High-Reynolds number wall turbulence

Annual Review of Fluid Mechanics

Volumn 43, Issue , 2011, Pages 353-375

  Smits, Alexander J ^a   McKeon, Beverley J ^b   Marusic, Ivan ^c  

^a Princeton University   (United States)

^b California Institute of Technology   (United States)

^c UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

boundary layers; channel flow; coherent motions; pipe flow; turbulence structure

Indexed keywords

COHERENT MOTION; COHERENT MOTIONS; ENERGY CONTENT; HIGH-REYNOLDS NUMBER; LOG-LAWS; MEAN FLOW; THEORETICAL FRAMEWORK; TURBULENCE STRUCTURE; WALL TURBULENCE; WALL-BOUNDED TURBULENT FLOWS;

BOUNDARY LAYERS; CHANNEL FLOW; HIGH ENERGY PHYSICS; PIPE; PIPE FLOW; REYNOLDS NUMBER; TURBULENCE; TURBULENT FLOW;

WALL FLOW;

BOUNDARY LAYER; CHANNEL FLOW; PIPE FLOW; PRESSURE GRADIENT; REYNOLDS NUMBER; THEORETICAL STUDY; TURBULENCE; WALL;

EID: 79551534313     PISSN: 00664189     EISSN: None     Source Type: Book Series    
DOI: 10.1146/annurev-fluid-122109-160753     Document Type: Article

References (142)

