019. The onset of transient turbulence in minimal plane Couette flow. J. Fluid Mech. 862:R2
    [Google Scholar]
  68. Manneville P. 2015. On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular. Eur. J. Mech. B 49:345–62
    [Google Scholar]
  69. Marensi E, Ding Z, Willis AP, Kerswell RR. 2020. Designing a minimal baffle to destabilise turbulence in pipe flows. J. Fluid Mech. 900:A31
    [Google Scholar]
  70. Matas JP, Morris JF, Guazzelli E. 2003. Transition to turbulence in particulate pipe flow. Phys. Rev. Lett. 90:1014501
    [Google Scholar]
  71. Mellibovsky F, Eckhardt B. 2012. From travelling waves to mild chaos: a supercritical bifurcation cascade in pipe flow. J. Fluid Mech. 709:149–90
    [Google Scholar]
  72. Mellibovsky F, Meseguer A. 2007. Pipe flow transition threshold following localized impulsive perturbations. Phys. Fluids 19:044102
    [Google Scholar]
  73. Mellibovsky F, Meseguer A, Schneider TM, Eckhardt B. 2009. Transition in localized pipe flow turbulence.. Phys. Rev. Lett. 103:5054502
    [Google Scholar]
  74. Meseguer A. 2003. Streak breakdown instability in pipe Poiseuille flow. Phys. Fluids 15:51203–13
    [Google Scholar]
  75. Meseguer A, Trefethen L. 2003. Linearized pipe flow to Reynolds number 107. J. Comput. Phys. 186:1178–97
    [Google Scholar]
  76. Moehlis J, Faisst H, Eckhardt B. 2004. A low-dimensional model for turbulent shear flows. New J. Phys. 6:156
    [Google Scholar]
  77. Monokrousos A, Bottaro A, Brandt L, Di Vita A, Henningson DS. 2011. Nonequilibrium thermodynamics and the optimal path to turbulence in shear flows. Phys. Rev. Lett. 106:13134502
    [Google Scholar]
  78. Moxey D, Barkley D. 2010. Distinct large-scale turbulent-laminar states in transitional pipe flow. PNAS 107:188091–96
    [Google Scholar]
  79. Mukund V, Hof B. 2018. The critical point of the transition to turbulence in pipe flow. J. Fluid Mech. 839:76–94
    [Google Scholar]
  80. Nemoto T, Alexakis A. 2021. Do extreme events trigger turbulence decay? A numerical study of turbulence decay time in pipe flows. J. Fluid Mech. 912:A38
    [Google Scholar]
  81. Nishi M, Ünsal B, Durst F, Biswas G. 2008. Laminar-to-turbulent transition of pipe flows through puffs and slugs. J. Fluid Mech. 614:425–46
    [Google Scholar]
  82. Noorani A, El Khoury G, Schlatter P 2013. Evolution of turbulence characteristics from straight to curved pipes. Int. J. Heat Fluid Flow 41:16–26
    [Google Scholar]
  83. Page J, Brenner MP, Kerswell RR. 2021. Revealing the state space of turbulence using machine learning. Phys. Rev. Fluids 6:3034402
    [Google Scholar]
  84. Peixinho J, Mullin T. 2006. Decay of turbulence in pipe flow. Phys. Rev. Lett. 96:9094501
    [Google Scholar]
  85. Peixinho J, Mullin T. 2007. Finite-amplitude thresholds for transition in pipe flow. J. Fluid Mech. 582:169–78
    [Google Scholar]
  86. Pfenniger W 1961. Transition in the inlet length of tubes at high Reynolds numbers. Boundary Layer and Flow Control, Its Principles and Applications G Lachman 970–80 Oxford, UK: Pergamon
    [Google Scholar]
  87. Philip J, Cohen J. 2010. Formation and decay of coherent structures in pipe flow. J. Fluid Mech. 655:258–79
    [Google Scholar]
  88. Pomeau Y. 1986. Front motion, metastability and subcritical bifurcations in hydrodynamics. Physica D 23:3–11
    [Google Scholar]
  89. Pringle CC, Kerswell RR. 2010. Using nonlinear transient growth to construct the minimal seed for shear flow turbulence. Phys. Rev. Lett. 105:15154502
    [Google Scholar]
  90. Pringle CC, Willis AP, Kerswell RR. 2015. Fully localised nonlinear energy growth optimals in pipe flow. Phys. Fluids 27:6064102
    [Google Scholar]
  91. Pringle CCT, Duguet Y, Kerswell RR. 2009. Highly symmetric travelling waves in pipe flow. Philos. Trans. R. Soc. A 367:1888457–72
    [Google Scholar]
  92. Pringle CCT, Kerswell RR. 2007. Asymmetric, helical, and mirror-symmetric traveling waves in pipe flow. Phys. Rev. Lett. 99:774502
    [Google Scholar]
  93. Reddy SC, Schmid PJ, Baggett JS, Hennignson DS. 1998. On stability of streamwise streaks and transition thresholds in plane channel flows. J. Fluid Mech. 365:269–303
    [Google Scholar]
  94. Reynolds O. 1883. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Philos. Trans. R. Soc. 174:935–82
    [Google Scholar]
  95. Rinaldi E, Canton J, Schlatter P. 2019. The vanishing of strong turbulent fronts in bent pipes. J. Fluid Mech. 866:487–502
    [Google Scholar]
  96. Riols A, Rincon F, Cossu C, Lesur G, Longaretti PY et al. 2013. Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow. J. Fluid Mech. 731:1–45
    [Google Scholar]
  97. Ritter P, Mellibovsky F, Avila M. 2016. Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow. New J. Phys. 18:8083031
