Skip to main content
SpringerLink
Log in

Eulerian and Lagrangian time scales of the turbulence above staggered arrays of cubical obstacles

  • Original Article
  • Published:
Environmental Fluid Mechanics Aims and scope Submit manuscript

Abstract

We present results from water-channel experiments on neutrally-stable turbulent flows over staggered arrays of cubical obstacles modelling idealised urban canopies. Attention is concentrated on the vertical profiles of the Eulerian (TE) and Lagrangian (TL) time scales of the turbulence above three canopies with different plan area fractions (λP = 0.1, 0.25 and 0.4). The results show that both the streamwise and vertical components of TL increase approximately linearly with height above the obstacles, supporting Raupach’s linear law. The comparisons with the Lagrangian time scales over canyon-type canopies in the skimming flow and wake interference regimes show that the staggered configuration of cubical obstacles increases the streamwise TL, while decreasing its vertical counterpart. A good agreement has also been found between the eddy viscosities (KT) estimated by applying Taylor’s theory and the classical first order closure relating the momentum flux to the velocity gradient. The results show that KT obeys Prandtl’s theory, particularly for λP = 0.25 and 0.4.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Di Bernardino A, Monti P, Leuzzi G, Querzoli G (2017) Water-channel estimation of Eulerian and Lagrangian time scales of the turbulence in idealized two-dimensional urban canopies. Bound-Layer Meteorol 165:251–276

    Google Scholar 

  2. Thomson DJ (1987) Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J Fluid Mech 180:529–556

    Google Scholar 

  3. Hanna SR (1981) Lagrangian and Eulerian time-scale in the daytime boundary layer. J Appl Meteorol 20:242–249

    Google Scholar 

  4. Anfossi D, Rizza U, Mangia C, Degrazia GA, Pereira Marques Filho E (2006) Estimation of the ratio between the Lagrangian and Eulerian time scales in an atmospheric boundary layer generated by large eddy simulation. Atmos Environ 40:326–337

    Google Scholar 

  5. Corrsin S (1963) Estimates of the relations between Eulerian and Lagrangian scales in large Reynolds number turbulence. J Atmos Sci 20:115–119

    Google Scholar 

  6. Mortarini L, Ferrero E, Falabino S, Trini Castelli S, Richiardone R, Anfossi D (2013) Low-frequency processes and turbulence structure in a perturbed boundary layer. Q J R Meteorol Soc 139:1059–1072

    Google Scholar 

  7. Harman IN, Böhm JJ Finnigan, Hughes D (2016) Spatial variability of the flow and turbulence within a model canopy. Bound-Layer Meteorol 160:357–396

    Google Scholar 

  8. Poggi D, Katul GG, Cassiani M (2008) On the anomalous behavior of the Lagrangian structure function similarity constant inside dense canopies. Atmos Environ 42:4212–4231

    Google Scholar 

  9. Haverd V, Leuning R, Griffith D, van Gorsel E, Cuntz M (2009) The turbulent Lagrangian time scale in forest canopies constrained by fluxes, concentrations and source distributions. Boundary-Layer Meteorol 130:209–228

    Google Scholar 

  10. Dallman A, Di Sabatino S, Fernando HJS (2013) Flow and turbulence in an industrial/suburban roughness canopy. Environ Fluid Mech 13:279–307

    Google Scholar 

  11. Castro IP, Cheng H, Reynolds R (2006) Turbulence over urban-type roughness: deductions from wind-tunnel measurements. Bound-Layer Meteorol 118:109–131

    Google Scholar 

  12. Raupach MR (1989) Applying Lagrangian fluid mechanics to infer scalar source distributions from concentration profiles in plant canopies. Agric For Meteorol 47:85–108

    Google Scholar 

  13. Taylor GI (1921) Diffusion by continuous movements. Proc Lond Math Soc 20:196

    Google Scholar 

  14. Rotach MW (1999) On the influence of the urban roughness sublayer on turbulence and dispersion. Atmos Environ 33:4001–4008

    Google Scholar 

  15. Roth M, Inagaki A, Sugawara H, Kanda M (2015) Small-scale spatial variability of turbulence statistics, (co)spectra and turbulent kinetic energy measured over a regular array of cube roughness. Environ Fluid Mech 15:329–348

    Google Scholar 

  16. Nosek S, Kukačka L, Kellnerova R, Jurčàkovà K, Jaňour Z (2016) Ventilation processes in a three-dimensional street canyon. Bound-Layer Meteorol 159:259–284

    Google Scholar 

  17. Buccolieri R, Vigö H, Sandberg N, Di Sabatino S (2017) Direct measurements of the drag force over aligned arrays of cubes exposed to boundary-layer flows. Environ Fluid Mech 17:373–394

    Google Scholar 

  18. Monnier B, Goudarzi SA, Vinuesa R, Wark C (2018) Turbulent structure of a simplified urban fluid flow studied through stereoscopic particle image velocimetry. Bound-Layer Meteorol 166:239–268

