Asymptotic coefficients of the attached-eddy model derived from an adiabatic atmosphere

Qin, Yue; Katul, Gabriel G.; Liu, Heping; Li, Dan

doi:10.1017/jfm.2025.394

Asymptotic coefficients of the attached-eddy model derived from an adiabatic atmosphere

Journal Article · Tue May 13 00:00:00 EDT 2025 · Journal of Fluid Mechanics

DOI:https://doi.org/10.1017/jfm.2025.394· OSTI ID:2566008

; ; ;

The attached-eddy model (AEM) predicts that the mean streamwise velocity and streamwise velocity variance profiles follow a logarithmic shape, while the vertical velocity variance remains invariant with height in the overlap region of high Reynolds number wall-bounded turbulent flows. Moreover, the AEM coefficients are presumed to attain asymptotically constant values at very high Reynolds numbers. Here, the AEM predictions are examined using sonic anemometer measurements in the near-neutral atmospheric surface layer, with a focus on the logarithmic behaviour of the streamwise velocity variance. Utilizing an extensive 210-day dataset collected from a 62 m meteorological tower located in the Eastern Snake River Plain, Idaho, USA, the inertial sublayer is first identified by analysing the measured momentum flux and mean velocity profiles. The logarithmic behaviour of the streamwise velocity variance and the associated ‘ $-1$$ ’ scaling of the streamwise velocity energy spectra are then investigated. The findings indicate that the Townsend–Perry coefficient ( $$A_1$$ ) is influenced by mild non-stationarity that manifests itself as a Reynolds number dependence. After excluding non-stationary runs, and requiring the bulk Reynolds number defined using the atmospheric boundary layer height to be larger than $$4 \times 10^{7}$$ , the inferred $$A_1$$ converges to values ranging between 1 and 1.25, consistent with laboratory experiments. Furthermore, nine benchmark cases selected through a restrictive quality control reveal a close relation between the ‘ $$-1$$ ’ scaling in the streamwise velocity energy spectrum and the logarithmic behaviour of streamwise velocity variance. However, additional data are required to determine whether the plateau value of the pre-multiplied streamwise velocity energy spectrum is identical to $$A_1$ .

View Journal Article

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0022072

OSTI ID:: 2566008

Journal Information:: Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 1011; ISSN 0022-1120

Publisher:: Cambridge University Press (CUP)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

References (72)

