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

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## Abstract

A field investigation of the mean streamwise length scale *L*_{x} of large-scale structures and the convection velocity is performed in a high-Reynolds-number (*Re*_{τ} ~ 10^{6}) atmospheric surface layer (ASL). Based on selected high-quality synchronous data obtained at different streamwise positions, the length scale *L*_{x} and global convection velocity *U*_{c} 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 *U*_{c} values are approximately 16% greater than the local mean streamwise velocity component *U*, and the value of *L*_{x} 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 *L*_{x} and the results estimated by Taylor’s hypothesis using the value of *U* is approximately 15%. However, the relative difference between the value of *L*_{x} and the results estimated from Taylor’s hypothesis using the convection velocity *U*_{c} instead of the mean streamwise velocity component *U* is reduced to 1 ± 6% (≈ zero). Thus, the convection velocity *U*_{c} is more appropriate than the mean streamwise velocity component *U* in obtaining *L*_{x} values in the near-neutral ASL.

## Keywords

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

### Acknowledgements

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.

## References

- 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 - 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
- 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
- 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
- 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
- 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
- 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
- Calaf M, Hultmark M, Oldroyd H, Simeonov V, Parlange M (2013) Coherent structures and the
*k*^{−1}spectral behaviour. Phys Fluids 25:125107CrossRefGoogle Scholar - Choi H, Moin P (1990) On the space–time characteristics of wall-pressure fluctuations. Phys Fluids A 2:1450–1460CrossRefGoogle Scholar
- Clauser FH (1956) The turbulent boundary layer. Adv Appl Mech 4:1–51CrossRefGoogle Scholar
- Claussen M (1985) A model of turbulence spectra in the atmospheric surface layer. Boundary-Layer Meteorol 33:151–172CrossRefGoogle Scholar
- Coleman HW, Steele WG (2009) Experimentation, validation, and uncertainty analysis for engineers. Wiley, New YorkCrossRefGoogle Scholar
- Davidson P, Nickels T, Krogstad P-Å (2006) The logarithmic structure function law in wall-layer turbulence. J Fluid Mech 550:51–60CrossRefGoogle Scholar
- 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
- de Kat R, Ganapathisubramani B (2015) Frequency-wavenumber mapping in turbulent shear flows. J Fluid Mech 783:166–190CrossRefGoogle Scholar
- Del Álamo JC, Jiménez J (2009) Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J Fluid Mech 640:5–26CrossRefGoogle Scholar
- 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
- 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
- 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
- Falco R (1977) Coherent motions in the outer region of turbulent boundary layers. Phys Fluids 20:S124–S132CrossRefGoogle Scholar
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Grant H (1958) The large eddies of turbulent motion. J Fluid Mech 4:149–190CrossRefGoogle Scholar
- 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
- Guala M, Metzger M, McKeon B (2011) Interactions within the turbulent boundary layer at high Reynolds number. J Fluid Mech 666:573–604CrossRefGoogle Scholar
- He G, Jin G, Yang Y (2017) Space–time correlations and dynamic coupling in turbulent flows. Annu Rev Fluid Mech 49:51–70CrossRefGoogle Scholar
- 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
- 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
- Hunt JC, Morrison JF (2000) Eddy structure in turbulent boundary layers. Eur J Mech (B/Fluids) 19:673–694CrossRefGoogle Scholar
- 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
- Hutchins N, Marusic I (2007b) Large-scale influences in near-wall turbulence. Philos Trans R Soc A 365:647–664CrossRefGoogle Scholar
- 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
- 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
