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; Germano, Massimo; Porporato, Amilcare

doi:10.1063/1.4961963

Title: Generalized logarithmic scaling for high-order moments of the longitudinal velocity component explained by the random sweeping decorrelation hypothesis

Journal Article · Wed Sep 07 00:00:00 EDT 2016 · Physics of Fluids

DOI:https://doi.org/10.1063/1.4961963· OSTI ID:1467882

Katul, Gabriel G. ^[1]; Banerjee, Tirtha ^[2]; Cava, Daniela ^[3];

^[4]; Porporato, Amilcare ^[1]

Duke Univ., Durham, NC (United States). Nicholas School of the Environment; Duke Univ., Durham, NC (United States). Dept. of Civil and Environmental Engineering
Karlsruhe Inst. of Technology (KIT) (Germany). Inst. of Meteorology and Climate Research, Atmospheric Environment Research (IMK-IFU)
Istituto di Scienze dell Atmosfera e del Clima, Lecce (Italy). Consiglio Nazionale delle Ricerche
Duke Univ., Durham, NC (United States). Dept. of Civil and Environmental Engineering

Expressions for the logarithmic variations of the normalized turbulent longitudinal velocity ($$\overline{u^2p}^+$$)1/p with normalized distance z/δ from a boundary for high-order (p) moments in the intermediate region of wall bounded flows characterized by thickness δ are derived. The ansatz that ($$\overline{u^2p}^+$$)1/p variation in ln(z/δ) originates from a compound effect of random sweeping and -1 power-law scaling in the longitudinal velocity spectrum E_u(k) is discussed, where k is the wavenumber. Using velocity time series sampled above a uniform ice sheet, an E_u(k) ~ k-1 scaling is confirmed for kz < 1 and kδ > 1. The data were then used to analyze assumptions required for the utility of the random sweeping decorrelation (RSD) hypothesis connecting the k-1 power-law with log-scaling in ($$\overline{u^2p}^+$$)1/p. It has been found out that while the RSD hypothesis is operationally applicable to scales associated with attached eddies bounded by kz < 1 and kδ > 1, significant interactions among high-order turbulent velocity and velocity increments lead to the conclusion that the RSD hypothesis cannot be exactly valid. Lastly, its operational utility stems from the observations that some of the interaction terms among the high-order velocity and velocity increments act in opposite directions thereby canceling their additive effects in RSD.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Duke Univ., Durham, NC (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Biological and Environmental Research (BER); National Science Foundation (NSF)

Grant/Contract Number:: SC0006967; SC0011461; NSF-EAR-1344703

OSTI ID:: 1467882

Alternate ID(s):: OSTI ID: 1322414

Journal Information:: Physics of Fluids, Vol. 28, Issue 9; ISSN 1070-6631

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 14 works

Citation information provided by
Web of Science

References (75)