Revisiting the formulations for the longitudinal velocity variance in the unstable atmospheric surface layer: Longitudinal Velocity Variance in Unstable Atmosphere Banerjee, T.; Katul, G. G.; Salesky, S. T. Quarterly Journal of the Royal Meteorological Society, Vol. 141, Issue 690 https://doi.org/10.1002/qj.2472	journal	November 2014
Structure of the PBL Wyngaard, John C. Lectures on Air Pollution Modeling https://doi.org/10.1007/978-1-935704-16-4_2	book	January 1988
Eddy Covariance Aubinet, Marc; Vesala, Timo; Papale, Dario https://doi.org/10.1007/978-94-007-2351-1	book	January 2012
A Note on the Businger-Dyer Profiles Businger, J. A. Topics in Micrometeorology. A Festschrift for Arch Dyer https://doi.org/10.1007/978-94-009-2935-7_11	book	January 1988
Spectra and correlation functions of surface layer atmospheric turbulence in unstable thermal stratification Kader, B. A.; Yaglom, A. M. Fluid Mechanics and Its Applications https://doi.org/10.1007/978-94-015-7904-9_24	book	January 1991
Spectral scaling in a high reynolds number laboratory boundary layer Antonia, R. A.; Raupach, M. R. Boundary-Layer Meteorology, Vol. 65, Issue 3 https://doi.org/10.1007/BF00705531	journal	August 1993
On the determination of the height of the Ekman boundary layer Zilitinkevich, S. S. Boundary-Layer Meteorology, Vol. 3, Issue 2 https://doi.org/10.1007/BF02033914	journal	December 1972
The characteristics of turbulent velocity components in the surface layer under convective conditions Panofsky, H. A.; Tennekes, H.; Lenschow, D. H. Boundary-Layer Meteorology, Vol. 11, Issue 3 https://doi.org/10.1007/BF02186086	journal	May 1977
A method for estimating wall friction in turbulent wall-bounded flows Kendall, Anthony; Koochesfahani, Manoochehr Experiments in Fluids, Vol. 44, Issue 5 https://doi.org/10.1007/s00348-007-0433-9	journal	November 2007
Monin-Obukhov Functions for Standard Deviations of Velocity Wilson, J. D. Boundary-Layer Meteorology, Vol. 129, Issue 3 https://doi.org/10.1007/s10546-008-9319-5	journal	October 2008
Coherent Structures and the Dissimilarity of Turbulent Transport of Momentum and Scalars in the Unstable Atmospheric Surface Layer Li, Dan; Bou-Zeid, Elie Boundary-Layer Meteorology, Vol. 140, Issue 2 https://doi.org/10.1007/s10546-011-9613-5	journal	April 2011
Towards Reconciling the Large-Scale Structure of Turbulent Boundary Layers in the Atmosphere and Laboratory Hutchins, Nicholas; Chauhan, Kapil; Marusic, Ivan Boundary-Layer Meteorology, Vol. 145, Issue 2 https://doi.org/10.1007/s10546-012-9735-4	journal	June 2012
Scaling of Wall-Normal Turbulence Intensity and Vertical Eddy Structures in the Atmospheric Surface Layer Yang, Haibo; Bo, Tianli Boundary-Layer Meteorology, Vol. 166, Issue 2 https://doi.org/10.1007/s10546-017-0306-6	journal	October 2017
Plume Dispersion in Low-Wind-Speed Conditions During Project Sagebrush Phase 2, with Emphasis on Concentration Variability Finn, D.; Carter, R. G.; Eckman, R. M. Boundary-Layer Meteorology, Vol. 169, Issue 1 https://doi.org/10.1007/s10546-018-0360-8	journal	May 2018
On the Influence of Large-Scale Atmospheric Motions on Near-Surface Turbulence: Comparison Between Flows Over Low-Roughness and Tall Vegetation Canopies Dupont, Sylvain; Patton, Edward G. Boundary-Layer Meteorology, Vol. 184, Issue 2 https://doi.org/10.1007/s10546-022-00710-z	journal	June 2022
Spectral measurements of temperature and longitudinal velocity fluctuations in fully developed pipe flow Bremhorst, K.; Bullock, K. J. International Journal of Heat and Mass Transfer, Vol. 13, Issue 8 https://doi.org/10.1016/0017-9310(70)90072-4	journal	August 1970
Tools for quality assessment of surface-based flux measurements Foken, Th.; Wichura, B. Agricultural and Forest Meteorology, Vol. 78, Issue 1-2 https://doi.org/10.1016/0168-1923(95)02248-1	journal	January 1996
The Turbulent Boundary Layer Clauser, Francis H. Advances in Applied Mechanics https://doi.org/10.1016/S0065-2156(08)70370-3	book	January 1956
Review and intercomparison of operational methods for the determination of the mixing height Seibert, P. Atmospheric Environment, Vol. 34, Issue 7 https://doi.org/10.1016/S1352-2310(99)00349-0	journal	January 2000
