Applicability of Taylor’s Hypothesis for Estimating the Mean Streamwise Length Scale of Large-Scale Structures in the Near-Neutral Atmospheric Surface Layer

  • GuoWen Han
  • GuoHua Wang
  • XiaoJing ZhengEmail author
Research Article


A field investigation of the mean streamwise length scale Lx of large-scale structures and the convection velocity is performed in a high-Reynolds-number (Reτ ~ 106) atmospheric surface layer (ASL). Based on selected high-quality synchronous data obtained at different streamwise positions, the length scale Lx and global convection velocity Uc are extracted in the logarithmic region of the near-neutral ASL at heights of 0.9 m, 1.71 m, 3.5 m, and 5 m. It is found that Uc values are approximately 16% greater than the local mean streamwise velocity component U, and the value of Lx obtained from spatially-separated measurements is greater than the results estimated from Taylor’s hypothesis using the value of U at the four heights. The mean relative difference between the value of Lx and the results estimated by Taylor’s hypothesis using the value of U is approximately 15%. However, the relative difference between the value of Lx and the results estimated from Taylor’s hypothesis using the convection velocity Uc instead of the mean streamwise velocity component U is reduced to 1 ± 6% (≈ zero). Thus, the convection velocity Uc is more appropriate than the mean streamwise velocity component U in obtaining Lx values in the near-neutral ASL.


Atmospheric surface layer Convection velocity Large-scale structures Streamwise length scale Taylor’s hypothesis 



This work was supported financially by grants from the National Natural Science Foundation of China (11490553, 11702122, and 11421062), and the Fundamental Research Funds for the Central Universities (lzujbky–2017–30). The authors would like to express their sincere appreciation for the support as well as the helpful comments from referees that led to a significant improvement in our work.


  1. Abe H, Kawamura H, Choi H (2004) Very large-scale structures and their effects on the wall shear-stress fluctuations in a turbulent channel flow up to Re τ = 640. J Fluid Eng 126:835–843CrossRefGoogle Scholar
  2. Anderson W, Meneveau C (2010) A large-eddy simulation model for boundary-layer flow over surfaces with horizontally resolved but vertically unresolved roughness elements. Boundary-Layer Meteorol 137:397–415CrossRefGoogle Scholar
  3. Anderson WC, Basu S, Letchford CW (2007) Comparison of dynamic subgrid-scale models for simulations of neutrally buoyant shear-driven atmospheric boundary layer flows. Environ Fluid Mech 7:195–215CrossRefGoogle Scholar
  4. Anderson W, Passalacqua P, Porté-Agel F, Meneveau C (2012) Large-eddy simulation of atmospheric boundary-layer flow over fluvial-like landscapes using a dynamic roughness model. Boundary-Layer Meteorol 144:263–286CrossRefGoogle Scholar
  5. Atkinson C, Buchmann NA, Soria J (2015) An experimental investigation of turbulent convection velocities in a turbulent boundary layer Flow. Flow Turbul Combust 94:79–95CrossRefGoogle Scholar
  6. Balakumar B, Adrian R (2007) Large-and very-large-scale motions in channel and boundary-layer flows. Philos Trans R Soc A 365:665–681CrossRefGoogle Scholar
  7. Bou-Zeid E, Higgins C, Huwald H, Meneveau C, Parlange MB (2010) Field study of the dynamics and modelling of subgrid-scale turbulence in a stable atmospheric surface layer over a glacier. J Fluid Mech 665:480–515CrossRefGoogle Scholar
  8. Calaf M, Hultmark M, Oldroyd H, Simeonov V, Parlange M (2013) Coherent structures and the k −1 spectral behaviour. Phys Fluids 25:125107CrossRefGoogle Scholar
  9. Choi H, Moin P (1990) On the space–time characteristics of wall-pressure fluctuations. Phys Fluids A 2:1450–1460CrossRefGoogle Scholar
  10. Clauser FH (1956) The turbulent boundary layer. Adv Appl Mech 4:1–51CrossRefGoogle Scholar
  11. Claussen M (1985) A model of turbulence spectra in the atmospheric surface layer. Boundary-Layer Meteorol 33:151–172CrossRefGoogle Scholar
