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Influence of the Reynolds number on the vortical structures in the logarithmic region of turbulent boundary layers

Published online by Cambridge University Press:  25 January 2013

Sophie Herpin ,
Michel Stanislas ,
Jean Marc Foucaut  and
Sebastien Coudert
Sophie Herpin
Affiliation:
Laboratoire de Mécanique de Lille (LML), Ecole Centrale de Lille, Bd Paul Langevin, Cite Scientifique, 59655 Villeneuve d’Ascq CEDEX, France
Michel Stanislas*
Affiliation:
Laboratoire de Mécanique de Lille (LML), Ecole Centrale de Lille, Bd Paul Langevin, Cite Scientifique, 59655 Villeneuve d’Ascq CEDEX, France
Jean Marc Foucaut
Affiliation:
Laboratoire de Mécanique de Lille (LML), Ecole Centrale de Lille, Bd Paul Langevin, Cite Scientifique, 59655 Villeneuve d’Ascq CEDEX, France
Sebastien Coudert
Affiliation:
Laboratoire de Mécanique de Lille (LML), Ecole Centrale de Lille, Bd Paul Langevin, Cite Scientifique, 59655 Villeneuve d’Ascq CEDEX, France
*
†Email address for correspondence: [email protected]
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Abstract

Near-wall turbulence is a subject of prime importance for turbulence modelling. Coherent structures were hypothesized early by Theodorsen in this flow region and have been the subject of intensive research ever since. The overall organization of these coherent structures has now been well assessed. Vortical structures appear to play a key role in this organization. Their characteristics and scaling have been studied by many authors as listed in the Introduction. The present contribution to the subject relies on high-resolution stereo particle image velocimetry (PIV) to study these structures. High-quality measurements are performed in a thick turbulent boundary layer at different values of the Reynolds number. The data quality is first assessed by comparing the statistics to those of hot-wire anemometry and direct numerical simulation data. The agreement between the two appears satisfactory. The PIV data are then processed in order to extract the vortex characteristics in a streamwise plane and in a spanwise plane. The statistical characteristics of these vortices are analysed in detail as a function of wall distance. The scaling of the data appears to be universal when the Kolmogorov scales are used. These results are analysed and discussed in terms of their probability density functions. This leads to a question regarding the Kolmogorov cascade in this region of the flow.

JFM classification

Boundary Layers: Boundary Layers Boundary Layers: Boundary layer structure Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 716 , 10 February 2013 , pp. 5 - 50
Copyright
©2013 Cambridge University Press

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Footnotes

‡

Present address: Oxylane Research, 4 Bv de Mons, 59665 Villeneuve d’Ascq, France.