- 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
- 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
- Kaimal J (1978) Horizontal velocity spectra in an unstable surface layer. J Atmos Sci 35:18–24CrossRefGoogle Scholar
- Kaimal JC, Finnigan JJ (1994) Atmospheric boundary layer flows: their structure and measurement. Oxford University Press, OxfordGoogle Scholar
- 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
- Kim K, Adrian R (1999) Very large-scale motion in the outer layer. Phys Fluids 11:417–422CrossRefGoogle Scholar
- Kim J, Hussain F (1993) Propagation velocity of perturbations in turbulent channel flow. Phys Fluids A Fluid Dyn 5:695–706CrossRefGoogle Scholar
- Krogstad P-Å, Kaspersen J, Rimestad S (1998) Convection velocities in a turbulent boundary layer. Phys Fluids 10:949–957CrossRefGoogle Scholar
- 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
- 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
- Lee JH, Sung HJ (2011) Very-large-scale motions in a turbulent boundary layer. J Fluid Mech 673:80–120CrossRefGoogle Scholar
- 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
- Ligrani PM, Moffat RJ (1986) Structure of transitionally rough and fully rough turbulent boundary layers. J Fluid Mech 162:69–98CrossRefGoogle Scholar
- Lin C (1953) On Taylor’s hypothesis and the acceleration terms in the Navier–Stokes equation. Quart Appl Math 10:295–306CrossRefGoogle Scholar
- 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
- Liu H, Wang G, Zheng X (2017b) Spatial length scales of large-scale structures in atmospheric surface layers. Phys Rev Fluids 2:064606CrossRefGoogle Scholar
- Lumley J (1965) Interpretation of time spectra measured in high-intensity shear flows. Phys Fluids 8:1056–1062CrossRefGoogle Scholar
- Marusic I, Kunkel GJ (2003) Streamwise turbulence intensity formulation for flat-plate boundary layers. Phys Fluids 15:2461–2464CrossRefGoogle Scholar
- 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
- Marusic I, Monty JP, Hultmark M, Smits AJ (2013) On the logarithmic region in wall turbulence. J Fluid Mech 713:R3CrossRefGoogle Scholar
- 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
- Moin P (2009) Revisiting Taylor’s hypothesis. J Fluid Mech 640:1–4CrossRefGoogle Scholar
- Monin AS, Yaglom AM (2013) Statistical fluid mechanics, volume II: mechanics of turbulence, vol 2. Courier Corporation, ChelmsfordGoogle Scholar
- 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
- 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
- Pope SB (2001) Turbulent flows. IOP Publishing, BristolGoogle Scholar
- 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
- 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 - Robinson SK (1991) Coherent motions in the turbulent boundary layer. Annu Rev Fluid Mech 23:601–639CrossRefGoogle Scholar
- 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 - Taylor GI (1938) The spectrum of turbulence. Proc R Soc Lond A 164:476–490CrossRefGoogle Scholar
- Tennekes H, Lumley JL (1972) A first course in turbulence. MIT Press, CambridgeGoogle Scholar
- Thuillier R, Lappe U (1964) Wind and temperature profile characteristics from observations on a 1400 ft tower. J Appl Meteorol 3:299–306CrossRefGoogle Scholar
- Townsend AA (1976) The structure of turbulent shear flow. Cambridge University Press, CambridgeGoogle Scholar
- 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
- 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
- Volino R, Schultz M, Flack K (2007) Turbulence structure in rough-and smooth-wall boundary layers. J Fluid Mech 592:263–293CrossRefGoogle Scholar
- Wang G, Zheng X (2016) Very large scale motions in the atmospheric surface layer: a field investigation. J Fluid Mech 802:464–489CrossRefGoogle Scholar
- Wilczak JM, Oncley SP, Stage SA (2001) Sonic anemometer tilt correction algorithms. Boundary-Layer Meteorol 99:127–150CrossRefGoogle Scholar
- Wills J (1964) On convection velocities in turbulent shear flows. J Fluid Mech 20:417–432CrossRefGoogle Scholar
- 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 - 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
- Zaman K, Hussain A (1981) Taylor hypothesis and large-scale coherent structures. J Fluid Mech 112:379–396CrossRefGoogle Scholar
- 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