Boundary-Layer Meteorology

, Volume 147, Issue 2, pp 217–236 | Cite as

Length-Scale Similarity of Turbulent Organized Structures over Surfaces with Different Roughness Types

  • Hiroshi TakimotoEmail author
  • Atsushi Inagaki
  • Manabu Kanda
  • Ayumu Sato
  • Takenobu Michioka


We examine the similarity of turbulent organized structures over smooth and very rough wall flows. Turbulent flow fields in horizontal cross-sections were measured using particle image velocimetry, and the characteristics of turbulent organized structures over four types of surfaces were investigated. Measurements were conducted at several measurement heights across the internal boundary layer. The length and width of turbulence structures were quantified using a two-point correlation method. We selected two thresholds of two-point correlation coefficients to consider both large-scale and small-scale structures; the validity of these choices was examined through the analyses using proper orthogonal decomposition. For large-scale structures, the length and aspect ratios (streamwise length/spanwise width) of structures were highly correlated with the velocity gradient for each measurement height and boundary-layer thickness. This relationship was also examined in the results of previous studies, and the scaling of the aspect ratio with the non-dimensional velocity gradient again showed the importance of the velocity gradient, with slight differences found between smooth and rough surfaces. In contrast, the small-scale structures exhibited weak dependency on the velocity gradient and boundary-layer thickness. Instantaneous snapshots of turbulent organized structures at the same shear level also displayed differences in small-scale structures, but the structures of the organized motions resembled each other, as in the results of the two-point correlation method.


Coherent flow structure Particle image velocimetry   Turbulent organized structures Urban-like canopy Wind tunnel 



This research was financially supported by a Grant-in Aid for JSPS Fellows from the Japan Society for the Promotion of Science.