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
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
Fluctuation spectra and variances in convective turbulent boundary layers: A reevaluation of old models Yaglom, A. M. Physics of Fluids, Vol. 6, Issue 2 https://doi.org/10.1063/1.868328	journal	February 1994
Direct numerical simulation of turbulent channel flow up to Lee, Myoungkyu; Moser, Robert D. Journal of Fluid Mechanics, Vol. 774 https://doi.org/10.1017/jfm.2015.268	journal	June 2015
Further comments on the equilibrium height of neutral and stable planetary boundary layers Zilitinkevich, Sergej; Esau, Igor; Baklanov, Alexander Quarterly Journal of the Royal Meteorological Society, Vol. 133, Issue 622 https://doi.org/10.1002/qj.27	journal	January 2007
Sweeping decorrelation in isotropic turbulence Chen, Shiyi; Kraichnan, Robert H. Physics of Fluids A: Fluid Dynamics, Vol. 1, Issue 12 https://doi.org/10.1063/1.857475	journal	December 1989
Models of the scalar spectrum for turbulent advection Hill, R. J. Journal of Fluid Mechanics, Vol. 88, Issue 3 https://doi.org/10.1017/S002211207800227X	journal	October 1978
Existence of $k^{- 1}$ power-law scaling in the equilibrium regions of wall-bounded turbulence explained by Heisenberg's eddy viscosity Katul, Gabriel G.; Porporato, Amilcare; Nikora, Vladimir Physical Review E, Vol. 86, Issue 6 https://doi.org/10.1103/PhysRevE.86.066311	journal	December 2012
On the spectrum of energy in turbulent shear flow Tchen, C. M. Journal of Research of the National Bureau of Standards, Vol. 50, Issue 1 https://doi.org/10.6028/jres.050.009	journal	January 1953
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
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
Turbulence Perturbations in the Neutrally Stratified Surface Layer due to the Interaction of a Katabatic Flow with a Steep Ridge Mammarella, I.; Tampieri, F.; Tagliazucca, M. Environmental Fluid Mechanics, Vol. 5, Issue 3 https://doi.org/10.1007/s10652-004-3268-4	journal	June 2005
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
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
Spectral scaling in boundary layers and pipes at very high Reynolds numbers Vallikivi, M.; Ganapathisubramani, B.; Smits, A. J. Journal of Fluid Mechanics, Vol. 771 https://doi.org/10.1017/jfm.2015.181	journal	April 2015
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
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
Spatio-temporal spectra in the logarithmic layer of wall turbulence: large-eddy simulations and simple models Wilczek, Michael; Stevens, Richard J. A. M.; Meneveau, Charles Journal of Fluid Mechanics, Vol. 769 https://doi.org/10.1017/jfm.2015.116	journal	March 2015
Kraichnan’s random sweeping hypothesis in homogeneous turbulent convection He, Xiaozhou; Tong, Penger Physical Review E, Vol. 83, Issue 3 https://doi.org/10.1103/PhysRevE.83.037302	journal	March 2011
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
L AGRANGIAN I NVESTIGATIONS OF T URBULENCE Yeung, P. K. Annual Review of Fluid Mechanics, Vol. 34, Issue 1 https://doi.org/10.1146/annurev.fluid.34.082101.170725	journal	January 2002
On the scaling in sink-flow turbulent boundary layers Dixit, Shivsai Ajit; Ramesh, O. N. Journal of Fluid Mechanics, Vol. 737 https://doi.org/10.1017/jfm.2013.566	journal	November 2013
A refined interpretation of the logarithmic structure function law in wall layer turbulence Davidson, P. A.; Krogstad, P. -Å.; Nickels, T. B. Physics of Fluids, Vol. 18, Issue 6 https://doi.org/10.1063/1.2214087	journal	January 2006
A modulated gradient model for large-eddy simulation: Application to a neutral atmospheric boundary layer Lu, Hao; Porté-Agel, Fernando Physics of Fluids, Vol. 22, Issue 1 https://doi.org/10.1063/1.3291073	journal	January 2010
Turbulent Flows Pope, Stephen B. https://doi.org/10.1017/CBO9780511840531	book	July 2012
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
Large-eddy simulation study of the logarithmic law for second- and higher-order moments in turbulent wall-bounded flow Stevens, Richard J. A. M.; Wilczek, Michael; Meneveau, Charles Journal of Fluid Mechanics, Vol. 757 https://doi.org/10.1017/jfm.2014.510	journal	September 2014
A model of turbulence spectra in the atmospheric surface layer Claussen, Martin Boundary-Layer Meteorology, Vol. 33, Issue 2 https://doi.org/10.1007/BF00123388	journal	October 1985
The k ⁻¹ scaling of air temperature spectra in atmospheric surface layer flows Li, D.; Katul, G. G.; Gentine, P. Quarterly Journal of the Royal Meteorological Society, Vol. 142, Issue 694 https://doi.org/10.1002/qj.2668	journal	October 2015
Interaction between large and small scales in the canopy sublayer: INTERACTION BETWEEN SCALES WITHIN THE CANOPY SUBLAYER Poggi, D.; Porporato, A.; Ridolfi, L. Geophysical Research Letters, Vol. 31, Issue 5 https://doi.org/10.1029/2003GL018611	journal	March 2004
The role of surface characteristics on intermittency and zero-crossing properties of atmospheric turbulence: CLUSTERING IN ATMOSPHERIC TURBULENCE Cava, Daniela; Katul, Gabriel George; Molini, Annalisa Journal of Geophysical Research: Atmospheres, Vol. 117, Issue D1 https://doi.org/10.1029/2011JD016167	journal	January 2012
The random sweeping decorrelation hypothesis in stratified turbulent flows Katul, Gabriel; Parlange, Marc; Albertson, John Fluid Dynamics Research, Vol. 16, Issue 5 https://doi.org/10.1016/0169-5983(95)00011-2	journal	October 1995
Structure Functions In A Wall-Turbulent Shear Flow Giostra, U.; Cava, D.; Schipa, S. Boundary-Layer Meteorology, Vol. 103, Issue 3 https://doi.org/10.1023/A:1014917120110	journal	June 2002
The “Inactive” Eddy Motion and the Large-Scale Turbulent Pressure Fluctuations in the Dynamic Sublayer Katul, Gabriel G.; Albertson, John D.; Parlange, Marc B. Journal of the Atmospheric Sciences, Vol. 53, Issue 17 https://doi.org/10.1175/1520-0469(1996)053<2512:TEMATL>2.0.CO;2	journal	September 1996
Characteristics of Gravity Waves over an Antarctic Ice Sheet during an Austral Summer Cava, Daniela; Giostra, Umberto; Katul, Gabriel Atmosphere, Vol. 6, Issue 9 https://doi.org/10.3390/atmos6091271	journal	August 2015
On higher-order spectra of turbulence Atta, C. W. Van; Wyngaard, J. C. Journal of Fluid Mechanics, Vol. 72, Issue 4 https://doi.org/10.1017/S0022112075003229	journal	December 1975
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
