Skip to main content
SpringerLink
Log in

A study of the three-dimensional spectral energy distribution in a zero pressure gradient turbulent boundary layer

  • Research Article
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

Time-resolved particle image velocimetry (PIV) measurements performed in wall parallel planes at three wall normal locations, y + = 34, 108, and 278, in a zero pressure gradient turbulent boundary layer at Re τ = 470 are used to illuminate the distribution of streamwise velocity fluctuations in a three-dimensional energy spectrum (2D in space and 1D in time) over streamwise, spanwise, and temporal wavelengths. Two high-speed cameras placed side by side in the streamwise direction give a 10δ × 5δ streamwise by spanwise field of view with a vector spacing of \(\Updelta x^+ = \Updelta z^+ \approx 37\) and a time step of \(\Updelta t^+=0.5\). Although 3D wavenumber--frequency spectra have been calculated in acoustics studies, to the authors’ knowledge this is the first time they has been calculated and presented for a turbulent boundary layer. The calculation and normalization of this spectrum, its relation to 2D and 1D spectra, and the effects of the PIV algorithm on its shape are carefully analyzed and outlined.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • Adrian RJ (1988) Statistical properties of particle image velocimetry measurement in turbulent flow. In: Laser anemometry in fluid mechanics III, pp 115–129

  • Balakumar BJ, Adrian RJ (2007) Large- and very-large-scale motions in channel and boundary-layer flows. Philos Trans R Soc A 365:665–681

    Article  MATH  Google Scholar 

  • Bobba KM (2004) Robust flow stability: theory, computations and experiments in near wall turbulence. PhD thesis, California Institute of Technology

  • Chung D, McKeon BJ (2010) Large-eddy simulation of large-scale structures in long channel flow. J Fluid Mech 661:341–364

    Article  MATH  Google Scholar 

  • DeGraaff DB, Eaton JK (2000) Reynolds-number scaling of the flat-plate turbulent boundary layer. J Fluid Mech 422:319–346

    Article  MATH  Google Scholar 

  • del Álamo JC, Jiménez J (2001) Direct numerical simulation of the very large anisotropic scales in a turbulent channel. Cent Turbul Res Annu Res Briefs 2001:329–341

    Google Scholar 

  • del Álamo JC, Jiménez J (2009) Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J Fluid Mech 640:5–26

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Flores O, Jiménez J (2006) Effect of wall-boundary disturbances on turbulent channel flows. J Fluid Mech 566:357–376

    Article  MATH  Google Scholar 

  • Foucaut JM, Carlier J, Stanislas M (2004) PIV optimization for the study of turbulent flow using spectral analysis. Meas Sci Tech 15:1046–1058

    Article  Google Scholar 

  • Ganapathisubramani B, Longmire EK, Marusic I (2003) Characteristics of vortex packets in turbulent boundary layers. J Fluid Mech 478:35–46

    Article  MATH  Google Scholar 

  • Goldschmidt V, Young M, Ott E (1981) Turbulent convective velocities (broadband and wavenumber dependent) in a plane jet. J Fluid Mech 105:327–345

    Article  Google Scholar 

  • Guala M, Metzger M, McKeon BJ (2011) Interactions within the turbulent boundary layer at high Reynolds number. J Fluid Mech 666:573–604

    Article  Google Scholar 

  • Hutchins N, Marusic I (2007) Large-scale influences in near-wall turbulence. Philos Trans R Soc A 365:647–664

    Article  MATH  Google Scholar 

  • Jacobi I, McKeon BJ (2011) Dynamic spatially-impulsive roughness perturbation of a turbulent boundary layer and the excitation of ‘critical layer’ velocity modes (submitted)

  • Jacobi I, Guala M, McKeon BJ (2010) Characteristics of a turbulent boundary layer perturbed by spatially-impulsive dynamic roughness. AIAA-2010-4474

  • Jiménez J, del Álamo JC, Flores O (2004) The large-scale dynamics of near-wall turbulence. J Fluid Mech 505:179–199