1. τ = 640. J. Fluids Eng. 126:835-43 (Pubitemid 40026591)
2. Adrian RJ. 2007. Hairpin vortex organization in wall turbulence. Phys. Fluids 19:041301
3. Adrian RJ, Meinhart CD, Tomkins CD. 2000. Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422:1-54 (Pubitemid 36154658)
4. Andreas EL, Claffey KJ, Jordan RE, Fairall CW, Guest PS, et al. 2006. Evaluations of the von Kármán constant in the atmospheric surface layer. J. Fluid Mech. 559:117-49 (Pubitemid 44110521)
5. Bailey SSC, Kunkel GJ, Hultmark M, Vallikivi M, Hill J, et al. 2010. Turbulence measurements using a nanoscale thermal anemometry probe. J. Fluid Mech. In press
6. Bailey SCC, Hultmark M, Smits AJ, Schultz MP. 2008. Azimuthal structure of turbulence in high Reynolds number pipe flow. J. Fluid Mech. 615:121-38
7. Bailey SCC, Smits AJ. 2010. Experimental investigation of the structure of large-and very large-scale motions in turbulent pipe flow. J. Fluid Mech. 651:339-56
8. Balakumar BJ, Adrian RJ. 2007. Large-and very-large-scale motions in channel and boundary-layer flows. Philos. Trans. R. Soc. Lond. A 365:665-81
9. Barenblatt GI. 1993. Scaling laws for fully developed turbulent shear flows. Part 1. Basic hypotheses and analysis. J. Fluid Mech. 248:513-20
10. Barenblatt GI, Chorin AJ, Hald OH, Prostokishin VM. 1997. Structureofthe zero-pressure-gradient turbulent boundary layer. Proc. Natl. Acad. Sci. USA 29:7817-19 (Pubitemid 27343731)
11. Bou-Zeid E, Meneveau C, Parlange M. 2005. A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys. Fluids 17:025105
12. Bou-Zeid E, Vercauteren N, Parlange M, Meneveau C. 2008. Scale dependence of subgrid-scale model coefficients: an a priori study. Phys. Fluids 20:115106
13. Brown GL, Thomas ASW. 1977. Large structure in a turbulent boundary layer. Phys. Fluids 20:234-52
14. Buschmann M, Indinger T, Gad-el Hak M. 2009. Near-wall behavior of turbulent wall-bounded flows. Int. J. Heat Fluid Flow 30:993-1006
15. Cantwell BJ. 1981. Organized motion in turbulent flow. Annu. Rev. Fluid Mech. 13:457-515
16. Carlier J, Stanislas M. 2005. Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry. J. Fluid Mech. 535:143-88 (Pubitemid 41052105)
17. Castillo L, Johansson TG. 2002. The effects of the upstream conditions on a low Reynolds number turbulent boundary layer with zero pressure gradient. J. Turbul. 3:31
18. Chauhan KA, Nagib HM. 2006. On the development of wall-bounded turbulent flows. In IUTAM Symp. Comput. Phys. New Perspect. Turbul., ed. Y Kaneda, pp. 183-89. New York: Springer
19. Chauhan KA, Nagib HM, Monkewitz PA. 2007. Evidence of non-universality of Karman constant. In Progress in Turbulence 2. Proc. iTi Conf. Turbul., ed. M Oberlack, G Khujadze, S Guenther, T Weller, M Frewer, et al., pp. 159-64. New York: Springer
20. Chung D, Pullin DI. 2009. Large-eddy simulation and wall modelling of turbulent channel flow.J. Fluid Mech. 631:281-309
21. Coles DE. 1956. The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1:191-226
22. Coles DE. 1962. The turbulent boundary layer in a compressible field. Tech. Rep. R-403-PR, Append. A, U.S. Air Force, Rand Corp.
23. DeGraaff DB, Eaton JK. 2000. Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422:319-46 (Pubitemid 36154669)
24. Del Alamo JC, Jimenez J. 2003. Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15(6):L41-44 (Pubitemid 36785185)
25. Del Alamo JC, Jimenez J. 2006. Linear energy amplification in turbulent channels. J. Fluid Mech. 559:205-13 (Pubitemid 44110523)
26. Del Alamo JC, Jimenez J. 2009. Estimation of turbulent convection velocities and corrections to Taylor's approximation. J. Fluid Mech. 640:5-26
27. Del Alamo JC, Jimenez J, Zandonade P, Moser RD. 2004. Scaling of the energy spectra of turbulent channels.J. Fluid Mech. 500:135-44 (Pubitemid 38300836)
