Skip to main content Accessibility help

Experimental study on low-speed streaks in a turbulent boundary layer at low Reynolds number

  • X. Y. Jiang (a1), C. B. Lee (a1), C. R. Smith (a2), J. W. Chen (a1) and P. F. Linden (a3)...


A study of low-speed streaks (LSSs) embedded in the near-wall region of a turbulent boundary layer is performed using selective visualization and analysis of time-resolved tomographic particle image velocimetry (tomo-PIV). First, a three-dimensional velocity field database is acquired using time-resolved tomo-PIV for an early turbulent boundary layer. Second, detailed time-line flow patterns are obtained from the low-order reconstructed database using ‘tomographic visualizations’ by Lagrangian tracking. These time-line patterns compare remarkably well with previously observed patterns using hydrogen bubble flow visualization, and allow local identification of LSSs within the database. Third, the flow behaviour in proximity to selected LSSs is examined at varying wall distances ( $10 < y^+ < 100$ ) and assessed using time-line and material surface evolution, to reveal the flow structure and evolution of a streak, and the flow structure evolving from streak development. It is observed that three-dimensional wave behaviour of the detected LSSs appears to develop into associated near-wall vortex flow structures, in a process somewhat similar to transitional boundary layer behaviour. Fourth, the presence of Lagrangian coherent structures is assessed in proximity to the LSSs using a Lagrangian-averaged vorticity deviation process. It is observed that quasi-streamwise vortices, adjacent to the sides of the streak-associated three-dimensional wave, precipitate an interaction with the streak. Finally, a hypothesis based on the behaviour of soliton-like coherent structures is made which explains the process of LSS formation, bursting behaviour and the generation of hairpin vortices. Comparison with other models is also discussed.


Corresponding author

Email address for correspondence:


Hide All
Acarlar, M. S. & Smith, C. R. 1987 a A study of hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance. J. Fluid Mech. 175, 141.
Acarlar, M. S. & Smith, C. R. 1987 b A study of hairpin vortices in a laminar boundary layer. Part 2. Hairpin vortices generated by fluid injection. J. Fluid Mech. 175, 4383.
Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.
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, 154.
Asai, M., Konishi, Y., Oizumi, Y. & Nishioka, M. 2007 Growth and breakdown of low-speed streaks leading to wall turbulence. J. Fluid Mech. 586, 371396.
Atkinson, C., Buchmann, N. A., Amili, O. & Soria, J. 2014 On the appropriate filtering of PIV measurements of turbulent shear flows. Exp. Fluids 55 (1), 1654.
Bernard, P. S. 2013 Vortex dynamics in transitional and turbulent boundary layers. AIAA J. 51 (8), 18281842.
Borodulin, V. I., Gaponenko, V. R., Kachanov, Y. S., Meyer, D. G. W., Rist, U., Lian, Q. X. & Lee, C. B. 2002 Late-stage transitional boundary-layer structures. Direct numerical simulation and experiment. Theor. Comput. Fluid Dyn. 15 (5), 317337.
Brandt, L. & Henningson, D. S. 2002 Transition of streamwise streaks in zero-pressure-gradient boundary layers. J. Fluid Mech. 472, 229261.
Chakraborty, P., Balachandar, S. & Adrian, R. J. 2005 On the relationships between local vortex identification schemes. J. Fluid Mech. 535, 189214.
Chen, W. 2013 Numerical simulation of boundary layer transition by combined compact difference method. PhD thesis, Nanyang Technological University, Singapore.
Chernyshenko, S. I. & Baig, M. F. 2005 The mechanism of streak formation in near-wall turbulence. J. Fluid Mech. 544, 99131.
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids 2 (5), 765777.
Deng, S., Pan, C., Wang, J. J. & He, G. 2018 On the spatial organization of hairpin packets in a turbulent boundary layer at low-to-moderate Reynolds number. J. Fluid Mech. 844, 635668.
Dennis, D. J. C. & Nickels, T. B. 2011 Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 1. Vortex packets. J. Fluid Mech. 673, 180217.
Elsinga, G. E., Kuik, D. J., van Oudheusden, B. W. & Scarano, F. 2007 Investigation of the three-dimensional coherent structures in a turbulent boundary layer with tomographic-PIV. AIAA Paper 2007–1305.
Gao, Q., Ortiz-Dueñas, C. & Longmire, E. 2013 Evolution of coherent structures in turbulent boundary layers based on moving tomographic PIV. Exp. Fluids 54 (12), 1625.
Green, M. A., Rowley, C. W. & Haller, G. 2007 Detection of Lagrangian coherent structures in three-dimensional turbulence. J. Fluid Mech. 572, 110120.
Hack, M. J. & Moin, P. 2018 Coherent instability in wall-bounded shear. J. Fluid Mech. 844, 917955.
Haidari, A. H. & Smith, C. R. 1994 The generation and regeneration of single hairpin vortices. J. Fluid Mech. 277, 135162.
Haller, G. 2005 An objective definition of a vortex. J. Fluid Mech. 525, 126.
Haller, G. 2016 Dynamic rotation and stretch tensors from a dynamic polar decomposition. J. Mech. Phys. Solids 86, 7093.
Haller, G., Hadjighasem, A., Farazmand, M. & Huhn, F. 2016 Defining coherent vortices objectively from the vorticity. J. Fluid Mech. 795, 136173.
Hama, F. R. 1962 Streaklines in a perturbed shear flow. Phys. Fluids 5 (6), 644650.
Hama, F. R. & Nutant, J. 1963 Detailed flow-field observations in the transition process in a thick boundary layer. In Proceedings of the Heat Transfer and Fluid Mech. Inst., pp. 77–93. Stanford University Press.
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297338.
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. Tech. Rep. CTR-S88. Center for Turbulence Research Report.
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
Jiang, X. Y., Lee, C. B., Chen, X., Smith, C. R. & Linden, P. F. 2020 Structure evolution at early stage of boundary-layer transition: simulation and experiment. J. Fluid Mech. 890, A11.
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213240.
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335359.
Kachanov, Y. S. 1994 Physical mechanisms of laminar-boundary-layer transition. Annu. Rev. Fluid Mech. 26 (1), 411482.
Kim, H., Kline, S. J. & Reynolds, W. C. 1971 The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50, 133–60.
Kim, J. & Lim, J. 2000 A linear process in wall-bounded turbulent shear flows. Phys. Fluids 12 (8), 18851888.
Kim, J. & Moin, P. 1986 The structure of the vorticity field in turbulent channel flow. Part 2. Study of ensemble-averaged fields. J. Fluid Mech. 162, 339363.
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30 (4), 741773.
Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98 (2), 243251.
Landahl, M. T. 1990 On sublayer streaks. J. Fluid Mech. 212, 593614.
Laurien, E. & Kleiser, L. 1989 Numerical simulation of boundary-layer transition and transition control. J. Fluid Mech. 199, 403440.
Lee, C. B. 1998 New features of CS solitons and the formation of vortices. Phys. Lett. A 247 (6), 397402.
Lee, C. B. 2000 Possible universal transitional scenario in a flat plate boundary layer: measurement and visualization. Phys. Rev. E 62 (3), 36593670.
Lee, C. B., Hong, Z. X., Kachanov, Y. S., Borodulin, V. I. & Gaponenko, V. V. 2000 A study in transitional flat plate boundary layers: measurement and visualization. Exp. Fluids 28 (3), 243251.
Lee, C. B & Li, R. Q. 2007 Dominant structure for turbulent production in a transitional boundary layer. J. Turbul. 8 (55), 134.
Lee, C. B. & Wu, J. Z. 2008 Transition in wall-bounded flows. Appl. Mech. Rev. 61, 030802.
Liu, C. Q., Wang, Y. Q., Yang, Y. & Duan, Z. W. 2016 New omega vortex identification method. Sci. China-Phys. Mech. Astron. 59 (8), 684711.
Lu, L. J. & Smith, C. R. 1991 Use of flow visualization data to examine spatial-temporal velocity and burst-type characteristics in a turbulent boundary layer. J. Fluid Mech. 232, 303340.
Lynch, K. P. & Scarano, F. 2015 An efficient and accurate approach to MTE-mart for time-resolved tomographic PIV. Exp. Fluids 56 (3), 66.