  12. Coleman HW, Steele WG (2009) Experimentation, validation, and uncertainty analysis for engineers. Wiley, New YorkCrossRefGoogle Scholar
  13. Davidson P, Nickels T, Krogstad P-Å (2006) The logarithmic structure function law in wall-layer turbulence. J Fluid Mech 550:51–60CrossRefGoogle Scholar
  14. Davies P, Fisher M, Barratt M (1963) The characteristics of the turbulence in the mixing region of a round jet. J Fluid Mech 15:337–367CrossRefGoogle Scholar
  15. de Kat R, Ganapathisubramani B (2015) Frequency-wavenumber mapping in turbulent shear flows. J Fluid Mech 783:166–190CrossRefGoogle Scholar
  16. Del Álamo JC, Jiménez J (2009) Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J Fluid Mech 640:5–26CrossRefGoogle Scholar
  17. Dennis DJ, Nickels TB (2008) On the limitations of Taylor’s hypothesis in constructing long structures in a turbulent boundary layer. J Fluid Mech 614:197–206CrossRefGoogle Scholar
  18. Dennis DJ, Nickels TB (2011a) Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 1. Vortex packets. J Fluid Mech 673:180–217CrossRefGoogle Scholar
  19. Dennis DJ, Nickels TB (2011b) Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 2. Long structures. J Fluid Mech 673:218–244CrossRefGoogle Scholar
  20. Falco R (1977) Coherent motions in the outer region of turbulent boundary layers. Phys Fluids 20:S124–S132CrossRefGoogle Scholar
  21. Fang J, Porté-Agel F (2015) Large-eddy simulation of very-large-scale motions in the neutrally stratified atmospheric boundary layer. Boundary-Layer Meteorol 155:397–416CrossRefGoogle Scholar
  22. Favre A, Gaviglio J, Dumas R (1957) Space–time double correlations and spectra in a turbulent boundary layer. J Fluid Mech 2:313–342CrossRefGoogle Scholar
  23. Favre A, Gaviglio J, Dumas R (1958) Further space–time correlations of velocity in a turbulent boundary layer. J Fluid Mech 3:344–356CrossRefGoogle Scholar
  24. Foken T, Göckede M, Mauder M, Mahrt L, Amiro B, Munger W (2004) Post-field data quality control. In: Lee X, Massman WJ, Law BE (eds) Handbook of micrometeorology. A guide for surface flux measurements, Kluwer, Dordrecht, pp 181–208Google Scholar
  25. Ganapathisubramani B, Hutchins N, Hambleton W, Longmire E, Marusic I (2005) Investigation of large-scale coherence in a turbulent boundary layer using two-point correlations. J Fluid Mech 524:57–80CrossRefGoogle Scholar
  26. Geng C, He G, Wang Y, Xu C, Lozano-Durán A, Wallace JM (2015) Taylor’s hypothesis in turbulent channel flow considered using a transport equation analysis. Phys Fluids 27:025111CrossRefGoogle Scholar
  27. Goldschmidt V, Young M, Ott E (1981) Turbulent convective velocities (broadband and wavenumber dependent) in a plane jet. J Fluid Mech 105:327–345CrossRefGoogle Scholar
  28. Grant H (1958) The large eddies of turbulent motion. J Fluid Mech 4:149–190CrossRefGoogle Scholar
  29. Guala M, Hommema S, Adrian R (2006) Large-scale and very-large-scale motions in turbulent pipe flow. J Fluid Mech 554:521–542CrossRefGoogle Scholar
  30. Guala M, Metzger M, McKeon B (2011) Interactions within the turbulent boundary layer at high Reynolds number. J Fluid Mech 666:573–604CrossRefGoogle Scholar
  31. He G, Jin G, Yang Y (2017) Space–time correlations and dynamic coupling in turbulent flows. Annu Rev Fluid Mech 49:51–70CrossRefGoogle Scholar
  32. Higgins CW, Froidevaux M, Simeonov V, Vercauteren N, Barry C, Parlange MB (2012) The effect of scale on the applicability of Taylor’s frozen turbulence hypothesis in the atmospheric boundary layer. Boundary-Layer Meteorol 143:379–391CrossRefGoogle Scholar
  33. Högström U (1990) Analysis of turbulence structure in the surface layer with a modified similarity formulation for near neutral conditions. J Atmos Sci 47:1949–1972CrossRefGoogle Scholar
  34. Hunt JC, Morrison JF (2000) Eddy structure in turbulent boundary layers. Eur J Mech (B/Fluids) 19:673–694CrossRefGoogle Scholar
  35. Hutchins N, Marusic I (2007a) Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J Fluid Mech 579:1–28CrossRefGoogle Scholar