28. Dennis DJC, Nickels TB. 2008. On the limitations of Taylor's hypothesis in constructing long structures in a turbulent boundary layer. J. Fluid Mech. 614:197-206
29. Donnelly RJ, Sreenivasan KR, eds. 1998. Flow at Ultra-High Reynolds and Rayleigh Numbers. Dordrecht: Kluwer
30. Eyink GL. 2008. Turbulent flow in pipes and channels as cross-stream "inverse cascades" of vorticity. Phys. Fluids 20:125101
31. Fernholz HH, Finley PJ. 1996. The incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data. Prog. Aerosp. Sci. 32:245-311 (Pubitemid 126359930)
32. Fernholz HH, Krause E, Nockemann M, Schober M. 1995. Comparative measurements in the canonical boundary layer at Reg
33. Flores O, Jimenez J. 2006. Effect of wall-boundary disturbances on turbulent channel flows. J. Fluid Mech. 566:357-76 (Pubitemid 44530262)
34. Flores O, Jimenez J, Del Alamo JC. 2007. Vorticity organization in the outer layer of turbulent channels with disturbed walls. J. Fluid Mech. 591:145-54
35. Folz A, Wallace JM. 2009. Near-surface turbulence in the atmospheric surface layer. Physica D 239:1305-17
36. Gad-el Hak M, Bandyopadhyay P. 1994. Reynolds number effects in wall-bounded turbulent flows. Appl. Mech. Rev. 47:307-65
37. Ganapathisubramani B, Longmire EK, Marusic I. 2003. Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478:35-46 (Pubitemid 36429924)
38. George WK. 2008. Is there an asymptotic effect of initial and upstream conditions on turbulenceProc. ASME 2008FluidsEng. Meet., Pap. FEDSM2008-55362
39. George WK, Castillo L. 1997. Zero-pressure-gradient turbulent boundary layer. Appl. Mech. Rev. 50:689-729
40. Guala M, Hommema SE, Adrian RJ. 2006. Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554:521-42
41. Head MR, Bandyopadhyay PR. 1981. New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107:297-337
42. Htes MH. 1997. Scaling of high-Reynolds number turbulent boundary layers in the National Diagnostic Facility. PhD thesis, Ill. Inst. Technol.
43. Hommema SE, Adrian RJ. 2003. Packet structure of surface eddies in the atmospheric boundary layer. Bound.-Layer Meteorol. 106:147-70 (Pubitemid 36199349)
44. t = 2003. Phys. Fluids 18:011702
45. Hu Z, Morley C, Sandman N 2006. Wall pressure and shear stress spectra from direct simulations of channel flow. AIAA J. 44:1541-49 (Pubitemid 44212398)
46. Hultmark MN, Bailey SCC, Smits AJ. 2010. Scaling of near-wall turbulence in pipe flow. J. Fluid Mech. 649:103-13
47. Hunt JCR, Morrison JF. 2001. Eddy structure in turbulent boundary layers. Eur. J. Mech. B Fluids 19:673-94
48. Hutchins N, Hambleton WT, Marusic I. 2005. Inclined cross-stream stereo particle image velocimetry measurements in turbulent boundary layers. J. Fluid Mech. 541:21-54 (Pubitemid 41581893)
49. Hutchins N, Marusic I. 2007a. Evidence of very long meandering streamwise structures in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579:1-28 (Pubitemid 47307197)
50. Hutchins N, Marusic I. 2007b. Large-scale influences in near-wall turbulence. Philos. Trans. R. Soc. Lond. A 365:647-64
51. Hutchins N, Nickels TB, Marusic I, Chong MS. 2009. Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 632:431-42
52. Jiménez J, Hoyas S. 2008. Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611:215-36
53. Jiménez J, Moser RD. 2007. What are we learning from simulating wall turbulencePhilos. Trans. R. Soc. Lond. A 365:715-32
54. Jiménez J, Pinelli A. 1999. The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389:335-59
55. Jones MB, Nickels TB, Marusic I. 2008. On the asymptotic similarity of the zero pressure-gradient turbulent boundary layer. J. Fluid Mech. 616:195-203
56. Khanna S, Brasseur JG. 1997. Analysis of Monin-Obukhov similarity from large-eddy simulation. J. Fluid Mech. 345:251-86
57. Khanna S, Brasseur JG. 1998. Three-dimensional buoyancy-and shear-induced local structure of the atmospheric boundary layer. J. Atmos. Sci. 55:710-43