    Google Scholar 

  19. Tomas JM, Eisma HE, Pourquie MJBM, Elsinga GE, Jonker HJJ, Westerweel J (2017) Pollutant dispersion in boundary layers exposed to rural-to-urban transitions: varying the spanwise length scale of the roughness. Bound-Layer Meteorol 163:225–251

    Google Scholar 

  20. Castro IP, Xie Z-T, Fuka V, Robins AG, Carpentieri M, Hayden P, Hertwig D, Coceal O (2017) Measurements and computations of flow in an urban street system. Bound-Layer Meteorol 162:207–230

    Google Scholar 

  21. Saeedi M, Wang B-C (2017) Large-eddy simulation of turbulent flow and structures within and above an idealized building array. Environ Fluid Mech 17:1127–1152

    Google Scholar 

  22. Goulart EV, Coceal O, Belcher SE (2018) Dispersion of a passive scalar within and above an urban street network. Bound-Layer Meteorol 166:351–366

    Google Scholar 

  23. Grimmond CSB, Oke TR (1999) Aerodynamic properties of urban areas derived from analysis of urban surface form. J Appl Meteorol 38:1261–1292

    Google Scholar 

  24. Coceal O, Thomas TG, Castro IP, Belcher SE (2006) Mean flow and turbulence statistics over groups of urban-like obstacles. Bound-Layer Meteorol 121:491–519

    Google Scholar 

  25. Takimoto H, Sato A, Barlow JF, Moriwaki R, Inagaki A, Onomura S, Kanda M (2011) Particle image velocimetry measurements of turbulent flow in outdoor and indoor urban scale models and flushing motions in urban canopy layers. Bound-Layer Meteorol 140:295–314

    Google Scholar 

  26. Coceal O, Goulart EV, Branford S, Thomas TG, Belcher SE (2014) Flow structure and near-field dispersion in arrays of building-like obstacles. J Wind Eng Ind Aerodyn 125:52–68

    Google Scholar 

  27. Belcher SE, Coceal O, Goulart EV, Rudd AC, Robins AG (2015) Process controlling atmospheric dispersion through city centers. J Fluid Mech 763:51–81

    Google Scholar 

  28. Huq P, Franzese P (2013) Measurements of turbulence and dispersion in three idealized urban canopies with different aspect ratios and comparisons with a Gaussian plume model. Bound-Layer Meteorol 147:103–121

    Google Scholar 

  29. Orlandi P, Leonardi S (2006) DNS of turbulent channel flows with two- and three-dimensional roughness. J Turbul. https://doi.org/10.1080/14685240600827526

    Article  Google Scholar 

  30. Carpentieri M, Robins AG (2015) Influence of urban morphology on air flow over building arrays. J Wind Eng Ind Aerod 145:61–74

    Google Scholar 

  31. Salvati A, Monti P, Coch Roura H, Cecere C (2019) Climatic performance of urban textures: analysis tools for a Mediterranean urban context. Energy Build 185:162–179

    Google Scholar 

  32. Di Bernardino A, Monti P, Leuzzi G, Querzoli G (2015) Water-channel study of flow and turbulence past a two-dimensional array of obstacles. Bound-Layer Meteorol 155:73–85

    Google Scholar 

  33. Tomasi C, Kanade T (1991) Detection and tracking of point. Detection and tracking of point features. Carnegie Mellon University Technical Report CMU-CS-91–132

  34. Cenedese A, Del Prete Z, Miozzi M, Querzoli G (2005) A laboratory investigation of the flow in the left ventricle of a human heart with prosthetic, tilting-disk valves. Exp Fluids 39:322–335

    Google Scholar 

  35. Lucas BD, Kanade T (1981) An iterative image registration technique with an application to stereo vision. In: Proceedings of the 1981 DARPA imaging understanding workshop, Washington, DC, April 1981, pp 121–130

  36. Shi J, Tomasi C (1994) Good features to track. In: Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR’94), Seattle, Washington

  37. Querzoli G (1996) A Lagrangian study of particle dispersion in the unstable boundary layer. Atmos Environ 30:282–291

    Google Scholar 

  38. Bendat JS, Piersol AG (2011) Random data: analysis and measurement procedures. Wiley, Hoboken

    Google Scholar 

  39. Monin AS, Yaglom AM (1971) Statistical fluid mechanics, vol 1. MIT Press, Cambridge

    Google Scholar 

  40. Wang QZ, Squires KD, Wu X (1995) Lagrangian statistics in turbulent channel flows. Atmos Environ 29:2417–2427

    Google Scholar 

  41. Guala M, Liberzon A, Tsinober A, Kinzelbach W (2007) An experimental investigation on Lagrangian correlations of small-scale turbulence at low Reynolds number. J Fluid Mech 574:405–427

    Google Scholar 

  42. Cheng H, Castro IP (2002) Near wall flow over urban-like roughness. Bound-Layer Meteorol 104:229–259

    Google Scholar 

  43. Finnigan J (2000) Turbulence in plant canopies. Annu Rev Fluid Mech 32:519–571

    Google Scholar 

  44. Salizzoni P, Marro M, Soulhac L, Grosjean N, Perkins RJ (2011) Turbulent transfer between street canyons and the overlying atmospheric boundary layer. Bound-Layer Meteorol 141:393–414