Turbulence profiles from a smooth flat-plate turbulent boundary layer at high Reynolds number Winkel, Eric S.; Cutbirth, James M.; Ceccio, Steven L. Experimental Thermal and Fluid Science, Vol. 40 https://doi.org/10.1016/j.expthermflusci.2012.02.009	journal	July 2012
Scaling of the streamwise velocity component in turbulent pipe flow Morrison, J. F.; McKEON, B. J.; Jiang, W. Journal of Fluid Mechanics, Vol. 508 https://doi.org/10.1017/S0022112004008985	journal	January 1999
Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using an atmospheric flow Kunkel, Gary J.; Marusic, Ivan Journal of Fluid Mechanics, Vol. 548, Issue -1 https://doi.org/10.1017/S0022112005007780	journal	February 2006
Evaluations of the von Kármán constant in the atmospheric surface layer Andreas, Edgar L.; Claffey, Kerry J.; Jordan, Rachel E. Journal of Fluid Mechanics, Vol. 559 https://doi.org/10.1017/S0022112006000164	journal	July 2006
‘Inactive’ motion and pressure fluctuations in turbulent boundary layers Bradshaw, P. Journal of Fluid Mechanics, Vol. 30, Issue 2 https://doi.org/10.1017/S0022112067001417	journal	November 1967
Scaling laws for pipe-flow turbulence Perry, A. E.; Abell, C. J. Journal of Fluid Mechanics, Vol. 67, Issue 2 https://doi.org/10.1017/S0022112075000298	journal	January 1975
Asymptotic similarity of turbulence structures in smooth- and rough-walled pipes Perry, A. E.; Abell, C. J. Journal of Fluid Mechanics, Vol. 79, Issue 04 https://doi.org/10.1017/S0022112077000457	journal	March 1977
Structural similarity in radial correlations and spectra of longitudinal velocity fluctuations in pipe flow Bullock, K. J.; Cooper, R. E.; Abernathy, F. H. Journal of Fluid Mechanics, Vol. 88, Issue 3 https://doi.org/10.1017/S0022112078002293	journal	October 1978
On the mechanism of wall turbulence Perry, A. E.; Chong, M. S. Journal of Fluid Mechanics, Vol. 119 https://doi.org/10.1017/S0022112082001311	journal	June 1982
A theoretical and experimental study of wall turbulence Perry, A. E.; Henbest, S.; Chong, M. S. Journal of Fluid Mechanics, Vol. 165, Issue -1 https://doi.org/10.1017/S002211208600304X	journal	April 1986
An experimental study of the turbulence structure in smooth- and rough-wall boundary layers Perry, A. E.; Lim, K. L.; Henbest, S. M. Journal of Fluid Mechanics, Vol. 177 https://doi.org/10.1017/S0022112087001034	journal	April 1987
Experimental support for the attached-eddy hypothesis in zero-pressure-gradient turbulent boundary layers Perry, A. E.; Li, J. D. Journal of Fluid Mechanics, Vol. 218, Issue -1 https://doi.org/10.1017/S0022112090001057	journal	September 1990
Low-Reynolds-number turbulent boundary layers Erm, Lincoln P.; Joubert, Peter N. Journal of Fluid Mechanics, Vol. 230 https://doi.org/10.1017/S0022112091000691	journal	September 1991
On the logarithmic region in wall turbulence Marusic, Ivan; Monty, Jason P.; Hultmark, Marcus Journal of Fluid Mechanics, Vol. 716 https://doi.org/10.1017/jfm.2012.511	journal	January 2013
Very large scale motions in the atmospheric surface layer: a field investigation Wang, Guohua; Zheng, Xiaojing Journal of Fluid Mechanics, Vol. 802 https://doi.org/10.1017/jfm.2016.439	journal	August 2016
Fully resolved measurements of turbulent boundary layer flows up to Samie, M.; Marusic, I.; Hutchins, N. Journal of Fluid Mechanics, Vol. 851 https://doi.org/10.1017/jfm.2018.508	journal	July 2018
Data-driven decomposition of the streamwise turbulence kinetic energy in boundary layers. Part 1. Energy spectra Baars, Woutijn J.; Marusic, Ivan Journal of Fluid Mechanics, Vol. 882 https://doi.org/10.1017/jfm.2019.834	journal	November 2019
The logarithmic variance of streamwise velocity and conundrum in wall turbulence Hwang, Yongyun; Hutchins, Nicholas; Marusic, Ivan Journal of Fluid Mechanics, Vol. 933 https://doi.org/10.1017/jfm.2021.1057	journal	December 2021
Identification of the energy contributions associated with wall-attached eddies and very-large-scale motions in the near-neutral atmospheric surface layer through wind LiDAR measurements Puccioni, Matteo; Calaf, Marc; Pardyjak, Eric R. Journal of Fluid Mechanics, Vol. 955 https://doi.org/10.1017/jfm.2022.1080	journal	January 2023