Mans, J., de Lange, H. C. & van Steenhoven, A. A. 2007 Sinuous breakdown in a flat plate boundary layer exposed to free-stream turbulence. Phys. Fluids 19 (8), 088101.
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193196.
Matsubara, M. & Alfredsson, P. H. 2001 Disturbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech. 430, 149168.
Matsuura, K. 2016 Direct numerical simulation of a straight vortex tube in a laminar boundary-layer flow. Intl J. Comput. Meth. Exp. Meas. 4 (4), 474483.
Matsuura, K., Matsui, K. & Tani, N. 2018 Effects of free-stream turbulence on the global pressure fluctuation of compressible transitional flows in a low-pressure turbine cascade. Intl J. Numer. Meth. Heat Fluid Flow 28, 11871202.
Moin, P. & Moser, R. D. 1989 Characteristic-eddy decomposition of turbulence in a channel. J. Fluid Mech. 200, 471509.
Musker, A. J. 1979 Explicit expression for the smooth wall velocity distribution in a turbulent boundary layer. AIAA J. 17 (6), 655657.
Naka, Y., Stanislas, M., Foucaut, J.-M., Coudert, S., Laval, J.-P. & Obi, S. 2015 Space-time pressure-velocity correlations in a turbulent boundary layer. J. Fluid Mech. 771, 624675.
Nishioka, M. & Asai, M. 1984 Evolution of Tollmien–Schlichting waves into wall turbulence. In Turbulence and Chaotic Phenomena in Fluids (ed. T. Tatsumi), pp. 87–92. North-Holland.
Nishioka, M., Asai, M. & Iida, S. 1981 Wall phenomena in the final stage of transition to turbulence. In Transition and Turbulence (ed. R. E. Meyer), pp. 113–126. Academic Press.
Purtell, L. P., Klebanoff, P. S. & Buckley, F. T. 1981 Turbulent boundary layer at low Reynolds number. Phys. Fluids 24, 802811.
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23 (1), 601639.
Sabatino, D. R., Praisner, T. J., Seal, C. V. & Smith, C. R. 2012 Hydrogen bubble visualization. In Flow Visualization: Techniques and Examples, 2nd edn (ed. A. J. Smith & T. T. Lim), pp. 27–45. Imperial College Press.
Sabatino, D. R. & Rossmann, T. 2016 Tomographic piv measurements of a regenerating hairpin vortex. Exp. Fluids 57 (1), 113.
Sayadi, T., Hamman, C. W. & Moin, P. 2013 Direct numerical simulation of complete h-type and K-type transitions with implications for the dynamics of turbulent boundary layers. J. Fluid Mech. 724, 480509.
Scarano, F 2013 Tomographic piv: principles and practice. Meas. Sci. Technol. 24 (1), 012001.
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57108.
Schröder, A., Geisler, R., Elsinga, G. E., Scarano, F. & Dierksheide, U. 2008 Investigation of a turbulent spot and a tripped turbulent boundary layer flow using time-resolved tomographic PIV. Exp. Fluids 44 (2), 305316.
Shadden, S. C., Dabiri, J. O. & Marsden, J. E. 2006 Lagrangian analysis of fluid transport in empirical vortex ring flows. Phys. Fluids 18 (4), 047105.
Shalev-Shwartz, S. & Ben-David, S. 2014 Understanding Machine Learning: From Theory to Algorithms. Cambridge University Press.
Smith, C. R. 1984 A synthesized model of the near-wall behavior in turbulent boundary layers. In Proceedings of the 8th Symposium of Turbulence (ed. G. K. Pattersonand & J. L. Zakin), pp. 1–27. University of Missouri-Rolla.
Smith, C. R. 1998 Vortex development and interactions in turbulent boundary layers: implications for surface drag reduction. In Proceedings of the International Symposium on Seawater Drag Reduction, pp. 39–45. Office of Naval Research.
Smith, C. R. & Metzler, S. P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 2754.
Smith, C. R., Walker, J. D. A., Haidari, A. H. & Sobrun, U. 1991 On the dynamics of near-wall turbulence. Phil. Trans. R. Soc. Lond. A 336 (1641), 131175.
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to $Re_\theta = 1410$. J. Fluid Mech. 187, 6198.
Spalding, D. B. 1961 A single formula for the ‘law of the wall’. J. Appl. Mech. 28 (3), 455458.
Stanislas, M. 2017 Near wall turbulence: an experimental view. Phys. Rev. Fluids 2, 100506.
Taira, K., Brunton, S. L., Dawson, S. T. M., Rowley, C. W., Colonius, T., McKeon, B. J., Schmidt, O. T., Gordeyev, S., Theofilis, V. & Ukeiley, L. S. 2017 Modal analysis of fluid flows: an overview. AIAA J. 55 (12), 40134041.
Tian, S. L., Gao, Y. S., Dong, X. R. & Liu, C. Q. 2018 Definitions of vortex vector and vortex. J. Fluid Mech. 849, 312339.
Titchener, N., Colliss, S. & Babinsky, H. 2015 On the calculation of boundary-layer parameters from discrete data. Exp. Fluids 56 (8), 159.
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9 (4), 883900.
Wieneke, B. 2008 Volume self-calibration for 3d particle image velocimetry. Exp. Fluids 45 (4), 549556.
Wortmann, F. X. 1981 Boundary-layer waves and transition. In Advances in Fluid Mechanics (ed. E. Krause), pp. 268–279. Springer.
Wu, J. Z., Ma, H. Y. & Zhou, M. D. 2015 Vortical structures in transitional and turbulent shear flows. In Vortical Flows, pp. 361–404. Springer.
Wu, X. & Moin, P. 2009 Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630, 541.
Wu, X. & Moin, P. 2010 Transitional and turbulent boundary layer with heat transfer. Phys. Fluids 22 (8), 085105.
Wu, X., Moin, P., Wallace, J. M., Skarda, J., Lozano-Durán, A. & Hickey, J.-P. 2017 Transitional–turbulent spots and turbulent–turbulent spots in boundary layers. Proc. Natl Acad. Sci. USA 114 (27), E5292E5299.
Wu, Y. 2014 A study of energetic large-scale structures in turbulent boundary layer. Phys. Fluids 26 (4), 045113.
Zhao, Y., Yang, Y. & Chen, S. 2016 Evolution of material surfaces in the temporal transition in channel flow. J. Fluid Mech. 793, 840876.
Zhao, Y. M., Xiong, S. Y., Yang, Y. & Chen, S. Y. 2018 Sinuous distortion of vortex surfaces in the lateral growth of turbulent spots. Phys. Rev. Fluids 3 (7), 074701.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Experimental study on low-speed streaks in a turbulent boundary layer at low Reynolds number

  • X. Y. Jiang (a1), C. B. Lee (a1), C. R. Smith (a2), J. W. Chen (a1) and P. F. Linden (a3)...


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.