Generalized logarithmic scaling for high-order moments of the longitudinal velocity component explained by the random sweeping decorrelation hypothesis
Abstract
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 Eu(k) is discussed, where k is the wavenumber. Using velocity time series sampled above a uniform ice sheet, an Eu(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 effectsmore »
- Authors:
-
- 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
- Publication Date:
- Research Org.:
- Duke Univ., Durham, NC (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Biological and Environmental Research (BER); National Science Foundation (NSF)
- OSTI Identifier:
- 1467882
- Alternate Identifier(s):
- OSTI ID: 1322414
- Grant/Contract Number:
- SC0006967; SC0011461; NSF-EAR-1344703
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Physics of Fluids
- Additional Journal Information:
- Journal Volume: 28; Journal Issue: 9; Journal ID: ISSN 1070-6631
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Katul, Gabriel G., Banerjee, Tirtha, Cava, Daniela, Germano, Massimo, and Porporato, Amilcare. Generalized logarithmic scaling for high-order moments of the longitudinal velocity component explained by the random sweeping decorrelation hypothesis. United States: N. p., 2016.
Web. doi:10.1063/1.4961963.
Katul, Gabriel G., Banerjee, Tirtha, Cava, Daniela, Germano, Massimo, & Porporato, Amilcare. Generalized logarithmic scaling for high-order moments of the longitudinal velocity component explained by the random sweeping decorrelation hypothesis. United States. https://doi.org/10.1063/1.4961963
Katul, Gabriel G., Banerjee, Tirtha, Cava, Daniela, Germano, Massimo, and Porporato, Amilcare. 2016.
"Generalized logarithmic scaling for high-order moments of the longitudinal velocity component explained by the random sweeping decorrelation hypothesis". United States. https://doi.org/10.1063/1.4961963. https://www.osti.gov/servlets/purl/1467882.
@article{osti_1467882,
title = {Generalized logarithmic scaling for high-order moments of the longitudinal velocity component explained by the random sweeping decorrelation hypothesis},
author = {Katul, Gabriel G. and Banerjee, Tirtha and Cava, Daniela and Germano, Massimo and Porporato, Amilcare},
abstractNote = {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 Eu(k) is discussed, where k is the wavenumber. Using velocity time series sampled above a uniform ice sheet, an Eu(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.},
doi = {10.1063/1.4961963},
url = {https://www.osti.gov/biblio/1467882},
journal = {Physics of Fluids},
issn = {1070-6631},
number = 9,
volume = 28,
place = {United States},
year = {Wed Sep 07 00:00:00 EDT 2016},
month = {Wed Sep 07 00:00:00 EDT 2016}
}
Web of Science
Works referenced in this record:
Spectra of Velocity and Temperature Fluctuations in the Atmospheric Boundary Layer Over the Sea
journal, July 1966
- Pond, S.; Smith, S. D.; Hamblin, P. F.
- Journal of the Atmospheric Sciences, Vol. 23, Issue 4
Experimental and theoretical evaluation of the k−11 spectral law
journal, January 1987
- Turan, Ö.; Azad, R. S.; Kassab, S. Z.
- Physics of Fluids, Vol. 30, Issue 11
Fluctuation spectra and variances in convective turbulent boundary layers: A reevaluation of old models
journal, February 1994
- Yaglom, A. M.
- Physics of Fluids, Vol. 6, Issue 2
Direct numerical simulation of turbulent channel flow up to
journal, June 2015
- Lee, Myoungkyu; Moser, Robert D.
- Journal of Fluid Mechanics, Vol. 774
Further comments on the equilibrium height of neutral and stable planetary boundary layers
journal, January 2007
- Zilitinkevich, Sergej; Esau, Igor; Baklanov, Alexander
- Quarterly Journal of the Royal Meteorological Society, Vol. 133, Issue 622
Sweeping decorrelation in isotropic turbulence
journal, December 1989
- Chen, Shiyi; Kraichnan, Robert H.