58. Kim KC, Adrian RJ. 1999. Very large-scale motion in the outer layer. Phys. Fluids 11:417-22 (Pubitemid 129658545)
59. Kim J, MoinP,Moser RD. 1987. Turbulence statistics infully developed channel flow at low Reynolds number. J. Fluid Mech. 177:133-66 (Pubitemid 17583594)
60. Klewicki JC. 2010. Reynolds number dependence, scaling and dynamics of turbulent boundary layers. J. Fluid Eng. In press
61. Klewicki JC, Fife P, Wei T. 2009. On the logarithmic mean profile. J. Fluid Mech. 638:73-93
62. θ ≈ 1,500,000. Phys. Fluids 7:857-63
63. Kline SJ, Reynolds WC, Schraub FA, Rundstadler PW. 1967. The structure of turbulent boundary layers. J. Fluid Mech. 30:741-73
64. Kunkel GJ, Marusic I. 2006. Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using an atmospheric flow. J. Fluid Mech. 548:375-402 (Pubitemid 43193146)
65. ̈ Lindgren B, Osterlund JM, Johansson AV. 2004. Evaluation of scaling laws derived from Lie group symmetry methods in zero-pressure-gradient turbulent boundary layers. J. Fluid Mech. 502:127-52 (Pubitemid 38498335)
66. Liu Z, Adrian RJ, Hanratty TJ. 2001. Large-scale modes of turbulent channel flow: transport and structure. J. Fluid Mech. 448:53-80 (Pubitemid 33087437)
67. Marusic I. 2001. On the role of large-scale structures in wall turbulence. Phys. Fluids 13(3):735-43 (Pubitemid 32329456)
68. Marusic I, Adrian RJ. 2010. The eddies and scales of wall turbulence. In The Nature of Turbulence, ed. PA Davidson, Y Kaneda, KR Sreenivasan. Cambridge, UK: Cambridge Univ. Press. In press
69. Marusic I, Heuer WD. 2007. Reynolds number invariance of the structure inclination angle in wall turbulence. Phys. Rev. Lett. 99:114504
70. Marusic I, Hutchins N. 2008. Study of the log-layer structure in wall turbulence over a very large range of Reynolds number. Flow Turbul. Combust. 81:115-30
71. Marusic I, Kunkel GJ. 2003. Streamwise turbulence intensity formulation for flat-plate boundary layers. Phys. Fluids 15:2461-64 (Pubitemid 37096666)
72. Marusic I, Mathis R, Hutchins N. 2010a. High Reynolds number effects in wall turbulence. Int. J. Heat Fluid Flow 31:418-28
73. Marusic I, Mathis R, Hutchins N. 2010b. Predictive model for wall-bounded turbulent flow. Science 329:193-96
74. Marusic I, McKeon BJ, Monkewitz PA, Nagib HM, Smits AJ, Sreenivasan KR. 2010c. Wall-bounded turbulent flows: recent advances and key issues. Phys. Fluids. 22:065103
75. Marusic I, Uddin M, Perry AE. 1997. Similarity law for the streamwise turbulence intensity in zero-pressure-gradient turbulent boundary layers. Phys. Fluids 12:3718-26 (Pubitemid 127652029)
76. Mathis R, Hutchins N, Marusic I. 2009a. Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628:311-37
77. Mathis R, Monty JP, Hutchins N, Marusic I. 2009b. Comparison of large-scale amplitude modulation in turbulent boundary layers, pipes, and channel flows. Phys. Fluids 21:111703
78. McKeon BJ, ed. 2007. Themed issue: scaling and structure in high Reynolds number wall-bounded flows. Philos. Trans. R. Soc. A 365(1852):633-876
79. McKeon BJ. 2008. Scaling in wall turbulence: scale separation and interaction. Presented at AIAA Theoret. Fluid Mech. Conf., 5th, Seattle, AIAA Pap. 2008-4237
80. McKeon BJ, Li J, Jiang W, Morrison JF, Smits AJ. 2004. Further observations on the mean velocity distribution in fully developed pipe flow. J. Fluid Mech. 501:135-47 (Pubitemid 38431412)
81. McKeon BJ, Morrison JF. 2007. Asymptotic scaling in turbulent pipe flow. Philos. Trans. R. Soc. Lond. A 365:771-87
82. McKeon BJ, Sharma AS. 2010. A critical layer model for turbulent pipe flow. J. Fluid Mech. 658:336-82
83. McKeon BJ, Zagarola MV, Smits AJ. 2005. A new friction factor relationship for fully developed pipe flow. J. Fluid Mech. 538:429-43 (Pubitemid 41320361)
84. Metzger MM. 2002. Scalar dispersion in high Reynolds number turbulent boundary layers. PhD thesis, Univ. Utah