  36. Hutchins N, Marusic I (2007b) Large-scale influences in near-wall turbulence. Philos Trans R Soc A 365:647–664CrossRefGoogle Scholar
  37. Hutchins N, Monty J, Ganapathisubramani B, Ng H, Marusic I (2011) Three-dimensional conditional structure of a high-Reynolds-number turbulent boundary layer. J Fluid Mech 673:255–285CrossRefGoogle Scholar
  38. Hutchins N, Chauhan K, Marusic I, Monty J, Klewicki J (2012) Towards reconciling the large-scale structure of turbulent boundary layers in the atmosphere and laboratory. Boundary-Layer Meteorol 145:273–306CrossRefGoogle Scholar
  39. Jacob C, Anderson W (2016) Conditionally averaged large-scale motions in the neutral atmospheric boundary layer: insights for aeolian processes. Boundary-Layer Meteorol 162:21–41CrossRefGoogle Scholar
  40. Kader B, Yaglom A (1991) Spectra and correlation functions of surface layer atmospheric turbulence in unstable thermal stratification. In: Métais O, Lesieur M (eds) Turbulence and coherent structures. Kluwer Academic Publication, Dordrecht, pp 387–412CrossRefGoogle Scholar
  41. Kaimal J (1978) Horizontal velocity spectra in an unstable surface layer. J Atmos Sci 35:18–24CrossRefGoogle Scholar
  42. Kaimal JC, Finnigan JJ (1994) Atmospheric boundary layer flows: their structure and measurement. Oxford University Press, OxfordGoogle Scholar
  43. Katul G, Chu C-R (1998) A theoretical and experimental investigation of energy-containing scales in the dynamic sublayer of boundary-layer flows. Boundary-Layer Meteorol 86:279–312CrossRefGoogle Scholar
  44. Kim K, Adrian R (1999) Very large-scale motion in the outer layer. Phys Fluids 11:417–422CrossRefGoogle Scholar
  45. Kim J, Hussain F (1993) Propagation velocity of perturbations in turbulent channel flow. Phys Fluids A Fluid Dyn 5:695–706CrossRefGoogle Scholar
  46. Krogstad P-Å, Kaspersen J, Rimestad S (1998) Convection velocities in a turbulent boundary layer. Phys Fluids 10:949–957CrossRefGoogle Scholar
  47. Kunkel GJ, Marusic I (2006) Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using an atmospheric flow. J Fluid Mech 548:375–402CrossRefGoogle Scholar
  48. Lauren MK, Menabde M, Seed AW, Austin GL (1999) Characterisation and simulation of the multiscaling properties of the energy-containing scales of horizontal surface-layer winds. Boundary-Layer Meteorol 90:21–46CrossRefGoogle Scholar
  49. Lee JH, Sung HJ (2011) Very-large-scale motions in a turbulent boundary layer. J Fluid Mech 673:80–120CrossRefGoogle Scholar
  50. Li Q, Zhi L, Hu F (2010) Boundary layer wind structure from observations on a 325 m tower. J Wind Eng Ind Aerodyn 98:818–832CrossRefGoogle Scholar
  51. Ligrani PM, Moffat RJ (1986) Structure of transitionally rough and fully rough turbulent boundary layers. J Fluid Mech 162:69–98CrossRefGoogle Scholar
  52. Lin C (1953) On Taylor’s hypothesis and the acceleration terms in the Navier–Stokes equation. Quart Appl Math 10:295–306CrossRefGoogle Scholar
  53. Liu H-Y, Bo T-L, Liang Y-R (2017a) The variation of large-scale structure inclination angles in high Reynolds number atmospheric surface layers. Phys Fluids 29:035104CrossRefGoogle Scholar
  54. Liu H, Wang G, Zheng X (2017b) Spatial length scales of large-scale structures in atmospheric surface layers. Phys Rev Fluids 2:064606CrossRefGoogle Scholar
  55. Lumley J (1965) Interpretation of time spectra measured in high-intensity shear flows. Phys Fluids 8:1056–1062CrossRefGoogle Scholar
  56. Marusic I, Kunkel GJ (2003) Streamwise turbulence intensity formulation for flat-plate boundary layers. Phys Fluids 15:2461–2464CrossRefGoogle Scholar
  57. Marusic I, McKeon B, Monkewitz P, Nagib H, Smits A, Sreenivasan K (2010) Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys Fluids 22:065103CrossRefGoogle Scholar
  58. Marusic I, Monty JP, Hultmark M, Smits AJ (2013) On the logarithmic region in wall turbulence. J Fluid Mech 713:R3CrossRefGoogle Scholar
  59. Metzger M, McKeon B, Holmes H (2007) The near-neutral atmospheric surface layer: turbulence and non-stationarity. Philos Trans R Soc A 365:859–876CrossRefGoogle Scholar