- Physics of Fluids A: Fluid Dynamics, Vol. 1, Issue 12
Models of the scalar spectrum for turbulent advection
journal, October 1978
- Hill, R. J.
- Journal of Fluid Mechanics, Vol. 88, Issue 3
Existence of power-law scaling in the equilibrium regions of wall-bounded turbulence explained by Heisenberg's eddy viscosity
journal, December 2012
- Katul, Gabriel G.; Porporato, Amilcare; Nikora, Vladimir
- Physical Review E, Vol. 86, Issue 6
On the spectrum of energy in turbulent shear flow
journal, January 1953
- Tchen, C. M.
- Journal of Research of the National Bureau of Standards, Vol. 50, Issue 1
Experimental support for the attached-eddy hypothesis in zero-pressure-gradient turbulent boundary layers
journal, September 1990
- Perry, A. E.; Li, J. D.
- Journal of Fluid Mechanics, Vol. 218, Issue -1
A Theoretical and Experimental Investigation of Energy-Containing Scales in the Dynamic Sublayer of Boundary-Layer Flows
journal, February 1998
- Katul, Gabriel; Chu, Chia-Ren
- Boundary-Layer Meteorology, Vol. 86, Issue 2
Turbulence Perturbations in the Neutrally Stratified Surface Layer due to the Interaction of a Katabatic Flow with a Steep Ridge
journal, June 2005
- Mammarella, I.; Tampieri, F.; Tagliazucca, M.
- Environmental Fluid Mechanics, Vol. 5, Issue 3
On the mechanism of wall turbulence
journal, June 1982
- Perry, A. E.; Chong, M. S.
- Journal of Fluid Mechanics, Vol. 119
Revisiting the formulations for the longitudinal velocity variance in the unstable atmospheric surface layer: Longitudinal Velocity Variance in Unstable Atmosphere
journal, November 2014
- Banerjee, T.; Katul, G. G.; Salesky, S. T.
- Quarterly Journal of the Royal Meteorological Society, Vol. 141, Issue 690
Spectral scaling in boundary layers and pipes at very high Reynolds numbers
journal, April 2015
- Vallikivi, M.; Ganapathisubramani, B.; Smits, A. J.
- Journal of Fluid Mechanics, Vol. 771
Structural similarity in radial correlations and spectra of longitudinal velocity fluctuations in pipe flow
journal, October 1978
- Bullock, K. J.; Cooper, R. E.; Abernathy, F. H.
- Journal of Fluid Mechanics, Vol. 88, Issue 3
Spectral scaling in a high reynolds number laboratory boundary layer
journal, August 1993
- Antonia, R. A.; Raupach, M. R.
- Boundary-Layer Meteorology, Vol. 65, Issue 3
Spatio-temporal spectra in the logarithmic layer of wall turbulence: large-eddy simulations and simple models
journal, March 2015
- Wilczek, Michael; Stevens, Richard J. A. M.; Meneveau, Charles
- Journal of Fluid Mechanics, Vol. 769
Kraichnan’s random sweeping hypothesis in homogeneous turbulent convection
journal, March 2011
- He, Xiaozhou; Tong, Penger
- Physical Review E, Vol. 83, Issue 3
Evidence of the Law in a High-Reynolds-Number Turbulent Boundary Layer
journal, August 2005
- Nickels, T. B.; Marusic, I.; Hafez, S.
- Physical Review Letters, Vol. 95, Issue 7
L AGRANGIAN I NVESTIGATIONS OF T URBULENCE
journal, January 2002
- Yeung, P. K.
- Annual Review of Fluid Mechanics, Vol. 34, Issue 1
On the scaling in sink-flow turbulent boundary layers
journal, November 2013
- Dixit, Shivsai Ajit; Ramesh, O. N.
- Journal of Fluid Mechanics, Vol. 737
A refined interpretation of the logarithmic structure function law in wall layer turbulence
journal, January 2006
- Davidson, P. A.; Krogstad, P. -Å.; Nickels, T. B.