85. Metzger MM, Klewicki JC. 2001. A comparative study of near-wall turbulence in high and low Reynolds number boundary layers. Phys. Fluids 13:692-701 (Pubitemid 32329453)
86. Metzger MM, McKeon BJ, Holmes H. 2007. The near-neutral atmospheric surface layer: turbulence and non-stationarity. Philos. Trans. R. Soc. Lond. A 365:859-76
87. Moin P. 2009. Revisiting Taylor's hypothesis. J. Fluid Mech. 640:1-4
88. Monkewitz PA, Chauhan KA, Nagib HM. 2007. Self-contained high-Reynolds-number asymptotics for zero-pressure-gradient turbulent boundary layers. Phys. Fluids 19:115101
89. Monkewitz PA, Chauhan KA, Nagib HM. 2008. Comparison of mean flow similarity laws in zero pressure gradient turbulent boundary layers. Phys. Fluids 20:105102
90. Monty JP. 2005. Developments in smooth wall turbulent duct flows. PhD thesis, Univ. Melbourne
91. Monty JP, Chong MS. 2009. Turbulent channel flow: comparison of streamwise velocity data fom experiments and direct numerical simulation. J. Fluid Mech. 633:461-74
92. Monty JP, Hutchins N, Ng HCH, Marusic I, Chong MS. 2009. A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632:431-42
93. Monty JP, Stewart JA, Williams RC, Chong MS. 2007. Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589:147-56 (Pubitemid 350214585)
94. Morris SC, Stolpa SR, Slaboch PE, Klewicki JC. 2007. Near surface particle image velocimetry measurements in a transitionally rough-wall atmospheric surface layer. J. Fluid Mech. 580:319-38 (Pubitemid 47307546)
95. Morrison JF. 2007. The interaction between inner and outer regions of turbulent wall-bounded flow. Philos. Trans. R. Soc. Lond. A 365:683-98
96. Morrison JF, McKeon BJ, Jiang W, Smits AJ. 2004. Scaling of the streamwise velocity component in turbulent pipe flow. J. Fluid Mech. 508:99-131 (Pubitemid 38783839)
97. τ = 590. Phys. Fluids 11:943-45 (Pubitemid 129518650)
98. Nagib HM, Chauhan KA. 2008. Variations of von Kármán coefficient in canonical flows. Phys. Fluids 20:101518
99. Nagib HM, Chauhan KA, Monkewitz PA. 2007. Approach to an asymptotic state for zero pressure gradient turbulent boundary layers. Philos. Trans. R. Soc. Lond. A 365:755-70
100. -1 law in a high-Reynolds-number turbulent boundary layer. Phys. Rev. Lett. 95:074501
101. Nickels TB, Marusic I, Hafez SM, Hutchins N, Chong MS. 2007. Some predictions of the attached eddy model for a high Reynolds number boundary layer. Philos. Trans. R. Soc. Lond. A 365:807-22
102. Oberlack M. 2001. A unified approach for symmetries in plane parallel turbulent shear flows. J. Fluid Mech. 427:299-328
103. Österlund JM. 1999. Experimental studies of zero pressure-gradient turbulent boundary layer. PhD thesis, KTH, Stockholm
104. Osterlund JM, Johansson AV, Nagib HM, Hites MH. 2000. Anoteonthe overlap regioninturbulent boundary layers. Phys. Fluids 12:1-4
105. Panton R, ed. 1997. Self-Sustaining Mechanisms of Wall Turbulence. Southampton, UK: Comp. Mech. Publ.
106. Panton RL. 2001. Overview of the self-sustaining mechanisms of wall turbulence. Prog. Aerosp. Sci. 37:341-83 (Pubitemid 32737101)
107. Panton RL. 2007. Composite asymptotic expansions and scaling wall turbulence. Philos. Trans. R. Soc. Lond. A 365:733-54
108. Perry AE, Chong MS. 1982. On the mechanism of wall turbulence. J. Fluid Mech. 119:173-217
109. Perry AE, Henbest SM, Chong MS. 1986. A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165:163-99 (Pubitemid 16550152)
110. Perry AE, Li JD. 1990. Experimental support for the attached-eddy hypothesis in zero-pressure-gradient turbulent boundary layers. J. Fluid Mech. 218:405-38
111. Perry AE, Marusic I. 1995. A wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis. J. Fluid Mech. 298:361-88 (Pubitemid 26463377)
112. Perry AE, Marusic I, Jones MB. 2002. On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients. J. Fluid Mech. 461:61-91
