Skip to main content
SpringerLink
Log in

Reynolds-number-dependence of the maximum in the streamwise velocity fluctuations in wall turbulence

  • Originals
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

A survey is made of the standard deviation of the streamwise velocity fluctuations in near-wall turbulence and in particular of the Reynolds-number-dependency of its peak value. The following canonical flow geometries are considered: an incompressible turbulent boundary layer under zero pressure gradient, a fully developed two-dimensional channel and a cylindrical pipe flow. Data were collected from 47 independent experimental and numerical studies, which cover a Reynolds number range of R θ=U ∞ θ/v=300−20,920 for the boundary layer with θ the momentum thickness and R +=u *R/v=100-4,300 for the internal flows with R the pipe radius or the channel half-width. It is found that the peak value of the rms-value normalised by the friction velocity, u *, is within statistical errors independent of the Reynolds number. The most probable value for this parameter was found to be 2.71±0.14 and 2.70±0.09 for the case of a boundary layer and an internal flow, respectively. The present survey also includes some data of the streamwise velocity fluctuations measured over a riblet surface. We find no significant difference in magnitude of the normalised peak value between the riblet and smooth surfaces and this property of the normalised peak value may for instance be exploited to estimate the wall shear stress from the streamwise velocity fluctuations. We also consider the skewness of the streamwise velocity fluctuations and find its value to be close to zero at the position where the variance has its peak value. This is explained with help of the equations of the third-order moment of velocity fluctuations. These results for the peak value of the rms of the streamwise velocity fluctuations and also the coincidence of this peak with the zero value of the third moment can be interpreted as confirmation of local equilibrium in the near-wall layer, which is the basis of inner-layer scaling. Furthermore, these results can be also used as a requirement which turbulence models for the second and triple velocity correlations should satisfy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alfredsson PH; Johansson AV (1984) On the detection of turbulentgenerating events. J Fluid Mech 139: 325–345

    Google Scholar 

  • Andreopoulos J; Durst F; Zaric Z; Javanović J (1984) Influence of Reynolds number on characteristics of turbulent wall boundary layers. Exp Fluids 2: 7–16

    Article  Google Scholar 

  • Antonia RA; Teitel M; Kim J; Browne LWB (1992) Low-Reynolds number effects in a fully developed turbulent channel flow. J Fluid Mech 236: 579–605

    Google Scholar 

  • Azad RE; Burhanuddin S (1983) Measurements of some features of turbulence in wall-proximity. Exp Fluids 1: 149–160

    Google Scholar 

  • Bakewell HP; Lumley JL (1967) Viscous sublayer and adjacent wall region in turbulent pipe flow. Phys Fluids 10: 1880–1889

    Article  Google Scholar 

  • Balint J-L; Wallace JM; Vukoslavčević P (1992) The velocity and vorticity vector fields of a turbulent boundary layer: Part 2: Statistical properties. J Fluid Mech 228: 53–86

    Google Scholar 

  • Becher EV; Smith CR (1985) A combined visualisation-anemometry study of the turbulent drag reducing mechanisms of triangular micro-groove surface modification. AIAA Paper 85-0548

  • Blackwelder RF; Haritonidis JH (1983) Scaling of the bursting frequency in turbulent boundary layers. J Fluid Mech 132: 87–103

    Google Scholar 

  • Bradshaw P (1967) “Inactive” motion and pressure fluctuations in turbulent boundary layers. J Fluid Mech 30: 241–258

    Google Scholar 

  • Bradshaw P; Huang GP (1995) The law of the wall in turbulent flows. Proc R Soc Lond A 451: 165–188

    Google Scholar 

  • Bruns J; Dengel P; Fernholz HH (1992) Mean flow and turbulence measurements in an incompressible turbulent boundary layer. Part 1: Data. Institutsbericht Nr. 02/92, Harmann-Föttinger-Institut für Thermo- und Fluiddynamik, Technische Universität Berlin

  • Ching CY; Djenidi L; Antonia RA (1995) Low-Reynolds-number effects in a turbulent boundary layer. Exp Fluids 19: 61–68

    Article  Google Scholar 

  • Choi H; Moin P; Kim J (1993) Direct numerical simulation of turbulent flow over riblets. J Fluid Mech 255: 503–539

    MathSciNet  Google Scholar 

  • Choi K-S (1989) Near-wall structure of turbulent boundary layers over smooth and riblet surfaces. J Fluid Mech 208: 417–458

    Google Scholar 

  • Coles D (1956) The law of the wake in the turbulent boundary layer. J Fluid Mech 1: 191–226

    MATH  MathSciNet  Google Scholar 

  • Dean RB (1978) Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. Trans ASME, J Fluids Eng 100: 215–223