Energy-Inertial Scale Interactions for Velocity and Temperature in the Unstable Atmospheric Surface Layer Katul, Gabriel; Hsieh, Cheng-I; Sigmon, John Boundary-Layer Meteorology, Vol. 82, Issue 1 https://doi.org/10.1023/A:1000178707511	journal	January 1997
A Theoretical and Experimental Investigation of Energy-Containing Scales in the Dynamic Sublayer of Boundary-Layer Flows Katul, Gabriel; Chu, Chia-Ren Boundary-Layer Meteorology, Vol. 86, Issue 2 https://doi.org/10.1023/A:1000657014845	journal	February 1998
Theory And Measurements For Turbulence Spectra And Variances In The Atmospheric Neutral Surface Layer Högström, Ulf; Hunt, J. C. R.; Smedman, Ann-Sofi Boundary-Layer Meteorology, Vol. 103, Issue 1 https://doi.org/10.1023/A:1014579828712	journal	April 2002
Sonic Anemometer Tilt Correction Algorithms Wilczak, James M.; Oncley, Steven P.; Stage, Steven A. Boundary-Layer Meteorology, Vol. 99, Issue 1 https://doi.org/10.1023/A:1018966204465	journal	April 2001
The Shuttle Radar Topography Mission Farr, Tom G.; Rosen, Paul A.; Caro, Edward Reviews of Geophysics, Vol. 45, Issue 2 https://doi.org/10.1029/2005RG000183	journal	January 2007
Low-wavenumber spectral characteristics of velocity and temperature in the atmospheric surface layer Katul, Gabriel G.; Chu, Chia R.; Parlange, Marc B. Journal of Geophysical Research, Vol. 100, Issue D7 https://doi.org/10.1029/94JD02616	journal	January 1995
Streamwise turbulence intensity formulation for flat-plate boundary layers Marusic, Ivan; Kunkel, Gary J. Physics of Fluids, Vol. 15, Issue 8 https://doi.org/10.1063/1.1589014	journal	August 2003
Variations of von Kármán coefficient in canonical flows Nagib, Hassan M.; Chauhan, Kapil A. Physics of Fluids, Vol. 20, Issue 10 https://doi.org/10.1063/1.3006423	journal	October 2008
Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues Marusic, I.; McKeon, B. J.; Monkewitz, P. A. Physics of Fluids, Vol. 22, Issue 6 https://doi.org/10.1063/1.3453711	journal	June 2010
Co-spectrum and mean velocity in turbulent boundary layers Katul, Gabriel G.; Porporato, Amilcare; Manes, Costantino Physics of Fluids, Vol. 25, Issue 9 https://doi.org/10.1063/1.4821997	journal	September 2013
Logarithmic scaling in the longitudinal velocity variance explained by a spectral budget Banerjee, T.; Katul, G. G. Physics of Fluids, Vol. 25, Issue 12 https://doi.org/10.1063/1.4837876	journal	December 2013
Generalized logarithmic scaling for high-order moments of the longitudinal velocity component explained by the random sweeping decorrelation hypothesis Katul, Gabriel G.; Banerjee, Tirtha; Cava, Daniela Physics of Fluids, Vol. 28, Issue 9 https://doi.org/10.1063/1.4961963	journal	September 2016
Experimental and theoretical evaluation of the k−11 spectral law Turan, Ö.; Azad, R. S.; Kassab, S. Z. Physics of Fluids, Vol. 30, Issue 11 https://doi.org/10.1063/1.866427	journal	January 1987
Similarity law for the streamwise turbulence intensity in zero-pressure-gradient turbulent boundary layers Marusic, I.; Uddin, A. K. M.; Perry, A. E. Physics of Fluids, Vol. 9, Issue 12 https://doi.org/10.1063/1.869509	journal	December 1997
A note on the overlap region in turbulent boundary layers Österlund, Jens M.; Johansson, Arne V.; Nagib, Hassan M. Physics of Fluids, Vol. 12, Issue 1 https://doi.org/10.1063/1.870250	journal	January 2000
Atmospheric Boundary Layer Flows: Their Structure and Measurement Kaimal, J. C.; Finnigan, J. J. https://doi.org/10.1093/oso/9780195062397.001.0001	book	March 1994
The Spectrum of Turbulence Taylor, G. I. Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, Vol. 164, Issue 919 https://doi.org/10.1098/rspa.1938.0032	journal	February 1938
Profiles of high-order moments of longitudinal velocity explained by the random sweeping decorrelation hypothesis Huang, Kelly Y.; Katul, Gabriel G. Physical Review Fluids, Vol. 7, Issue 4 https://doi.org/10.1103/PhysRevFluids.7.044603	journal	April 2022
Turbulent Pipe Flow at Extreme Reynolds Numbers Hultmark, M.; Vallikivi, M.; Bailey, S. C. C. Physical Review Letters, Vol. 108, Issue 9 https://doi.org/10.1103/PhysRevLett.108.094501	journal	February 2012