Hierarchical random additive process and logarithmic scaling of generalized high order, two-point correlations in turbulent boundary layer flow Yang, X. I. A.; Marusic, I.; Meneveau, C. Physical Review Fluids, Vol. 1, Issue 2 https://doi.org/10.1103/PhysRevFluids.1.024402	journal	June 2016
The sweeping decorrelation hypothesis and energy–inertial scale interaction in high Reynolds number flows Praskovsky, Alexander A.; Gledzer, Evgeny B.; Karyakin, Mikhail Yu. Journal of Fluid Mechanics, Vol. 248 https://doi.org/10.1017/S0022112093000862	journal	March 1993
Scaling of second- and higher-order structure functions in turbulent boundary layers de Silva, C. M.; Marusic, I.; Woodcock, J. D. Journal of Fluid Mechanics, Vol. 769 https://doi.org/10.1017/jfm.2015.122	journal	March 2015
The logarithmic structure function law in wall-layer turbulence Davidson, P. A.; Nickels, T. B.; Krogstad, P. -Å. Journal of Fluid Mechanics, Vol. 550, Issue -1 https://doi.org/10.1017/S0022112005008001	journal	February 2006
Numerical and Experimental Investigation of the Neutral Atmospheric Surface Layer Drobinski, Philippe; Carlotti, Pierre; Redelsperger, Jean-Luc Journal of the Atmospheric Sciences, Vol. 64, Issue 1 https://doi.org/10.1175/JAS3831.1	journal	January 2007
Random-sweeping hypothesis for passive scalars in isotropic turbulence Yeung, P. K.; Sawford, Brian L. Journal of Fluid Mechanics, Vol. 459 https://doi.org/10.1017/S0022112002008248	journal	May 2002
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
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
A wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis Perry, A. E.; Marušić, Ivan Journal of Fluid Mechanics, Vol. 298 https://doi.org/10.1017/S0022112095003351	journal	September 1995
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
Inertial-Range Spectrum of Hydromagnetic Turbulence Kraichnan, Robert H. Physics of Fluids, Vol. 8, Issue 7 https://doi.org/10.1063/1.1761412	journal	January 1965
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
Generalized logarithmic law for high-order moments in turbulent boundary layers Meneveau, Charles; Marusic, Ivan Journal of Fluid Mechanics, Vol. 719 https://doi.org/10.1017/jfm.2013.61	journal	February 2013
Higher-Order Correlations in a Turbulent Field Frenkiel, François N. Physics of Fluids, Vol. 10, Issue 3 https://doi.org/10.1063/1.1762145	journal	January 1967
Coherent structures and the k ⁻¹ spectral behaviour Calaf, M.; Hultmark, M.; Oldroyd, H. J. Physics of Fluids, Vol. 25, Issue 12 https://doi.org/10.1063/1.4834436	journal	December 2013
A Spectral Budget Model for the Longitudinal Turbulent Velocity in the Stable Atmospheric Surface Layer Banerjee, Tirtha; Li, Dan; Juang, Jehn-Yih Journal of the Atmospheric Sciences, Vol. 73, Issue 1 https://doi.org/10.1175/JAS-D-15-0066.1	journal	January 2016
Turbulent fluctuations above the buffer layer of wall-bounded flows JimÉNez, Javier; Hoyas, Sergio Journal of Fluid Mechanics, Vol. 611 https://doi.org/10.1017/S0022112008002747	journal	September 2008
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
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
Space‐time correlations in turbulence: Kinematical versus dynamical effects Yakhot, Victor; Orszag, Steven A.; She, Zhen‐Su Physics of Fluids A: Fluid Dynamics, Vol. 1, Issue 2 https://doi.org/10.1063/1.857486	journal	February 1989
Time correlations and random sweeping in isotropic turbulence Nelkin, Mark; Tabor, M. Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 1 https://doi.org/10.1063/1.857684	journal	January 1990
Transport Processes as Foundations of the Heisenberg and Obukhoff Theories of Turbulence Tchen, Chan-Mou Physical Review, Vol. 93, Issue 1 https://doi.org/10.1103/PhysRev.93.4	journal	January 1954
Spectral measurements of turbulent momentum transfer in fully developed pipe flow Bremhorst, K.; Walker, T. B. Journal of Fluid Mechanics, Vol. 61, Issue 1 https://doi.org/10.1017/S0022112073000637	journal	October 1973
The physics of wall turbulence Jiménez, Javier Physica A: Statistical Mechanics and its Applications, Vol. 263, Issue 1-4 https://doi.org/10.1016/S0378-4371(98)00507-X	journal	February 1999
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
Modelling velocity spectra in the lower part of the planetary boundary layer Olesen, H. R.; Larsen, S. E.; H�jstrup, J. Boundary-Layer Meteorology, Vol. 29, Issue 3 https://doi.org/10.1007/BF00119794	journal	July 1984
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
Turbulent Kinetic Energy Dissipation in the Surface Layer Charuchittipan, D.; Wilson, J. D. Boundary-Layer Meteorology, Vol. 132, Issue 2 https://doi.org/10.1007/s10546-009-9399-x	journal	June 2009
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
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
Bottlenecks in turbulent kinetic energy spectra predicted from structure function inflections using the Von Kármán-Howarth equation Katul, Gabriel G.; Manes, Costantino; Porporato, Amilcare Physical Review E, Vol. 92, Issue 3 https://doi.org/10.1103/PhysRevE.92.033009	journal	September 2015
Bottleneck effect in three-dimensional turbulence simulations Dobler, Wolfgang; Haugen, Nils Erland L.; Yousef, Tarek A. Physical Review E, Vol. 68, Issue 2 https://doi.org/10.1103/PhysRevE.68.026304	journal	August 2003
Some observed properties of atmospheric turbulence Dutton, John A.; Deaven, Dennis G. Statistical Models and Turbulence https://doi.org/10.1007/3-540-05716-1_21	book	January 1972
Magnetic pumping model for energizing superthermal particles applied to observations of the Earth's bow shock Lichko, E.; Egedal, J. Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-16660-4	journal	June 2020
Higher-Order Correlations in a Turbulent Field Frenkiel, François N. Physics of Fluids, Vol. 10, Issue 9 https://doi.org/10.1063/1.1762474	journal	January 1967
The Spectrum of Turbulence De Feriet, J. Kampe Journal of the Aeronautical Sciences, Vol. 7, Issue 12 https://doi.org/10.2514/8.1235	journal	October 1940
Turbulent Flows Pope, Stephen B. Measurement Science and Technology, Vol. 12, Issue 11 https://doi.org/10.1088/0957-0233/12/11/705	journal	October 2001
Large-eddy simulation study of the logarithmic law for second and higher-order moments in turbulent wall-bounded flow Stevens, Richard J. A. M.; Wilczek, Michael; Meneveau, Charles arXiv https://doi.org/10.48550/arxiv.1405.0950	text	January 2014