- Physics of Fluids, Vol. 18, Issue 6
A modulated gradient model for large-eddy simulation: Application to a neutral atmospheric boundary layer
journal, January 2010
- Lu, Hao; Porté-Agel, Fernando
- Physics of Fluids, Vol. 22, Issue 1
Asymptotic similarity of turbulence structures in smooth- and rough-walled pipes
journal, March 1977
- Perry, A. E.; Abell, C. J.
- Journal of Fluid Mechanics, Vol. 79, Issue 04
Large-eddy simulation study of the logarithmic law for second- and higher-order moments in turbulent wall-bounded flow
journal, September 2014
- Stevens, Richard J. A. M.; Wilczek, Michael; Meneveau, Charles
- Journal of Fluid Mechanics, Vol. 757
A model of turbulence spectra in the atmospheric surface layer
journal, October 1985
- Claussen, Martin
- Boundary-Layer Meteorology, Vol. 33, Issue 2
The k −1 scaling of air temperature spectra in atmospheric surface layer flows
journal, October 2015
- Li, D.; Katul, G. G.; Gentine, P.
- Quarterly Journal of the Royal Meteorological Society, Vol. 142, Issue 694
Interaction between large and small scales in the canopy sublayer: INTERACTION BETWEEN SCALES WITHIN THE CANOPY SUBLAYER
journal, March 2004
- Poggi, D.; Porporato, A.; Ridolfi, L.
- Geophysical Research Letters, Vol. 31, Issue 5
The role of surface characteristics on intermittency and zero-crossing properties of atmospheric turbulence: CLUSTERING IN ATMOSPHERIC TURBULENCE
journal, January 2012
- Cava, Daniela; Katul, Gabriel George; Molini, Annalisa
- Journal of Geophysical Research: Atmospheres, Vol. 117, Issue D1
The random sweeping decorrelation hypothesis in stratified turbulent flows
journal, October 1995
- Katul, Gabriel; Parlange, Marc; Albertson, John
- Fluid Dynamics Research, Vol. 16, Issue 5
Structure Functions In A Wall-Turbulent Shear Flow
journal, June 2002
- Giostra, U.; Cava, D.; Schipa, S.
- Boundary-Layer Meteorology, Vol. 103, Issue 3
The “Inactive” Eddy Motion and the Large-Scale Turbulent Pressure Fluctuations in the Dynamic Sublayer
journal, September 1996
- Katul, Gabriel G.; Albertson, John D.; Parlange, Marc B.
- Journal of the Atmospheric Sciences, Vol. 53, Issue 17
Characteristics of Gravity Waves over an Antarctic Ice Sheet during an Austral Summer
journal, August 2015
- Cava, Daniela; Giostra, Umberto; Katul, Gabriel
- Atmosphere, Vol. 6, Issue 9
On higher-order spectra of turbulence
journal, December 1975
- Atta, C. W. Van; Wyngaard, J. C.
- Journal of Fluid Mechanics, Vol. 72, Issue 4
Logarithmic scaling in the longitudinal velocity variance explained by a spectral budget
journal, December 2013
- Banerjee, T.; Katul, G. G.
- Physics of Fluids, Vol. 25, Issue 12
Hierarchical random additive process and logarithmic scaling of generalized high order, two-point correlations in turbulent boundary layer flow
journal, June 2016
- Yang, X. I. A.; Marusic, I.; Meneveau, C.
- Physical Review Fluids, Vol. 1, Issue 2
The sweeping decorrelation hypothesis and energy–inertial scale interaction in high Reynolds number flows
journal, March 1993
- Praskovsky, Alexander A.; Gledzer, Evgeny B.; Karyakin, Mikhail Yu.
- Journal of Fluid Mechanics, Vol. 248
Scaling of second- and higher-order structure functions in turbulent boundary layers
journal, March 2015
- de Silva, C. M.; Marusic, I.; Woodcock, J. D.
