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A predictive inner–outer model for streamwise turbulence statistics in wall-bounded flows

Published online by Cambridge University Press:  05 July 2011

ROMAIN MATHIS ,
NICHOLAS HUTCHINS  and
IVAN MARUSIC
ROMAIN MATHIS
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
NICHOLAS HUTCHINS
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
IVAN MARUSIC*
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
*
†Email address for correspondence: [email protected]
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Abstract

A model is proposed with which the statistics of the fluctuating streamwise velocity in the inner region of wall-bounded turbulent flows are predicted from a measured large-scale velocity signature from an outer position in the logarithmic region of the flow. Results, including spectra and all moments up to sixth order, are shown and compared to experimental data for zero-pressure-gradient flows over a large range of Reynolds numbers. The model uses universal time-series and constants that were empirically determined from zero-pressure-gradient boundary layer data. In order to test the applicability of these for other flows, the model is also applied to channel, pipe and adverse-pressure-gradient flows. The results support the concept of a universal inner region that is modified through a modulation and superposition of the large-scale outer motions, which are specific to the geometry or imposed streamwise pressure gradient acting on the flow.

JFM classification

Boundary Layers: Boundary Layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 681 , 25 August 2011 , pp. 537 - 566
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Abe, H., Kawamura, H. & Choi, H. 2004 Very large-scale structures and their effects on the wall shear-stress fluctuations in a turbulent channel flow up to Re τ = 640. Trans. ASME: J. Fluid Engng 126, 835–843.Google Scholar
Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.CrossRefGoogle Scholar
Adrian, R. J. 2010 Closing in on models of wall turbulence. Science 329 (5988), 155–156.CrossRefGoogle Scholar
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.CrossRefGoogle Scholar
del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), L41–L44.CrossRefGoogle Scholar
del Álamo, J. C. & Jiménez, J. 2006 Linear energy amplification in turbulent channels. J. Fluid Mech. 559, 205–213.CrossRefGoogle Scholar
del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144.CrossRefGoogle Scholar
Bailey, S. C. C., Kunkel, G. J., Hultmark, M., Vallikivi, M., Hill, J. P., Meyer, K. A., Tsay, C., Arnold, C. B. & Smits, A. J. 2010 Turbulence measurements using a nanoscale thermal anemometry probe. J. Fluid Mech. 663, 160–179.CrossRefGoogle Scholar
Bandyopadhyay, P. R. & Hussain, A. K. M. F. 1984 The coupling between scales in shear flows. Phys. Fluids 27 (9), 2221–2228.CrossRefGoogle Scholar
Boppe, R. S., Neu, W. L. & Shuai, H. 1999 Large-scale motions in the marine atmospheric surface layer. Boundary-Layer Meteorol. 92 (2), 165–183.CrossRefGoogle Scholar
Bradshaw, P. 1967 The turbulence structure of equilibrium boundary layers. J. Fluid Mech. 29 (4), 625–645.CrossRefGoogle Scholar
Brown, G. L. & Thomas, A. S. W. 1977 Large structure in a turbulent boundary layer. Phys. Fluids 20 (10), S243–S251.CrossRefGoogle Scholar
Buschmann, M. H. & Gad-el-Hak, M. 2010 Normal and cross-flow Reynolds stresses: differences between confined and semi-confined flows. Exp. Fluids 49, 213–223.CrossRefGoogle Scholar
Carper, M. A. & Porte-Agel, F. 2004 The role of coherent structures in subfilter-scale dissipation of turbulence measured in the atmospheric surface layer. J. Turbulence 5 (N40), 1–24.CrossRefGoogle Scholar
Chauhan, K. A., Ng, H. C. H. & Marusic, I. 2010 Empirical mode decomposition and Hilbert transforms for analysis of oil-film interferograms. Meas. Sci. Tech. 21, 105404.CrossRefGoogle Scholar
Chin, C. C., Hutchins, N., Ooi, A. S. H. & Marusic, I. 2009 Use of direct numerical simulation (DNS) data to investigate spatial resolution issues in measurements of wall-bounded turbulence. Meas. Sci. Techol. 20, 115401.CrossRefGoogle Scholar
DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
Fernholz, H. H. & Finley, P. J. 1996 The incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data. Prog. Aerospace Sci. 32, 245–311.CrossRefGoogle Scholar
Folz, A. & Wallace, J. M. 2010 Near-surface turbulence in the atmospheric boundary layer. Physica D 239, 1305–1317.CrossRefGoogle Scholar