    Google Scholar 

  • deBisschop JR; Nieuwstadt FTM (1995) A turbulent boundary layer in an adverse pressure gradient: The effectiveness of riblets. AIAA J (in press)

  • den Toonder JMJ; Nieuwstadt FTM (1996) Reynolds number effects in a turbulent pipe flow for low to moderate Re. (submitted to Physics of Fluids)

  • Dussauge J-P; Fernholtz HH; Finley PJ; Smith RW; Smits AJ; Spina EF (1995) Turbulent boundary layers in subsonic and supersonic flow. AGARDograph 335

  • Durst F; Jovanović J; Sender J (1995) LDA measurements in the near wall region of a turbulent pipe flow. J Fluid Mech 295: 305–339

    Google Scholar 

  • Durst F; Kikura H; Lekakis I; Jovanović J; Ye Q (1996) Wall shear stress determination from near-wall mean velocity data in turbulent pipe and channel flows. Unpublished manuscript

  • Eggels JGM; Unger F; Weiss MH; Westerweel J; Adrian RJ; Friedrich R; Nieuwstadt FTM (1994) Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J Fluid Mech 268: 175–209

    Google Scholar 

  • Erm LP; Joubert PN (1991) Low-Reynolds-number turbulent boundary layers. J Fluid Mech 230: 1–44

    Google Scholar 

  • Fontaine AA; Deutsch S (1994) Three-component, time-resolved velocity statistics in the wall region of a turbulent pipe flow. Exp Fluids 18: 168–173

    Google Scholar 

  • Gad-el-Hak M; Bandyopadhyay PR (1994) Reynolds number effects in wall-bounded turbulent flows. Appl Mech Rev 47: 307–365

    Google Scholar 

  • Gupta AK; Kaplan RE (1972) Statistical characteristics of Reynolds stress in a turbulent boundary layer. Phys Fluids 15: 981–985

    Google Scholar 

  • Hanjalić K; Launder BE (1972) A Reynolds stress model of turbulence and its application to thin shear flows. J Fluid Mech 52: 609–638

    Google Scholar 

  • Hinze JO (1975) Turbulence. 2nd edition, McGraw-Hill

  • Hooshmand A; Youngs RA; Wallace JM; Balint J-L (1983) An experimental study of changes in the structure of a turbulent boundary layer due to surface geometry changes. AIAA Paper 83-0230

  • Johansson AV; Alfredsson AV (1982) On the structure of turbulent channel flow. J Fluid Mech 122: 295–314

    Google Scholar 

  • Johansson AV; Alfredsson AV (1983) Effects of imperfect spatial resolution on measurements of wall-bounded turbulent shear flows. J Fluid Mech 137: 409–421

    Google Scholar 

  • Johansson AV; Her J-Y; Haritonidis JH (1987) On the generation of high-amplitude wall-pressure peaks in turbulent boundary layers and spots. J Fluid Mech 175: 119–142

    Google Scholar 

  • Jovanovic J; Durst F; Johansson TG (1993) Statistical analysis of the dynamical equations for higher-order moments in turbulent wall bounded flows. Phys Fluids A5: 2886–2900

    Google Scholar 

  • Karlsson RI; Johansson TG (1988) LDV measurements of higher order moments of velocity fluctuations in a turbulent boundary layer. In: Laser anemometry in fluid mechanics III (eds. R. J. Adrian, T. Asanuma, D. F. G. Durão, F. Durst and J. H. Whitelaw), Lisbon, Portugal: 273–289

  • Kim J; Moin P; Moser R (1987) Turbulence statistics in fully developed channel flow at low Reynolds number. J Fluid Mech 177: 133–166

    Google Scholar 

  • Klewicki JC; Falco RE (1990) On accurately measuring statistics associated with small-scale structure in turbulent boundary layers using hot-wire probes. J Fluid Mech 219: 119–142

    Google Scholar 

  • Kunen JMG (1984) On the detection of coherent structures in turbulent flows. Ph.D. Thesis Delft University of Technology

  • Kuroda A; Kasagi N; Hirata M (1993) Direct numerical simulation of the turbulent Cuette-Poiseulle flows: Effect of mean shear on the near wall turbulence structures. In: Ninth Symposium on Turbulent Shear Flows (eds. F. Durst, N. Kasagi, B. E. Launder, F. W. Schmidt, K. Suzuki and J. H. Whitelaw), Springer-Verlag, 241-257

  • Kreplin H-P; Eckelmann H (1979) Behaviour of the three fluctuating velocity components in the wall region. Phys Fluids 22: 1233–1239

    Google Scholar 

  • Laufer J (1953) The structure of turbulence in fully developed pipe flow. NACA Report 1174