- Journal of Fluid Mechanics, Vol. 769
The logarithmic structure function law in wall-layer turbulence
journal, February 2006
- Davidson, P. A.; Nickels, T. B.; Krogstad, P. -Å.
- Journal of Fluid Mechanics, Vol. 550, Issue -1
Numerical and Experimental Investigation of the Neutral Atmospheric Surface Layer
journal, January 2007
- Drobinski, Philippe; Carlotti, Pierre; Redelsperger, Jean-Luc
- Journal of the Atmospheric Sciences, Vol. 64, Issue 1
Random-sweeping hypothesis for passive scalars in isotropic turbulence
journal, May 2002
- Yeung, P. K.; Sawford, Brian L.
- Journal of Fluid Mechanics, Vol. 459
On the determination of the height of the Ekman boundary layer
journal, December 1972
- Zilitinkevich, S. S.
- Boundary-Layer Meteorology, Vol. 3, Issue 2
Origin of the “ ” Spectral Law in Wall-Bounded Turbulence
journal, July 1999
- Nikora, Vladimir
- Physical Review Letters, Vol. 83, Issue 4
A wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis
journal, September 1995
- Perry, A. E.; Marušić, Ivan
- Journal of Fluid Mechanics, Vol. 298
An experimental study of the turbulence structure in smooth- and rough-wall boundary layers
journal, April 1987
- Perry, A. E.; Lim, K. L.; Henbest, S. M.
- Journal of Fluid Mechanics, Vol. 177
Inertial-Range Spectrum of Hydromagnetic Turbulence
journal, January 1965
- Kraichnan, Robert H.
- Physics of Fluids, Vol. 8, Issue 7
On the logarithmic region in wall turbulence
journal, January 2013
- Marusic, Ivan; Monty, Jason P.; Hultmark, Marcus
- Journal of Fluid Mechanics, Vol. 716
Generalized logarithmic law for high-order moments in turbulent boundary layers
journal, February 2013
- Meneveau, Charles; Marusic, Ivan
- Journal of Fluid Mechanics, Vol. 719
Higher-Order Correlations in a Turbulent Field
journal, January 1967
- Frenkiel, François N.
- Physics of Fluids, Vol. 10, Issue 3
Coherent structures and the k −1 spectral behaviour
journal, December 2013
- Calaf, M.; Hultmark, M.; Oldroyd, H. J.
- Physics of Fluids, Vol. 25, Issue 12
A Spectral Budget Model for the Longitudinal Turbulent Velocity in the Stable Atmospheric Surface Layer
journal, January 2016
- Banerjee, Tirtha; Li, Dan; Juang, Jehn-Yih
- Journal of the Atmospheric Sciences, Vol. 73, Issue 1
Turbulent fluctuations above the buffer layer of wall-bounded flows
journal, September 2008
- JimÉNez, Javier; Hoyas, Sergio
- Journal of Fluid Mechanics, Vol. 611
Energy-Inertial Scale Interactions for Velocity and Temperature in the Unstable Atmospheric Surface Layer
journal, January 1997
- Katul, Gabriel; Hsieh, Cheng-I; Sigmon, John
- Boundary-Layer Meteorology, Vol. 82, Issue 1
Turbulent Pipe Flow at Extreme Reynolds Numbers
journal, February 2012
- Hultmark, M.; Vallikivi, M.; Bailey, S. C. C.
- Physical Review Letters, Vol. 108, Issue 9
Space‐time correlations in turbulence: Kinematical versus dynamical effects
journal, February 1989
- Yakhot, Victor; Orszag, Steven A.; She, Zhen‐Su
- Physics of Fluids A: Fluid Dynamics, Vol. 1, Issue 2
Time correlations and random sweeping in isotropic turbulence
journal, January 1990
- Nelkin, Mark; Tabor, M.
- Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 1
Transport Processes as Foundations of the Heisenberg and Obukhoff Theories of Turbulence
journal, January 1954
- Tchen, Chan-Mou
- Physical Review, Vol. 93, Issue 1
Spectral measurements of turbulent momentum transfer in fully developed pipe flow
journal, October 1973
- Bremhorst, K.; Walker, T. B.
- Journal of Fluid Mechanics, Vol. 61, Issue 1
The physics of wall turbulence
journal, February 1999
- Jiménez, Javier
- Physica A: Statistical Mechanics and its Applications, Vol. 263, Issue 1-4
Low-wavenumber spectral characteristics of velocity and temperature in the atmospheric surface layer
journal, January 1995
- Katul, Gabriel G.; Chu, Chia R.; Parlange, Marc B.
- Journal of Geophysical Research, Vol. 100, Issue D7
Modelling velocity spectra in the lower part of the planetary boundary layer
journal, July 1984
- Olesen, H. R.; Larsen, S. E.; H�jstrup, J.
- Boundary-Layer Meteorology, Vol. 29, Issue 3
A theoretical and experimental study of wall turbulence
journal, April 1986
- Perry, A. E.; Henbest, S.; Chong, M. S.
- Journal of Fluid Mechanics, Vol. 165, Issue -1
Turbulent Kinetic Energy Dissipation in the Surface Layer
journal, June 2009
- Charuchittipan, D.; Wilson, J. D.
- Boundary-Layer Meteorology, Vol. 132, Issue 2
The Spectrum of Turbulence
journal, February 1938
- Taylor, G. I.
- Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, Vol. 164, Issue 919
Scaling laws for pipe-flow turbulence
journal, January 1975
- Perry, A. E.; Abell, C. J.
- Journal of Fluid Mechanics, Vol. 67, Issue 2
Bottlenecks in turbulent kinetic energy spectra predicted from structure function inflections using the Von Kármán-Howarth equation
journal, September 2015
- Katul, Gabriel G.; Manes, Costantino; Porporato, Amilcare
- Physical Review E, Vol. 92, Issue 3
Bottleneck effect in three-dimensional turbulence simulations
journal, August 2003
- Dobler, Wolfgang; Haugen, Nils Erland L.; Yousef, Tarek A.
- Physical Review E, Vol. 68, Issue 2
Some observed properties of atmospheric turbulence
book, January 1972
- Dutton, John A.; Deaven, Dennis G.
- Statistical Models and Turbulence
Magnetic pumping model for energizing superthermal particles applied to observations of the Earth's bow shock
journal, June 2020
- Lichko, E.; Egedal, J.
- Nature Communications, Vol. 11, Issue 1
Higher-Order Correlations in a Turbulent Field
journal, January 1967
- Frenkiel, François N.
- Physics of Fluids, Vol. 10, Issue 9
The Spectrum of Turbulence
journal, October 1940
- De Feriet, J. Kampe
- Journal of the Aeronautical Sciences, Vol. 7, Issue 12
Turbulent Flows
journal, October 2001
- Pope, Stephen B.
- Measurement Science and Technology, Vol. 12, Issue 11
Large-eddy simulation study of the logarithmic law for second and higher-order moments in turbulent wall-bounded flow
text, January 2014
- Stevens, Richard J. A. M.; Wilczek, Michael; Meneveau, Charles
- arXiv
Works referencing / citing this record:
Modeling space-time correlations of velocity fluctuations in wind farms
journal, March 2018
- Lukassen, Laura J.; Stevens, Richard J. A. M.; Meneveau, Charles
- Wind Energy, Vol. 21, Issue 7
Impact of phenomenological theory of turbulence on pragmatic approach to fluvial hydraulics
journal, April 2018
- Ali, Sk Zeeshan; Dey, Subhasish
- Physics of Fluids, Vol. 30, Issue 4
Modeling space-time correlations of velocity fluctuations in wind farms
text, January 2017
- Lukassen, Laura J.; Stevens, Richard J. A. M.; Meneveau, Charles
- arXiv