  1. Adrian RJ, Meinhart CD, Tomkins CD (2000) Vortex organization in the outer region of the turbulent boundary layer. J Fluid Mech 422:1–54CrossRefGoogle Scholar
  2. Blackwelder RF, Kaplan RE (1976) On the wall structure of the turbulent boundary layer. J Fluid Mech 76:89–120CrossRefGoogle Scholar
  3. Cheng H, Hayden P, Robins AG, Castro IP (2007) Flow over cube arrays of different packing densities. J Wind Eng Ind Aerodyn 95:715–740CrossRefGoogle Scholar
  4. Christensen KT, Adrian RJ (2001) Statistical evidence of hairpin vortex packets in wall turbulence. J Fluid Mech 431:433–443CrossRefGoogle Scholar
  5. Coceal O, Dobre A, Thomas TG, Belcher SE (2007) Structure of turbulent flow over regular arrays of cubical roughness. J Fluid Mech 589:375–409CrossRefGoogle Scholar
  6. Del Álamo JC, Jiménez J, Zandonade P, Moser RD (2006) Self-similar vortex clusters in the turbulent logarithmic region. J Fluid Mech 561:329–358CrossRefGoogle Scholar
  7. Flores O, Jiménez J, Del Álamo JC (2007) Vorticity organization in the outer layer of turbulent channels with disturbed walls. J Fluid Mech 591:145–154CrossRefGoogle Scholar
  8. Ganapathisubramani B, Longmire EK, Marusic I (2003) Characteristics of vortex packets in turbulent boundary layers. J Fluid Mech 478:35–46CrossRefGoogle Scholar
  9. Ganapathisubramani B, Hutchins N, Hambleton WT, Longmire EK, Marusic I (2005) Investigation of large-scale coherence in a turbulent boundary layer using two-point correlations. J Fluid Mech 524:57–80CrossRefGoogle Scholar
  10. Hellström LHO, Sinha A, Smits AJ (2011) Visualizing the very-large-scale motions in turbulent pipe flow. Phys Fluids 23:011703CrossRefGoogle Scholar
  11. Hommema SE, Adrian RJ (2003) Packet structure of surface eddies in the atmospheric boundary layer. Boundary-Layer Meteorol 106:147–170CrossRefGoogle Scholar
  12. Hunt JCR, Morrison JF (2000) Eddy structure in turbulent boundary layers. Eur J Mech B Fluids 19:673–694CrossRefGoogle Scholar
  13. Hutchins N, Marusic I (2007) Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J Fluid Mech 579:1–28CrossRefGoogle Scholar
  14. Inagaki A, Kanda M (2008) Turbulent flow similarity over an array of cubes in near-neutrally stratified atmospheric flow. J Fluid Mech 615:101–120CrossRefGoogle Scholar
  15. Inagaki A, Kanda M (2010) Organized structure of active turbulence over an array of cubes within the logarithmic layer of atmospheric flow. Boundary-Layer Meteorol 135:209–228CrossRefGoogle Scholar
  16. Inagaki A, Maruyama A, Kanda M (2009) Spatial and temporal scales of coherent turbulence over outdoor reduced urban scale model. In: The 7th international conference on urban climate, P2-12Google Scholar
  17. Jiménez J (2004) Turbulent flows over rough walls. Annu Rev Fluid Mech 36:173–196CrossRefGoogle Scholar
  18. Kanda M (2006) Large-eddy simulations on the effects of surface geometry of building arrays on turbulent organized structures. Boundary-layer Meteorol 118:151–168CrossRefGoogle Scholar
  19. Kanda M, Moriwaki R, Kasamatsu F (2004) Large-eddy simulation of turbulent organized structures within and above explicitly resolved cube arrays. Boundary-layer Meteorol 112:343–368CrossRefGoogle Scholar
  20. Kim KC, Adrian RJ (1999) Very large-scale motion in the outer layer. Phys Fluids 11:417–422CrossRefGoogle Scholar
  21. Lee JH, Sung HJ, Krogstad P-Å (2011) Direct numerical simulation of the turbulent boundary layer over a cube-roughened wall. J Fluid Mech 669:397–431CrossRefGoogle Scholar
  22. Marusic I, McKeon BJ, Monkewith PA, Nagib HM, Smits AJ, Sreenivasan KR (2010) Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys Fluids 22:065103CrossRefGoogle Scholar
  23. Mason PJ (1989) Large-eddy simulation of the convective atmospheric boundary layer. J Atmos Sci 46:1492–1516CrossRefGoogle Scholar
  24. Michioka T, Sato A, Takimoto H, Kanda M (2011a) Large-eddy simulation for the mechanism of pollutant removal from a two-dimensional street canyon. Boundary-Layer Meteorol 138:195–213Google Scholar
  25. Michioka T, Sato A, Sada K (2011b) Wind-tunnel experiments for gas dispersion in an atmospheric boundary layer with large-scale turbulent motion. Boundary-Layer Meteorol 141:35–51Google Scholar
  26. Panton RL (2001) Overview of the self-sustaining mechanisms of wall turbulence. Prog Aerosp Sci 37:341–383CrossRefGoogle Scholar
  27. Perry AE, Schofield WH, Joubert P (1969) Rough wall turbulent boundary layers. J Fluid Mech 37:383–413CrossRefGoogle Scholar
  28. Reynolds RT, Hayden P, Castro IP, Robins AG (2007) Spanwise variations in nominally two-dimensional rough-wall boundary layers. Exp Fluids 42:311–320CrossRefGoogle Scholar
  29. Sato A, Takimoto H, Michioka T (2009) Impact of wall heating on air flow in urban street canyons. In: Proceedings of the conference on physical modelling of flow and dispersion phenomena, E4.1–E4.7Google Scholar
  30. Shaw RH (1982) Aerodynamic roughness of a plant canopy: a numerical experiment. Agric Meteorol 26:51–65CrossRefGoogle Scholar
  31. Shaw RH, Brunet Y, Finnigan JJ, Raupach MR (1995) A wind tunnel study of air flow in waving wheat: two-point velocity statistics. Boundary-Layer Meteorol 76:349–376CrossRefGoogle Scholar
  32. Tanahashi M, Kang SJ, Miyamoto T, Shiokawa S, Miyauchi T (2004) Scaling law of fine scale eddies in turbulent channel flows up to \(\text{ Re}_{\tau }= 800\). Int J Heat Fluid Flow 25:331–340CrossRefGoogle Scholar
  33. Tomkins CD, Adrian RJ (2003) Spanwise structure and scale growth in turbulent boundary layers. J Fluid Mech 490:37–74CrossRefGoogle Scholar
  34. Watanabe T (2004) Large-eddy simulation of coherent turbulence structures associated with scalar ramps over plant canopies. Boundary-Layer Meteorol 112:307–341CrossRefGoogle Scholar
  35. Willmarth WW, Lu SS (1971) Structure of Reynolds stress near the wall. J Fluid Mech 55:65–92CrossRefGoogle Scholar
  36. Wu Y, Christensen KT (2010) Spatial structure of a turbulent boundary layer with irregular surface roughness. J Fluid Mech 655:380–418CrossRefGoogle Scholar
  37. Zhou J, Adrian RJ, Balachandar S, Kendall TM (1999) Mechanisms for generating coherent packets of hairpin vortices in channel flow. J Fluid Mech 287:353–396CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Hiroshi Takimoto
    • 1
    Email author
  • Atsushi Inagaki
    • 2
  • Manabu Kanda
    • 2
  • Ayumu Sato
    • 1
  • Takenobu Michioka
    • 1
  1. 1.Environmental Science Research LaboratoryCentral Research Institute of Electric Power IndustryChibaJapan
  2. 2.Department of International Development EngineeringTokyo Institute of TechnologyTokyoJapan

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