Generalizing Monin-Obukhov Similarity Theory (1954) for Complex Atmospheric Turbulence Stiperski, Ivana; Calaf, Marc Physical Review Letters, Vol. 130, Issue 12 https://doi.org/10.1103/PhysRevLett.130.124001	journal	March 2023
Origin of the “ − 1 ” Spectral Law in Wall-Bounded Turbulence Nikora, Vladimir Physical Review Letters, Vol. 83, Issue 4 https://doi.org/10.1103/PhysRevLett.83.734	journal	July 1999
Evidence of the k 1 − 1 Law in a High-Reynolds-Number Turbulent Boundary Layer Nickels, T. B.; Marusic, I.; Hafez, S. Physical Review Letters, Vol. 95, Issue 7 https://doi.org/10.1103/PhysRevLett.95.074501	journal	August 2005
Attached Eddy Model of Wall Turbulence Marusic, Ivan; Monty, Jason P. Annual Review of Fluid Mechanics, Vol. 51, Issue 1 https://doi.org/10.1146/annurev-fluid-010518-040427	journal	January 2019
High–Reynolds Number Wall Turbulence Smits, Alexander J.; McKeon, Beverley J.; Marusic, Ivan Annual Review of Fluid Mechanics, Vol. 43, Issue 1 https://doi.org/10.1146/annurev-fluid-122109-160753	journal	January 2011
Atmospheric Turbulence Wyngaard, J. C. Annual Review of Fluid Mechanics, Vol. 24, Issue 1 https://doi.org/10.1146/annurev.fl.24.010192.001225	journal	January 1992
How Long Is Long Enough When Measuring Fluxes and Other Turbulence Statistics? Lenschow, D. H.; Mann, J.; Kristensen, L. Journal of Atmospheric and Oceanic Technology, Vol. 11, Issue 3 https://doi.org/10.1175/1520-0426(1994)011<0661:HLILEW>2.0.CO;2	journal	June 1994
Spectra of Velocity and Temperature Fluctuations in the Atmospheric Boundary Layer Over the Sea Pond, S.; Smith, S. D.; Hamblin, P. F. Journal of the Atmospheric Sciences, Vol. 23, Issue 4 https://doi.org/10.1175/1520-0469(1966)023<0376:SOVATF>2.0.CO;2	journal	July 1966
Horizontal Velocity Spectra in an Unstable Surface Layer Kaimal, J. C. Journal of the Atmospheric Sciences, Vol. 35, Issue 1 https://doi.org/10.1175/1520-0469(1978)035<0018:HVSIAU>2.0.CO;2	journal	January 1978
Comments on “Horizontal Velocity Spectra in an Unstable Surface Layer” Bradshaw, P. Journal of the Atmospheric Sciences, Vol. 35, Issue 9 https://doi.org/10.1175/1520-0469(1978)035<1768:COVSIA>2.0.CO;2	journal	September 1978
Project Sagebrush: Revisiting the Value of the Horizontal Plume Spread Parameter σ _y Finn, D.; Clawson, K. L.; Eckman, R. M. Journal of Applied Meteorology and Climatology, Vol. 55, Issue 6 https://doi.org/10.1175/JAMC-D-15-0283.1	journal	June 2016
Mechanisms for Wind Direction Changes in the Very Stable Boundary Layer Finn, D.; Eckman, R. M.; Gao, Z. Journal of Applied Meteorology and Climatology, Vol. 57, Issue 11 https://doi.org/10.1175/JAMC-D-18-0065.1	journal	November 2018
Turbulent Velocity-Variance Profiles in the Stable Boundary Layer Generated by a Nocturnal Low-Level Jet Banta, Robert M.; Pichugina, Yelena L.; Brewer, W. Alan Journal of the Atmospheric Sciences, Vol. 63, Issue 11 https://doi.org/10.1175/JAS3776.1	journal	November 2006
The local isotropy hypothesis and the turbulent kinetic energy dissipation rate in the atmospheric surface layer Chamecki, M.; Dias, N. L. Quarterly Journal of the Royal Meteorological Society, Vol. 130, Issue 603 https://doi.org/10.1256/qj.03.155	journal	October 2004
Uncertainties in temperature statistics and fluxes determined by sonic anemometers due to wind-induced vibrations of mounting arms Gao, Zhongming; Liu, Heping; Li, Dan Atmospheric Measurement Techniques, Vol. 17, Issue 13 https://doi.org/10.5194/amt-17-4109-2024	journal	July 2024

Similar Records

Prandtl number effects on extreme mixing events in forced stratified turbulence

Journal Article · Mon Mar 11 20:00:00 EDT 2024 · Journal of Fluid Mechanics · OSTI ID:2323351

A data-driven method for modelling dissipation rates in stratified turbulence

Journal Article · Mon Dec 18 19:00:00 EST 2023 · Journal of Fluid Mechanics · OSTI ID:2246688

Flow in additively manufactured super-rough channels

Journal Article · Thu Jul 28 20:00:00 EDT 2022 · Flow · OSTI ID:1878655

Asymptotic coefficients of the attached-eddy model derived from an adiabatic atmosphere

Citation Formats

References (72)

Similar Records

Related Subjects