Cited By (3)

Modeling space-time correlations of velocity fluctuations in wind farms Lukassen, Laura J.; Stevens, Richard J. A. M.; Meneveau, Charles Wind Energy, Vol. 21, Issue 7 https://doi.org/10.1002/we.2172	journal	March 2018
Impact of phenomenological theory of turbulence on pragmatic approach to fluvial hydraulics Ali, Sk Zeeshan; Dey, Subhasish Physics of Fluids, Vol. 30, Issue 4 https://doi.org/10.1063/1.5025218	journal	April 2018
Modeling space-time correlations of velocity fluctuations in wind farms Lukassen, Laura J.; Stevens, Richard J. A. M.; Meneveau, Charles arXiv https://doi.org/10.48550/arxiv.1710.01659	text	January 2017

Similar Records

A Kolmogorov-Brutsaert structure function model for evaporation into a turbulent atmosphere

Journal Article · Tue Apr 11 00:00:00 EDT 2017 · Water Resources Research · OSTI ID:1467882

Katul, Gabriel; Liu, Heping

Multiple mechanisms generate a universal scaling with dissipation for the air-water gas transfer velocity

Journal Article · Fri Feb 24 00:00:00 EST 2017 · Geophysical Research Letters · OSTI ID:1467882

Katul, Gabriel; Liu, Heping

Scaling and Similarity of the Anisotropic Coherent Eddies in Near-Surface Atmospheric Turbulence

Journal Article · Thu Mar 01 00:00:00 EST 2018 · Journal of the Atmospheric Sciences · OSTI ID:1467882

Ghannam, Khaled; Katul, Gabriel G.; Bou-Zeid, Elie; +2 more

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS

Title: Generalized logarithmic scaling for high-order moments of the longitudinal velocity component explained by the random sweeping decorrelation hypothesis

Citation Formats

References (75)

Cited By (3)

Similar Records

Related Subjects