    Google Scholar 

  45. Pelliccioni A, Monti P, Leuzzi G (2016) Wind-speed profile and roughness sublayer depth modelling in urban boundary layers. Bound-Layer Meteorol 160:225–248

    Google Scholar 

  46. Snyder WH (1972) Similarity Criteria for the application of fluid models to the study of air pollution meteorology. Bound-Layer Meteorol 3:113–134

    Google Scholar 

  47. Uehara K, Wakamatsu S, Ooka R (2003) Studies on critical Reynolds number indices for wind-tunnel experiments on flow within urban areas. Bound-Layer Meteorol 107:353–370

    Google Scholar 

  48. Leonardi S, Castro IP (2010) Channel flow over large cube roughness: a direct numerical simulation study. J Fluid Mech 651:519–539

    Google Scholar 

  49. Jimenez J (2004) Turbulent flows over rough walls. Annu Rev Fluid Mech 36:173–196

    Google Scholar 

  50. Leonardi S, Orlandi P, Djenidi L, Antonia RA (2004) Structure of turbulent channel flow with square bars on one wall. Int J Heat Fluid Flow 25:384–392

    Google Scholar 

  51. Leonardi S, Orlandi P, Antonia RA (2007) Properties of d- and k-type roughness in a turbulent channel flow. Phys Fluids 19:125101

    Google Scholar 

  52. Pasquill F (1974) Atmospheric diffusion. Wiley, New York, p 429

    Google Scholar 

  53. Michioka T, Sato A, Takimoto H, Kanda M (2011) Large-Eddy simulation for the mechanism of pollutant removal from a two-dimensional street canyon. Bound-Layer Meteorol 138:195–213

    Google Scholar 

  54. Badas MG, Querzoli G (2011) Spatial structures and scaling in the convective bound layer. Exp Fluids 50:1093–1107

    Google Scholar 

  55. Reynolds RT, Castro IP (2008) Measurements in an urban-type boundary layer. Exp Fluids 45:141–156

    Google Scholar 

  56. Badas MG, Ferrari S, Garau M, Querzoli G (2017) On the effect of gable roof on natural ventilation in two-dimensional urban canyons. J Wind Eng Ind Aerodyn 162:24–34

    Google Scholar 

  57. Ferrari S, Badas MG, Garau M et al (2017) The air quality in narrow two-dimensional urban canyons with pitched and flat roof buildings. Int J Environ Pollut 62:347–368

    Google Scholar 

  58. Garau M, Badas MG, Ferrari S et al (2018) Turbulence and air exchange in a two-dimensional urban street canyon between gable roof buildings. Bound-Layer Meteorol 167:123–143

    Google Scholar 

  59. Di Bernardino A, Monti P, Leuzzi G, Querzoli G (2018) Pollutant fluxes in two-dimensional urban canopies. Urban Clim 24:80–93

    Google Scholar 

  60. Leuning R, Denmead OT, Miyata A, Kim J (2000) Source/sink distributions of heat, water vapour, carbon dioxide and methane in a rice canopy estimated using Lagrangian dispersion analysis. Agric For Meteorol 104:233–249

    Google Scholar 

  61. Brunet Y, Finnigan JJ, Raupach MR (1994) A wind tunnel study of air flow in waving wheat: single-point velocity statistics. Bound-Layer Meteorol 70:95–132

    Google Scholar 

  62. Kanda M, Inagaki A, Miyamoto T, Gryschka M, Raasch S (2013) A new aerodynamic parametrization for real urban surfaces. Bound-Layer Meteorol 148:357–377

    Google Scholar 

  63. Koeltzsch K (1999) On the relationship between the Lagrangian and Eulerian time scale. Atmos Environ 33:117–128

    Google Scholar 

  64. Foken T (2008) Micrometeorology. Springer, Berlin

    Google Scholar 

Download references

Acknowledgements

This research was supported by the RG11715C7D43B2B6 fund from the University of Rome “La Sapienza”. The assistance of Manuel Mastrangelo and Cristina Grossi (Master degree students at the University of Rome “La Sapienza”) to the measurements was greatly appreciated.

Author information

Authors and Affiliations

  1. Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, 00185, Rome, Italy

    Annalisa Di Bernardino

  2. DICEA, Università di Roma “La Sapienza”, Via Eudossiana 18, 00184, Rome, Italy

    Paolo Monti & Giovanni Leuzzi

  3. DICAAR, Università degli Studi di Cagliari, Via Marengo 2, 09123, Cagliari, Italy

    Giorgio Querzoli

Authors
  1. Annalisa Di Bernardino
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paolo Monti
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Giovanni Leuzzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Giorgio Querzoli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paolo Monti.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Di Bernardino, A., Monti, P., Leuzzi, G. et al. Eulerian and Lagrangian time scales of the turbulence above staggered arrays of cubical obstacles. Environ Fluid Mech 20, 987–1005 (2020). https://doi.org/10.1007/s10652-020-09736-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10652-020-09736-8

Keywords

Search

Navigation