  • Ligrani PM; Bradshaw P (1987) Spatial resolution and measurement of turbulence in the viscous sublayer using subminiature hot-wire probes. Exp Fluids 5: 407–417

    Article  Google Scholar 

  • Murlis J; Tsai HM; Bradshaw P (1981) Structure of turbulent boundary layers at low Reynolds numbers. J Fluid Mech 122: 13–56

    Google Scholar 

  • Nagano Y; Tagawa M; Tsuji T (1993) Effects of adverse pressure gradients on mean flows and turbulence statistics in a boundary layer. In: Eighth Symposium on Turbulent Shear Flows (eds. F. Durst, R. Friedrich, B. E. Launder, F. W. Schmidt, U. Schumann and J. H. Whitelaw), Springer-Verlag, 7–12

  • Niederschulte MA; Adrian RJ; Hanratty TJ (1990) Measurements of turbulent flow in a channel at low Reynolds numbers. Exp Fluids 9: 222–230

    Article  Google Scholar 

  • Nockemann M; Abstiens R; Schober M; Bruns J; Eckert D (1994) Vermessung der Wandgrenzschicht im Deutsch-Niederländischen Windkanal bei hohen Reynolds-zahlen. Institutsreport, Aerodynamisches Institut RWTH Aachen

  • Panofsky HA; Dutton JA (1984) Atmospheric Turbulence; Models and Methods for Engineering Applications. New York: Wiley

    Google Scholar 

  • Perry AE; Abell CJ (1975) Scaling laws for pipe-flow turbulence. J Fluid Mech 67: 257–271

    Google Scholar 

  • Purtell LP; Klebanoff PS; Buckley FT (1981) Turbulent boundary layer at low Reynolds number. Phys Fluids 24: 802–811

    Google Scholar 

  • Schewe G (1983) On the structure and resolution of wall-pressure fluctuations associated with turbulent boundary-layer flow. J Fluid Mech 134: 311–328

    Google Scholar 

  • Schildknecht M; Miller JA; Meier GEA (1979) The influence of suction on the structure of turbulence in fully developed pipe flow. J Fluid Mech 90: 67–107

    Google Scholar 

  • Schwarz-van Manen AD; Geloven AFM; Nieuwenhuizen J; Stouthart JC; Prasad KK; Nieuwstadt FTM (1993) Friction velocity and virtual origin estimates for mean velocity profiles above smooth and triangular riblet surfaces. Appl Sci Res 50: 233–254

    Google Scholar 

  • Spalart PR (1988) Direct simulation of a turbulent boundary layer up to R 0 = 1410. J Fluid Mech 187: 61–98

    MATH  Google Scholar 

  • Tang YP; Clark DG (1993) On near-wall turbulence-generating events in turbulent boundary layer over a riblet surface. Appl Sci Res 50: 215–232

    Google Scholar 

  • Tennekes H; Lumley JL (1972) A first course in turbulence. The MIT Press

  • Thiele B; Eckelmann H (1993) Application of a partly submerged two component laser-doppler anemometer in a turbulent flow. Exp Fluids 17: 390–396

    Google Scholar 

  • Ueda H; Hinze JO (1975) Fine structure turbulence in the wall region of a turbulent boundary layer. J Fluid Mech 67: 125–143

    Google Scholar 

  • Vukoslavčević P; Wallace JM; Balint J-L (1987) On the mechanism of viscous drag reduction using streamwise allined riblets: A review with new results. Turbulent drag reduction by passive means (Three days international conference), Vol. 2, The Royal Aeronautical Society, London: 290–309

    Google Scholar 

  • Wei T; Willmarth WW (1989) Reynolds number effects on the structure of a turbulent channel flow. J Fluid Mech 204: 57–95

    Google Scholar 

Download references

Author information

Author notes

  1. S. Mochizuki

    Present address: Yamaguchi University, 755, Tokiwadai Ube, Japan

Authors and Affiliations

  1. Laboratory for Aero and Hydrodynamics Delft University of Technology, NL-2628 AL, Delft, The Netherlands

    S. Mochizuki & F. T. M. Nieuwstadt

Authors
  1. S. Mochizuki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. T. M. Nieuwstadt
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The authors are indebted to Prof. P. Bradshaw for making available his list of references on this topic and for his remarks on “active” and “inactive” motions. We also gratefully acknowledge discussions with Prof. I. Castro regarding the value of σ +u above rough walls.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mochizuki, S., Nieuwstadt, F.T.M. Reynolds-number-dependence of the maximum in the streamwise velocity fluctuations in wall turbulence. Experiments in Fluids 21, 218–226 (1996). https://doi.org/10.1007/BF00191694

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00191694

Keywords

Search

Navigation