    Article  MathSciNet  MATH  Google Scholar 

  • Keane RD, Adrian RJ (1990) Optimisation of particle image velocimeters-part I: double pulsed systems. Meas Sci Technol 1:1202–1215

    Article  Google Scholar 

  • Kim J, Hussain F (1993) Propagation velocity of perturbations in turbulent channel flow. Phys Fluids A 5(3):695–706

    Article  Google Scholar 

  • Kim KC, Adrian RJ (1999) Very large-scale motion in the outer layer. Phys Fluids 11(2):417–422

    Article  MathSciNet  MATH  Google Scholar 

  • Krogstad PA, Kaspersen JH, Rimestad S (1998) Convection velocities in a turbulent boundary layer. Phys Fluids 10(4):949–957

    Article  Google Scholar 

  • LeHew J, Guala M, McKeon BJ (2010) A study of convection velocities in a zero pressure gradient turbulent boundary layer. AIAA-2010-4474

  • McKeon BJ, Sharma AS (2010) A critical layer model for turbulent pipe flow. J Fluid Mech 658:336–382

    Article  MathSciNet  MATH  Google Scholar 

  • Monty JP, Chong MS (2009) Turbulent channel flow: comparison of streamwise velocity data from experiments and direct numerical simulation. J Fluid Mech 633:461–474

    Article  MATH  Google Scholar 

  • Monty JP, Hutchins N, Ng HCH, Marusic I, Chong MS (2009) A comparison of turbulent pipe, channel and boundary layer flows. J Fluid Mech 632:431–442

    Article  MATH  Google Scholar 

  • Morrison WRB, Kronauer RE (1969) Structural similarity for fully developed turbulence in smooth tubes. J Fluid Mech 39:117–141

    Article  Google Scholar 

  • Morrison WRB, Bullock KJ, Kronauer RE (1971) Experimental evidence of waves in the sublayer. J Fluid Mech 47:639–656

    Article  Google Scholar 

  • Spalding DB (1961) A single formula for the law of the wall. Trans ASME E 28:455–458

    MATH  Google Scholar 

  • Taylor GI (1938) The spectrum of turbulence. Proc R Soc Lond A 164:476–490

    Article  Google Scholar 

  • Tomkins CD, Adrian RJ (2005) Energetic spanwise modes in the logarithmic layer of a turbulent boundary layer. J Fluid Mech 545:141–162

    Article  MATH  Google Scholar 

  • Wernet MP (2007) Temporally resolved PIV for space-time correlations in both cold and hot jet flows. Meas Sci Technol 18:1387–1403

    Article  Google Scholar 

  • Willert CE, Gharib M (1991) Digital particle image velocimetry. Exp Fluids 10:181–193

    Article  Google Scholar 

Download references

Acknowledgments

We would like to acknowledge and thank Prof. Mory Gharib and Dr. David Jeon for their assistance and allowing us to use their free surface water tunnel facility at Caltech in which all the experiments presented were performed. We would also like to acknowledge the Air Force Office of Scientific Research (AFOSR) for their continued support of this research under award number #FA9550-09-1-0701.

Author information

Author notes

  1. M. Guala

    Present address: Department of Civil Engineering, University of Minnesota, 500 Pillsbury Drive S.E, Minneapolis, MN, 55455, USA

Authors and Affiliations

  1. Graduate Aerospace Laboratories, California Institute of Technology, 1200 E. California Blvd. MC 205-45, Pasadena, CA, 91125, USA

    J. LeHew, M. Guala & B. J. McKeon

Authors
  1. J. LeHew
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Guala
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. J. McKeon
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Guala.

Additional information

M. Guala worked on this project at the California Institute of Technology but is currently at the University of Minnesota.

Rights and permissions

Reprints and permissions

About this article

Cite this article

LeHew, J., Guala, M. & McKeon, B.J. A study of the three-dimensional spectral energy distribution in a zero pressure gradient turbulent boundary layer. Exp Fluids 51, 997–1012 (2011). https://doi.org/10.1007/s00348-011-1117-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00348-011-1117-z

Keywords

Search

Navigation