# Determining Longitudinal Integral Turbulence Scales in the Near-Neutral Atmospheric Surface Layer

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## Abstract

We briefly assess approaches used to date for the estimation of the longitudinal integral turbulence scale \(L_u^x\) in the near-neutral atmospheric surface layer, and propose an approach based on recent theory and measurements. A closed-form expression is derived according to which \(L_u^x\) is proportional to the height *z* above the surface. The factor of proportionality depends upon two non-dimensional parameters: the measured lowest Monin frequency \(f_s\) for which the non-dimensional spectrum conforms to Kolmogorovs two-thirds law, and the ratio \(\beta = \overline{u^2}/{u_{*}^2}\), where \(\overline{u^2}\) and \(u_{*}\) denote the mean square value of the longitudinal velocity fluctuations and the friction velocity, respectively.

## Keywords

Atmospheric surface layer Integral length scale Monin frequency Neutral stratification Turbulence spectra.## References

- ASCE/SEI, (2012) Wind tunnel testing for buildings and other structures. ASCE/SEI. American Society of Civil Engineers/Structural Engineering Institute, Reston, VA, pp 49–12Google Scholar
- Banerjee T, Katul G (2013) Logarithmic scaling in the longitudinal velocity variance explained by a spectral budget. Phys Fluids 25(12):125,106CrossRefGoogle Scholar
- Banerjee T, Katul G, Salesky S, Chamecki M (2015) Revisiting the formulations for the longitudinal velocity variance in the unstable atmospheric surface layer. Q J R Meteorol Soc 141(690):1699–1711CrossRefGoogle Scholar
- Banerjee T, Li D, Juang JY, Katul G (2016) A spectral budget model for the longitudinal turbulent velocity in the stable atmospheric surface layer. J Atmos Sci 73(1):145–166CrossRefGoogle Scholar
- Biétry J, Sacré C, Simiu E (1978) Mean wind profiles and changes of terrain roughness. J Str Div ASCE 104:1585–1593Google Scholar
- Carlotti P (2002) Two-point properties of atmospheric turbulence very close to the ground: comparison of a high resolution les with theoretical models. Boundary-Layer Meteorol 104(3):381–410CrossRefGoogle Scholar
- Counihan J (1975) Adiabatic atmospheric boundary layers: a review and analysis of data from the period 1880–1972. Atmos Environ 9:871–905CrossRefGoogle Scholar
- Davenport AG (1961) The spectrum of horizontal gustiness near the ground in high winds. Q J R Meteorol Soc 87:194–211CrossRefGoogle Scholar
- Drobinsky P, Carlotti P, Newsom RK, Banta RM, Foster RC, Redelsperger JL (2004) The structure of the near-neutral atmospheric surface layer. J Atmos Sci 61:699–714CrossRefGoogle Scholar
- Harris R (1990) Some further thoughts on the spectrum of gustiness in strong winds. J Wind Eng Ind Aerodyn 33(3):461–477CrossRefGoogle Scholar
- Ho TCE, Surry D, Morrish DP (2003) NIST/TTU cooperative agreement - windstorm mitigation initiative: Wind tunnel experiments on generic low buildings. National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD, Tech Rep BLWT-SS20-2003Google Scholar
- Högström U, Hunt J, Smedman AS (2002) Theory and measurements for turbulence spectra and variances in the atmospheric neutral surface layer. Boundary-Layer Meteorol 103(1):101–124CrossRefGoogle Scholar
- Hunt JCR, Carlotti P (2001) Statistical structure at the wall of the high reynolds number turbulent boundary layer. Flow Turbul Combust 66:453–475CrossRefGoogle Scholar
- Kaimal JC, Wyngaard JC, Izumi Y, Coté OR (1972) Spectral characteristics of surface-layer turbulence. Q J R Meteorol Soc 98:563–589CrossRefGoogle Scholar
- Katul G, Chu CR (1998) A theoretical and experimental investigation of energy-containing scales in the dynamic sublayer of boundary-layer flows. Boundary-Layer Meteorol 86(2):279–312CrossRefGoogle 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(1):21–46CrossRefGoogle Scholar
- Panofsky HA, Dutton JA (1984) Atmospheric turbulence: models and methods for engineering applications. Wiley-Interscience, New YorkGoogle Scholar
- Pasquill F, Butler HE (1964) A note on determining the scale of turbulence. Q J R Meteorol Soc 90:79–84CrossRefGoogle Scholar
- Richards P, Fong S, Hoxey R (1997) Anisotropic turbulence in the atmospheric surface layer. J Wind Eng Ind Aerodyn 69:903–913CrossRefGoogle Scholar
- Stull R (2015) Practical meteorology. An algebra-based survey of atmospheric science. University of British Columbia, ColumbiaGoogle Scholar
- Tchen C (1953) On the spectrum of energy in turbulent shear flow. J Res Natl Bur Stand pp 51–62Google Scholar
- Tchen CM (1954) Transport processes as foundations of the Heisenberg and Obukhoff theories of turbulence. Phys Rev 93(1):4CrossRefGoogle Scholar
- von Kármán T (1948) Progress in the statistical theory of turbulence. Proc Natl Acad Sci 34(11):530–539CrossRefGoogle Scholar