Gad-el-Hak, M. & Bandyopadhyay, P. R. 1994 Reynolds number effects in wall-bounded flows. Trans. ASME: J. Fluid Engng 116 (1), 2–3.Google Scholar
Ganapathisubramani, B., Hambleton, N., Hutchins, W. T., Longmire, E. K. & Marusic, I. 2005 Investigation of large-scale coherence in a turbulent boundary layer using two-point correlation. J. Fluid Mech. 524, 57–80.CrossRefGoogle Scholar
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 35–46.CrossRefGoogle Scholar
George, W. K. & Tutkun, M. 2009 Mind the gap: a guideline for large eddy simulation. Phil. Trans. R. Soc. Lond. A 367, 2839–2847.Google Scholar
Grinvald, D. & Nikora, V. 1988 Rechnaya turbulentsiya (River Turbulence). Hydrometeoizdat (in Russian).Google Scholar
Hafez, S., Chong, M. S., Marusic, I. & Jones, M. B. 2004 Observations on high Reynolds number turbulent boundary layer measurements. In Proc. 15th Australasian Fluid Mech. Conf. AFMC00200.Google Scholar
Hambleton, W. T., Hutchins, N. & Marusic, I. 2006 Simultaneous orthogonal-plane particle image velocimetry measurements in a turbulent boundary layer. J. Fluid Mech. 560, 53–64.CrossRefGoogle Scholar
Harun, Z., Kulandaivelu, V., Nugroho, B., Khashehchi, M., Monty, J. P. & Marusic, I. 2010 Large scale structures in an adverse pressure gradient turbulent boundary layer. In 8th Intl ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurements. Marseille, France.Google Scholar
Heuer, W. D. C. & Marusic, I. 2005 Turbulence wall-shear stress sensor for the atmospheric surface layer. Meas. Sci. Techol. 16, 1644–1649.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re τ = 2003. Phys. Fluids 18, 011702.CrossRefGoogle Scholar
Hristov, T., Friehe, C. & Miller, S. 1998 Wave-coherent fields in air flow over ocean waves: identification of cooperative behaviour buried in turbulence. Phys. Rev. Lett. 98, 5245–5248.CrossRefGoogle Scholar
Huang, N. E., Shen, Z. & Long, S. R. 1999 A new view of the nonlinear water waves: the Hilbert spectrum. Annu. Rev. Fluid Mech. 31, 417–457.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 a Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365, 647–664.Google ScholarPubMed
Hutchins, N., Monty, J. P., Ganapathisubramani, B., Ng, H. C. H. & Marusic, I. 2011 Three-dimensional conditional structure of a high Reynolds number turbulent boundary layer. J. Fluid Mech. 673, 255–285.CrossRefGoogle Scholar
Hutchins, N., Nickels, T., Marusic, I. & Chong, M. S. 2009 Spatial resolution issues in hot-wire anemometry. J. Fluid Mech. 635, 103–136.CrossRefGoogle Scholar
Jiménez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215–236.CrossRefGoogle Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.CrossRefGoogle Scholar
Jones, M. B., Marusic, I. & Perry, A. E. 2001 Evolution and structure of sink-flow turbulent boundary layers. J. Fluid Mech. 428, 1–27.CrossRefGoogle Scholar
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11, 417–422.CrossRefGoogle Scholar
Klewicki, J. C., Metzger, M. M., Kelner, E. & Thurlow, E. M. 1995 Viscous sublayer flow visualizations at Reθ = 1500000. Phys. Fluids 7, 857–963.CrossRefGoogle Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Rundstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.CrossRefGoogle Scholar
Krogstad, P.-Å. & Skåre, P. E. 1995 Influence of a strong adverse pressure gradient on the turbulent structure in a boundary layer. Phys. Fluids 7, 2014–2024.CrossRefGoogle Scholar
Kunkel, G. J. & Marusic, I. 2006 Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using atmospheric flow. J. Fluid Mech. 548, 375–402.CrossRefGoogle Scholar
Lee, J.-H. & Sung, H. J. 2009 Structures in turbulent boundary layers subjected to adverse pressure gradients. J. Fluid Mech. 639, 101–131.CrossRefGoogle Scholar
Ligrani, P. M. & Bradshaw, P. 1987 Spatial resolution and measurement of turbulence in the viscous sublayer using subminiature hot-wire probes. Exp. Fluids 5, 407–417.CrossRefGoogle Scholar
Marusic, I. 2001 On the role of large-scale structures in wall turbulence. Phys. Fluids 13, 735–743.CrossRefGoogle Scholar
Marusic, I. & Heuer, W. D. C. 2007 Reynolds number invariance of the structure angle in wall turbulence. Phys. Rev. Lett. 99, 114501.CrossRefGoogle ScholarPubMed
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, 115–130.CrossRefGoogle Scholar
