Skip to main content Accessibility help
×
Home

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

  • Sophie Herpin (a1), Michel Stanislas (a1), Jean Marc Foucaut (a1) and Sebastien Coudert (a1)

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.

Copyright

Corresponding author

Email address for correspondence: michel.stanislas@ec-lille.fr

Footnotes

Hide All

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

Footnotes

References

Hide All
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, 141.
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, 4383.
Adrian, R. J., Christensen, K. T. & Liu, Z.-C. 2000a Analysis and interpretation of instantaneous turbulent velocity fields. Exp. Fluids 29, 275290.
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, 154.
Alamo, J. C. Del, Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of energy spectra of turbulent channels. J. Fluid Mech. 500, 135144.
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, 329358.
Blackwelder, R. F. & Eckelmann, H. 1979 Streamwise vortices associated with the bursting phenomenon. J. Fluid Mech. 94, 577594.
Cantwell, B. 1981 Organized motion in turbulent flow. Annu. Rev. Fluid Mech. 13, 437515.
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.
Carlier, J. & Stanislas, M. 2005 Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry. J. Fluid Mech. 535, 143188.
Corino, E. R. & Brodkey, R. S. 1969 A visual investigation of the wall region in turbulent flow. J. Fluid Mech. 37, 130.
Coudert, S. & Schon, J. P. 2001 Back-projection algorithm with misalignment corrections for 2D3C stereoscopic PIV. Meas. Sci. Technol. 12, 13711381.
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, 5571.
Falco, R. E. 1977 Coherent motions in the outer region of turbulent boundary layers. Phys. Fluids 20 (10), S124S132.
Foucaut, J. M., Carlier, J. & Stanislas, M. 2004 PIV optimization for the study of turbulent flow using spectral analysis. Meas. Sci. Technol. 15, 10461058.
Frisch, U. 1995 Turbulence. Cambridge University Press.
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 3546.
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2006 Experimental investigation of vortex properties in a turbulent boundary layer. Phys. Fluids 18, 0551050105510514.
Gao, Q., Ortiz-Duenas, C. & Longmire, E. K. 2011 Analysis of vortex populations in turbulent wall-bounded flow. J. Fluid Mech. 678, 87123.
George, W. K. & Hussain, H. J. 1991 Locally axisymmetric turbulence. J. Fluid Mech. 233, 123.
Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large scale and very large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521542.
Hambleton, W. T., Hutchins, N. & Marusic, I. 2006 Simultaneous orthogonal-plane particle image velocimetry measurements in a turbulent boundary layer. J. Fluid Mech. 560, 5364.
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary layer structure. J. Fluid Mech. 107, 297338.
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.
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, 130.
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, 745763.
Hinze, J. O. 1975 Turbulence. McGraw Hill.
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.
Hutchins, N., Hambleton, W. T. & Marusic, I. 2005 Inclined cross-stream stereo particle image velocimetry measurements in turbulent boundary layers. J. Fluid Mech. 541, 2154.
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 128.
Jeong, J., Hussain, F., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185214.
Kang, S.-J., Tanahashi, M. & Miyauchi, T. 2007 Dynamics of fine scale eddy clusters in turbulent channel flows. J. Turbul. 8 (52).
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417422.
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.
Kline, S. J., Reynolds, W. C., Schraub, W. C. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741773.
Kolmogorov, A. N. 1941a Dissipation of energy in a locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 1618.
Kolmogorov, A. N. 1941b The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl. Akad. Nauk SSSR 30, 299303.
Kolmogorov, A. N. 1941c On decay of isotropic turbulence in incompressible viscous fluid. Dokl. Akad. Nauk SSSR 31, 538540.
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, 8285.
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.
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, 9991013.
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).
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, 115130.
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, vol. 2. MIT.
Nychas, S. G., Hershey, H. C. & Brodkey, R. S. 1973 A visual study of turbulent shear flow. J. Fluid Mech. 61, 513540.
Panton, R. L. (Ed.) 1997 Self-Sustaining Mechanisms of Wall Turbulence. Computational Mechanics Publications.
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173217.
Perry, A. E., Henbest, S. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163199.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Prasad, A. K. 2000 Stereoscopic particle image velocimetry. Exp. Fluids 29, 103116.
Raffel, M., Willert, C., Wereley, S. T. & Kompenhans, J. 1998 Particle Image Velocimetry – a Practical Guide, 1st edn. Springer.
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601639.
Schlichting, H. & Gersten, K. 2001 Boundary Layer Theory, 8th revised and enlarged edition.
Schoppa, W. & Hussain, F. 1997 Genesis and Dynamics of Coherent Structures in Near-Wall Turbulence: a New Look. Computational Mechanics Publications.
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57108.
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, 10231035.
Soloff, S. M., Adrian, R. J. & Liu, Z.-C. 1997 Distortion compensation for generalized stereoscopic particle image velocimetry. Meas. Sci. Technol. 8, 14411454.
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, 221233.
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, 312.
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, 327342.
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, 331340.
Theodorsen, T. 1952 Mechanism of turbulence. In Proceedings of 2nd Midwestern Conference on Fluid Mechanics. Ohio State University.
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 3774.
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.
Wallace, J. M., Eckelmann, H. & Brodkey, R. S. 1972 The wall region in turbulent shear flow. J. Fluid Mech. 54, 3948.
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, 2028.
Willert, C. 1997 Stereoscopic digital particle image velocimetry for application in wind-tunnel flows. Meas. Sci. Technol. 8, 14651479.
Wu, Y. & Christensen, K. T. 2006 Population trends of spanwise vortices in wall turbulence. J. Fluid Mech. 568, 5576.
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, 353396.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Related content

Powered by UNSILO

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

  • Sophie Herpin (a1), Michel Stanislas (a1), Jean Marc Foucaut (a1) and Sebastien Coudert (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.