References

Acarlar, M. S. & Smith, C. R. 1987a A study of hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by hemisphere protuberance. J. Fluid Mech. 175, 1–41.CrossRefGoogle Scholar
Acarlar, M. S. & Smith, C. R. 1987b A study of hairpin vortices in a laminar boundary layer. Part 2. Hairpin vortices generated by a fluid injection. J. Fluid Mech. 175, 43–83.CrossRefGoogle Scholar
Adrian, R. J., Christensen, K. T. & Liu, Z.-C. 2000a Analysis and interpretation of instantaneous turbulent velocity fields. Exp. Fluids 29, 275–290.CrossRefGoogle Scholar
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000b Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.CrossRefGoogle Scholar
Alamo, J. C. Del, Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144.Google Scholar
Alamo, J. C. Del, Jiménez, J., Zandonade, P. & Moser, R. D. 2006 Self-similar vortex clusters in the turbulent logarithmic region. J. Fluid Mech. 561, 329–358.CrossRefGoogle Scholar
Blackwelder, R. F. & Eckelmann, H. 1979 Streamwise vortices associated with the bursting phenomenon. J. Fluid Mech. 94, 577–594.CrossRefGoogle Scholar
Cantwell, B. 1981 Organized motion in turbulent flow. Annu. Rev. Fluid Mech. 13, 437–515.CrossRefGoogle Scholar
Carlier, J. 2001 Etude des structures coherentes de la turbulence de paroi a grand nombre de Reynolds par velocimetrie par images de particules. PhD thesis, Universite des Sciences et des Technologies de Lille.CrossRefGoogle Scholar
Carlier, J. & Stanislas, M. 2005 Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry. J. Fluid Mech. 535, 143–188.CrossRefGoogle Scholar
Corino, E. R. & Brodkey, R. S. 1969 A visual investigation of the wall region in turbulent flow. J. Fluid Mech. 37, 1–30.CrossRefGoogle Scholar
Coudert, S. & Schon, J. P. 2001 Back-projection algorithm with misalignment corrections for 2D3C stereoscopic PIV. Meas. Sci. Technol. 12, 1371–1381.CrossRefGoogle Scholar
Das, S. K., Tanahashi, M., Shoji, K. & Miyauchi, T. 2006 Statistical properties of coherent fine eddies in wall-bounded turbulent flows by direct numerical simulation. Theor. Comput. Fluid Dyn. 20, 55–71.CrossRefGoogle Scholar
Falco, R. E. 1977 Coherent motions in the outer region of turbulent boundary layers. Phys. Fluids 20 (10), S124–S132.CrossRefGoogle Scholar
Foucaut, J. M., Carlier, J. & Stanislas, M. 2004 PIV optimization for the study of turbulent flow using spectral analysis. Meas. Sci. Technol. 15, 1046–1058.CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence. Cambridge University Press.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
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2006 Experimental investigation of vortex properties in a turbulent boundary layer. Phys. Fluids 18, 05510501–05510514.CrossRefGoogle Scholar
Gao, Q., Ortiz-Duenas, C. & Longmire, E. K. 2011 Analysis of vortex populations in turbulent wall-bounded flow. J. Fluid Mech. 678, 87–123.CrossRefGoogle Scholar
George, W. K. & Hussain, H. J. 1991 Locally axisymmetric turbulence. J. Fluid Mech. 233, 1–23.CrossRefGoogle Scholar
Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large scale and very large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542.CrossRefGoogle 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
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary layer structure. J. Fluid Mech. 107, 297–338.CrossRefGoogle Scholar
Herpin, S. 2009 Study of the influence of the Reynolds number on the organization of wall-bounded turbulence. PhD thesis, Ecole Centrale de Lille and Monash University.Google Scholar
Herpin, S., Stanislas, M. & Soria, J. 2010 The organization of near-wall turbulence: a comparison between boundary layer SPIV data and channel flow DNS data. J. Turbul. 11, 1–30.CrossRefGoogle Scholar
Herpin, S., Wong, C. Y., Stanislas, M. & Soria, J. 2008 Stereoscopic PIV measurements of a turbulent boundary layer with a large spatial dynamic range. Exp. Fluids 45, 745–763.CrossRefGoogle Scholar
Hinze, J. O. 1975 Turbulence. McGraw Hill.Google Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels in turbulent channels up to $R{e}_{\tau } = 2003$ . Phys. Fluids 18, 011702.CrossRefGoogle Scholar
Hutchins, N., Hambleton, W. T. & Marusic, I. 2005 Inclined cross-stream stereo particle image velocimetry measurements in turbulent boundary layers. J. Fluid Mech. 541, 21–54.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Jeong, J., Hussain, F., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185–214.CrossRefGoogle Scholar
Kang, S.-J., Tanahashi, M. & Miyauchi, T. 2007 Dynamics of fine scale eddy clusters in turbulent channel flows. J. Turbul. 8 (52).CrossRefGoogle Scholar
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417–422.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Kline, S. J., Reynolds, W. C., Schraub, W. C. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.CrossRefGoogle Scholar