113. Robinson SK. 1991. Coherent motions in turbulent boundary layers. Annu. Rev. Fluid Mech. 23:601-39
114. θ = 4,300. Int. J. Heat Fluid Flow 31(3):251-61
115. S̈chlatter P, Orlü R. 2010. Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659:116-26
116. θ = 2,500 studied through simulation and experiment. Phys. Fluids 21:051702
117. Schoppa W, Hussain F. 2002. Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453:57-108
118. Smits AJ, ed 2004. IUTAM Symposium on Reynolds Number Scaling in Turbulent Flow. Dordrecht: Kluwer
119. θ = 1, 410. J. Fluid Mech. 187 61-98
120. Spalart PR, Allmaras SR. 1992. A one-equation turbulence model for aerodynamic flows. Presented at AIAA Aerosp. Sci. Meet. Exhib., 30th, Reno, AIAA Pap. 1992-0439
121. Sreenivasan KR. 1989. The turbulent boundary layer. In Frontiers in Experimental Fluid Mechanics, ed. M Gad el Hak, pp. 139-209. New York: Springer-Verlag
122. Sreenivasan KR, Sahay A. 1997. The persistence of viscous effects in the overlap region and the mean velocity in turbulent pipe and channel flows. See Panton 1997, pp. 253-71
123. Stanislas M, Perret L, Foucaut JM. 2008. Vortical structures in the turbulent boundary layer: a possible route to a universal representation. J. Fluid Mech. 602:327-82 (Pubitemid 351606723)
124. Talamelli A, Persiani F, Fransson JHM, Alfredsson H, Johansson AV, et al. 2009. CICLoPE: a response to the need for high Reynolds number experiments. Fluid Dyn. Res. 41:021407
125. Taylor GI. 1938. The spectrum of turbulence. Proc. R. Soc. Lond. 164:476-90
126. Theodorsen T. 1952. Mechanism of turbulence. In Proc. 2nd Midwest. Conf. Fluid Mech., Mar. 17-19, pp. 1-19. Columbus: Ohio State Univ.
127. Tomkins CD, Adrian RJ. 2003. Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490:37-74 (Pubitemid 37164462)
128. Tomkins CD, Adrian RJ. 2005. Energetic spanwise modes in the logarithmic layer of a turbulent boundary layer. J. Fluid Mech. 545:141-62 (Pubitemid 43091238)
129. Townsend AA. 1976. The Structure of Turbulent Shear Flow. Cambridge: Cambridge Univ. Press
130. Tutkun M, George WK, Delville J, Stanislas M, Johansson PBV, et al. 2009. Two-point correlations in high Reynolds number flat plate turbulent boundary layers. J. Turbul. 10:1-23
131. Walker JDA, ed 1991. Turbulent Flow Structure Near Walls. London: The Royal Society
132. Wei T, Fife P, Klewicki JC, McMurtry P. 2005. Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows. J. Fluid Mech. 522:303-27 (Pubitemid 40217893)
133. Wills J. 1964. On convection velocities in turbulent shear flows. J. Fluid Mech. 20:417-32
134. Wosnik M, Castillo L, George WK. 2000. A theory for turbulent pipe and channel flows. J. Fluid Mech. 421:115-45
135. Wu X, Moin P. 2009. Direct numerical simulation of turbulence in a nominally-zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630:5-41
136. Yakhot V, Bailey SCC, Smits AJ. 2010. Scaling of global properties of turbulence and skin friction in pipe and channel flows. J. Fluid Mech. 653:65-73
137. Zagarola MV, Smits AJ. 1998. Mean-flow scaling of turbulent pipe flow. J. Fluid Mech. 373:33-79 (Pubitemid 128488706)
138. Zaman KBMQ, Hussain AKMF. 1981. Taylor hypothesis and large-scale coherent structures. J. Fluid Mech. 112:379-96 (Pubitemid 12474603)
139. Zanoun ES, Durst F, Nagib H. 2003. Evaluating the law of the wall in two-dimensional fully developed turbulent channel flows. Phys. Fluids 15:3079-89 (Pubitemid 37358701)
140. f relation for turbulent channels and consequences for high Re experiments. Fluid Dyn. Res. 41:021405
141. Zhao R, Smits AJ. 2007. Scaling of the wall-normal turbulence component in high-Reynolds-number pipe flow. J. Fluid Mech. 576:457-73 (Pubitemid 47039357)
142. Zhou J, Adrian RJ, Balachandar S, Kendall TM. 1999. Mechanisms for generating coherent packets of hairpin vortices in channel flows. J. Fluid Mech. 387:353-96