Marusic, I. & Kunkel, G. J. 2003 Streamwise turbulence intensity formulation for flat-plate boundary layers. Phys. Fluids 15, 2461–2464.CrossRefGoogle Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 a High Reynolds number effects in wall turbulence. Intl J. Heat Fluid Flow 31 (3), 418–428 (Sixth International Symposium on Turbulence and Shear Flow Phenomena).CrossRefGoogle Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 b Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193–196.CrossRefGoogle ScholarPubMed
Marusic, I., McKeon, B. J., Monkewitz, P. A., Nagib, H. M., Smits, A. J. & Sreenivasan, K. R. 2010 c Wall-bounded turbulent flows: recent advances and key issues. Phys. Fluids 22, 065103.CrossRefGoogle Scholar
Marusic, I. & Perry, A. E. 1995 A wall wake model for the turbulent structure of boundary layers. Part 2. Further experimental support. J. Fluid Mech. 298, 389–407.CrossRefGoogle Scholar
Marusic, I., Uddin, A. K. M. & Perry, A. E. 1997 Similarity law for the streamwise turbulence intensity in zero-pressure-gradient turbulent boundary layers. Phys. Fluids 9, 3718–3726.CrossRefGoogle Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2009 a Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.CrossRefGoogle Scholar
Mathis, R., Monty, J., Hutchins, N. & Marusic, I. 2009 b Comparison of large-scale amplitude modulation in turbulent boundary layers, pipes and channel flows. Phys. Fluids 21, 111703.CrossRefGoogle Scholar
Metzger, M. M. & Klewicki, J. C. 2001 A comparative study of near-wall turbulence in high and low Reynolds number boundary layers. Phys. Fluids 13, 692–701.CrossRefGoogle Scholar
Mochizuki, S. & Nieuwstadt, F. T. M. 1999 Reynolds-number-dependence of the maximum in the streamwise velocity fluctuations in wall turbulence. Exp. Fluids 21, 218.CrossRefGoogle Scholar
Monty, J. P., Hutchins, N., Ng, H. C. H., Marusic, I. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431–442.CrossRefGoogle Scholar
Monty, J. P., Stewart, J. A., Williams, R. C. & Chong, M. S. 2007 Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147–156.CrossRefGoogle Scholar
Morrison, J., McKeon, B., Jiang, W. & Smits, A. 2004 Scaling of the streamwise velocity component in turbulent pipe flow. J. Fluid Mech. 508, 99–131.CrossRefGoogle Scholar
Nagano, Y., Tsuji, T. & Houra, T. 1998 Structure of turbulent boundary layer subjected to adverse pressure gradient. Intl J. Heat Fluid Flow 19 (5), 563–572.CrossRefGoogle Scholar
Nagib, H. M. & Chauhan, K. A. 2008 Variations of von Kármán coefficient in canonical flows. Phys. Fluids 20, 101518.CrossRefGoogle Scholar
Nickels, T. B., Marusic, I., Hafez, S. & Chong, M. S. 2005 Evidence of the k 1−1 law in high-Reynolds number turbulent boundary layer. Phys. Rev. Lett. 95, 074501.CrossRefGoogle Scholar
Nikora, V., Nokes, R., Veale, W., Davidson, M. & Jirka, G. H. 2007 Large-scale turbulent structure of uniform shallow free-surface flows. Environ. Fluid Mech. 7 (2), 159–172.CrossRefGoogle Scholar
Ouergli, A. 2002 Hilbert transform from wavelet analysis to extract the envelope of an atmospheric model: examples. J. Atmos. Ocean. Technol. 19, 1082–1086.2.0.CO;2>CrossRefGoogle Scholar
Panton, R. L. 2001 Overview of the self-sustaining mechanisms of wall turbulence. Prog. Aerosp. Sci. 37, 341–383.CrossRefGoogle Scholar
Perry, A. E., Marusic, I. & Jones, M. B. 2002 On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients. J. Fluid Mech. 461, 61–91.CrossRefGoogle Scholar
Piomelli, U. & Balaras, E. 2002 Wall-layer models for large-eddy simulation. Annu. Rev. Fluid Mech. 34, 349–379.CrossRefGoogle Scholar
Rao, K. N., Narasimha, R. & Badri Narayanan, M. A. 1971 The ‘bursting’ phenomena in a turbulent boundary layer. J. Fluid Mech. 48, 339–352.CrossRefGoogle Scholar
Robinson, S. K. 1986 Instantaneous velocity profile measurements in a turbulent boundary layer. Chem. Engng Commun. 43 (4–6), 347–369.CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.CrossRefGoogle Scholar
Spark, E. H. & Dutton, J. A. 1972 Phase angle consideration in the modeling of the intermittent turbulence. J. Atmos. Sci. 29, 300–303.2.0.CO;2>CrossRefGoogle Scholar
Sreenivasan, K. R. 1989 The Turbulent Boundary Layer, pp. 159–209. Springer.Google Scholar
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37–74.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Tutkun, M., George, W. K., Delville, J., Stanislas, M., Johansson, P., Foucaut, J.-M. & Coudert, S. 2009 Two-point correlations in high Reynolds number flat plate turbulent boundary layers. J. Turbulence 10 (N21), 1–23.CrossRefGoogle Scholar