    [Google Scholar]
  98. Rolland J. 2018. Extremely rare collapse and build-up of turbulence in stochastic models of transitional wall flows. Phys. Rev. E 97:2023109
    [Google Scholar]
  99. Rolland J. 2022. Collapse of transitional wall turbulence captured using a rare events algorithm. J. Fluid Mech. 931:A22
    [Google Scholar]
  100. Rotta JC. 1956. Experimenteller Beitrag zur Entstehung turbulenter Strömung im Rohr. Arch. Appl. Mech. 24:4258–81
    [Google Scholar]
  101. Salwen H, Cotton FW, Grosch CE. 1980. Linear stability of Poiseuille flow in a circular pipe. J. Fluid Mech. 98:2273–84
    [Google Scholar]
  102. Samanta D, De Lozar A, Hof B. 2011. Experimental investigation of laminar turbulent intermittency in pipe flow. J. Fluid Mech. 681:193–204
    [Google Scholar]
  103. Samanta D, Dubief Y, Holzner M, Schäfer C, Morozov AN et al. 2013. Elasto-inertial turbulence. PNAS 110:2610557–62
    [Google Scholar]
  104. Schmid PJ. 2007. Nonmodal stability theory. Annu. Rev. Fluid Mech. 39:129–62
    [Google Scholar]
  105. Schmid PJ, Henningson DS. 1994. Optimal energy density growth in Hagen–Poiseuille flow. J. Fluid Mech. 277:197–225
    [Google Scholar]
  106. Schmid PJ, Henningson DS. 2001. Stability and Transition in Shear Flows New York: Springer
  107. Schneider TM, Eckhardt B, Yorke JA. 2007. Turbulence transition and the edge of chaos in pipe flow. Phys. Rev. Lett. 99:3034502
    [Google Scholar]
  108. Shih HY, Hsieh TL, Goldenfeld N. 2016. Ecological collapse and the emergence of travelling waves at the onset of shear turbulence. Nat. Phys. 12:245–48
    [Google Scholar]
  109. Shimizu M, Manneville P, Duguet Y, Kawahara G. 2014. Splitting of a turbulent puff in pipe flow. Fluid Dyn. Res. 46:6061403
    [Google Scholar]
  110. Skufca JD, Yorke JA, Eckhardt B. 2006. Edge of chaos in a parallel shear flow. Phys. Rev. Lett. 96:17174101
    [Google Scholar]
  111. Song B, Barkley D, Hof B, Avila M. 2017. Speed and structure of turbulent fronts in pipe flow. J. Fluid Mech. 813:1045–59
    [Google Scholar]
  112. Sreenivasan K, Strykowski P. 1983. Stabilization effects in flow through helically coiled pipes. Exp. Fluids 1:131–36
    [Google Scholar]
  113. Takeishi K, Kawahara G, Wakabayashi H, Uhlmann M, Pinelli A. 2015. Localized turbulence structures in transitional rectangular-duct flow. J. Fluid Mech. 782:368–79
    [Google Scholar]
  114. Tél T, Lai YC. 2008. Chaotic transients in spatially extended systems. Phys. Rep. 460:245–75
    [Google Scholar]
  115. Trefethen LN, Trefethen AE, Reddy SC, Driscoll TA. 1993. Hydrodynamic stability without eigenvalues. Science 261:5121578–84
    [Google Scholar]
  116. Tuckerman LS, Chantry M, Barkley D. 2020. Patterns in wall-bounded shear flows. Annu. Rev. Fluid Mech. 52:343–67
    [Google Scholar]
  117. van Doorne C. 2004. Stereoscopic PIV on transition in pipe flow PhD Thesis, TU Delft
  118. van Doorne CW, Westerweel J. 2009. The flow structure of a puff. Philos. Trans. R. Soc. A 367:1888489–507
    [Google Scholar]
  119. Waleffe F 1995. Transition in shear flows. Nonlinear normality versus non-normal linearity. Phys. Fluids 7:123060–66
    [Google Scholar]
  120. Wedin H, Kerswell RR. 2004. Exact coherent structures in pipe flow: travelling wave solutions. J. Fluid Mech. 508:333–71
    [Google Scholar]
  121. Willis AP, Cvitanović P, Avila M. 2013. Revealing the state space of turbulent pipe flow by symmetry reduction. J. Fluid Mech. 721:514–40
    [Google Scholar]
  122. Willis AP, Kerswell RR. 2007. Critical behavior in the relaminarization of localized turbulence in pipe flow. Phys. Rev. Lett. 98:1014501
    [Google Scholar]
  123. Wu X, Moin P, Adrian RJ, Baltzer JR 2015. Osborne Reynolds pipe flow: direct simulation from laminar through gradual transition to fully developed turbulence. PNAS 112:267920–24
    [Google Scholar]
  124. Wygnanski I, Champagne F. 1973. On transition in a pipe. 1. The origin of puffs and slugs and the flow in a turbulent slug. J. Fluid Mech. 59:281–335
    [Google Scholar]
  125. Wygnanski IJ, Sokolov M, Friedman D. 1975. On transition in a pipe. 2. The equilibrium puff. J. Fluid Mech. 69:283–304
    [Google Scholar]
  126. Xu D, Varshney A, Ma X, Song B, Riedl M et al. 2020. Nonlinear hydrodynamic instability and turbulence in pulsatile flow. PNAS 117:2111233–39
    [Google Scholar]
  127. Zammert S, Eckhardt B. 2015. Crisis bifurcations in plane Poiseuille flow. Phys. Rev. E 91:4041003
    [Google Scholar]
/content/journals/10.1146/annurev-fluid-120720-025957
Loading
/content/journals/10.1146/annurev-fluid-120720-025957
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error