  60. Moin P (2009) Revisiting Taylor’s hypothesis. J Fluid Mech 640:1–4CrossRefGoogle Scholar
  61. Monin AS, Yaglom AM (2013) Statistical fluid mechanics, volume II: mechanics of turbulence, vol 2. Courier Corporation, ChelmsfordGoogle Scholar
  62. Monty J, Chong M (2009) Turbulent channel flow: comparison of streamwise velocity data from experiments and direct numerical simulation. J Fluid Mech 633:461–474CrossRefGoogle Scholar
  63. Monty J, Stewart J, Williams R, Chong M (2007) Large-scale features in turbulent pipe and channel flows. J Fluid Mech 589:147–156CrossRefGoogle Scholar
  64. Pope SB (2001) Turbulent flows. IOP Publishing, BristolGoogle Scholar
  65. Powell DC, Elderkin C (1974) An investigation of the application of Taylor’s hypothesis to atmospheric boundary layer turbulence. J Atmos Sci 31:990–1002CrossRefGoogle Scholar
  66. Renard N, Deck S (2015) On the scale-dependent turbulent convection velocity in a spatially developing flat plate turbulent boundary layer at Reynolds number Re θ = 13000. J Fluid Mech 775:105–148CrossRefGoogle Scholar
  67. Robinson SK (1991) Coherent motions in the turbulent boundary layer. Annu Rev Fluid Mech 23:601–639CrossRefGoogle Scholar
  68. Sillero JA, Jiménez J, Moser RD (2014) Two-point statistics for turbulent boundary layers and channels at Reynolds numbers up to δ + ≈ 2000. Phys Fluids 26:105109CrossRefGoogle Scholar
  69. Taylor GI (1938) The spectrum of turbulence. Proc R Soc Lond A 164:476–490CrossRefGoogle Scholar
  70. Tennekes H, Lumley JL (1972) A first course in turbulence. MIT Press, CambridgeGoogle Scholar
  71. Thuillier R, Lappe U (1964) Wind and temperature profile characteristics from observations on a 1400 ft tower. J Appl Meteorol 3:299–306CrossRefGoogle Scholar
  72. Townsend AA (1976) The structure of turbulent shear flow. Cambridge University Press, CambridgeGoogle Scholar
  73. Tutkun M, George WK, Delville J, Stanislas M, Johansson P, Foucaut J-M, Coudert S (2009) Two-point correlations in high Reynolds number flat plate turbulent boundary layers. J Turbul 10:N21CrossRefGoogle Scholar
  74. Vallikivi M, Ganapathisubramani B, Smits A (2015) Spectral scaling in boundary layers and pipes at very high Reynolds numbers. J Fluid Mech 771:303–326CrossRefGoogle Scholar
  75. Volino R, Schultz M, Flack K (2007) Turbulence structure in rough-and smooth-wall boundary layers. J Fluid Mech 592:263–293CrossRefGoogle Scholar
  76. Wang G, Zheng X (2016) Very large scale motions in the atmospheric surface layer: a field investigation. J Fluid Mech 802:464–489CrossRefGoogle Scholar
  77. Wilczak JM, Oncley SP, Stage SA (2001) Sonic anemometer tilt correction algorithms. Boundary-Layer Meteorol 99:127–150CrossRefGoogle Scholar
  78. Wills J (1964) On convection velocities in turbulent shear flows. J Fluid Mech 20:417–432CrossRefGoogle Scholar
  79. Wu X, Baltzer J, Adrian R (2012) Direct numerical simulation of a 30R long turbulent pipe flow at R += 685: large-and very large-scale motions. J Fluid Mech 698:235–281CrossRefGoogle Scholar
  80. Yang H, Bo T (2017) Scaling of wall-normal turbulence intensity and vertical eddy structures in the atmospheric surface layer. Boundary-Layer Meteorol 166:199–216CrossRefGoogle Scholar
  81. Zaman K, Hussain A (1981) Taylor hypothesis and large-scale coherent structures. J Fluid Mech 112:379–396CrossRefGoogle Scholar
  82. Zheng X, Zhang J, Wang G, Liu H, Zhu W (2013) Investigation on very large scale motions (VLSMs) and their influence in a dust storm. Sci China Phys Mech Astron 56:306–314CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Key Laboratory of Mechanics on Disaster and Environment in Western China, The Ministry of Education of China, Department of MechanicsLanzhou UniversityLanzhouChina
  2. 2.Research Center for Applied Mechanics, School of Mechano-Electronic EngineeringXidian UniversityXi’anChina
  3. 3.School of Civil EngineeringLanzhou Jiaotong UniversityLanzhouChina

Personalised recommendations