Kolmogorov, A. N. 1941a Dissipation of energy in a locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 16–18.Google Scholar
Kolmogorov, A. N. 1941b The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl. Akad. Nauk SSSR 30, 299–303.Google Scholar
Kolmogorov, A. N. 1941c On decay of isotropic turbulence in incompressible viscous fluid. Dokl. Akad. Nauk SSSR 31, 538–540.Google Scholar
Kolmogorov, A. N. 1962 A refinement of previous hypothesis concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13, 82–85.CrossRefGoogle Scholar
Kostas, J., Foucaut, J. M. & Stanislas, M. 2005 Application of double SPIV on the near wall turbulence structure of an adverse pressure gradient turbulent boundary layer. 6th International Symposium on PIV, Pasadena, California.Google Scholar
Lin, J., Laval, J.-P., Foucaut, J.-M. & Stanislas, M. 2008 Quantitative characterization of coherent structures in the buffer layer of near-wall turbulence. Part 1. Streaks. Exp. Fluids 45, 999–1013.CrossRefGoogle Scholar
Lin, J., Laval, J.-P., Foucaut, J.-M. & Stanislas, M. 2011 Quantitative characterization of coherent structures in the buffer layer of near wall turbulence. Part 2. Ejections, sweeps, vortices and synthesis. Exp. Fluids (submitted).Google Scholar
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
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, vol. 2. MIT.Google Scholar
Nychas, S. G., Hershey, H. C. & Brodkey, R. S. 1973 A visual study of turbulent shear flow. J. Fluid Mech. 61, 513–540.CrossRefGoogle Scholar
Panton, R. L. (Ed.) 1997 Self-Sustaining Mechanisms of Wall Turbulence. Computational Mechanics Publications.Google Scholar
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173–217.CrossRefGoogle Scholar
Perry, A. E., Henbest, S. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163–199.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Prasad, A. K. 2000 Stereoscopic particle image velocimetry. Exp. Fluids 29, 103–116.CrossRefGoogle Scholar
Raffel, M., Willert, C., Wereley, S. T. & Kompenhans, J. 1998 Particle Image Velocimetry – a Practical Guide, 1st edn. Springer.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.CrossRefGoogle Scholar
Schlichting, H. & Gersten, K. 2001 Boundary Layer Theory, 8th revised and enlarged edition.CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 1997 Genesis and Dynamics of Coherent Structures in Near-Wall Turbulence: a New Look. Computational Mechanics Publications.Google Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.CrossRefGoogle Scholar
Sheng, J., Malkiel, E. & Katz, J. 2008 Using digital holographic microscopy for simultaneous measurements of 3D near wall velocity and wall shear stress in a turbulent boundary layer. Exp. Fluids 45, 1023–1035.CrossRefGoogle Scholar
Soloff, S. M., Adrian, R. J. & Liu, Z.-C. 1997 Distortion compensation for generalized stereoscopic particle image velocimetry. Meas. Sci. Technol. 8, 1441–1454.CrossRefGoogle Scholar
Soria, J. 1996 An investigation of the near wake of a circular cylinder using a video-based digital cross-correlation particle image velocimetry technique. Exp. Therm. Fluid Sci. 12, 221–233.CrossRefGoogle Scholar
Soria, J., Cater, J. & Kostas, J. 1999 High resolution multigrid cross-correlation digital PIV measurements of a turbulent starting jet using half frame image shift shift recording. Opt. Laser Technol. 31, 3–12.CrossRefGoogle Scholar
Stanislas, M., Perret, L. & Foucaut, J.-M. 2008 Vortical structures in the turbulent boundary layer: a possible route to a universal representation. J. Fluid Mech. 602, 327–342.CrossRefGoogle Scholar
Tanahashi, M., Kang, S.-J., Miyamoto, T., Shiokawa, S. & Miyauchi, T. 2004 Scaling law of fine scale eddies in turbulent channel flow up to $R{e}_{\tau } = 800$ . Intl J. Heat Fluid Flow 25, 331–340.CrossRefGoogle Scholar
Theodorsen, T. 1952 Mechanism of turbulence. In Proceedings of 2nd Midwestern Conference on Fluid Mechanics. Ohio State University.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
Tutkun, M., George, W. K., Delville, J., Stanislas, M., Foucaut, J.-M. & Coudert, S. 2009 Two-point correlations in high Reynolds number flat plate turbulent boundary layer. J. Turbul. doi:10.1080/14685240902878045.CrossRefGoogle Scholar
Wallace, J. M., Eckelmann, H. & Brodkey, R. S. 1972 The wall region in turbulent shear flow. J. Fluid Mech. 54, 39–48.CrossRefGoogle Scholar
Westerweel, J., Dabiri, D. & Gharib, M. 1997 The effect of a discrete window offset on the accuracy of cross-correlation analysis of piv. Exp. Fluids 23, 20–28.CrossRefGoogle Scholar
Willert, C. 1997 Stereoscopic digital particle image velocimetry for application in wind-tunnel flows. Meas. Sci. Technol. 8, 1465–1479.CrossRefGoogle Scholar
Wu, Y. & Christensen, K. T. 2006 Population trends of spanwise vortices in wall turbulence. J. Fluid Mech. 568, 55–76.CrossRefGoogle Scholar
Zhou, J., Adrian, R. J., Balachander, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.CrossRefGoogle Scholar