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Wall-attached and wall-detached eddies in wall-bounded turbulent flows

Published online by Cambridge University Press:  27 December 2019

Ruifeng Hu Open the ORCID record for Ruifeng Hu [Opens in a new window] ,
Xiang I. A. Yang Open the ORCID record for Xiang I. A. Yang [Opens in a new window]  and
Xiaojing Zheng
Ruifeng Hu
Affiliation:
Key Laboratory of Mechanics on Disaster and Environment in Western China, Ministry of Education, and Department of Mechanics and Engineering Sciences, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou731000, China Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA Research Center for Applied Mechanics, School of Mechano-Electronic Engineering, Xidian University, Xi’an710071, China
Xiang I. A. Yang*
Affiliation:
Department of Mechanical Engineering, Pennsylvania State University, State College,PA 16802, USA
Xiaojing Zheng*
Affiliation:
Research Center for Applied Mechanics, School of Mechano-Electronic Engineering, Xidian University, Xi’an710071, China
*
†Email addresses for correspondence: xiangyang@psu.edu, xjzheng@xidian.edu.cn
†Email addresses for correspondence: xiangyang@psu.edu, xjzheng@xidian.edu.cn
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Abstract

According to Townsend’s attached eddy hypothesis (AEH), a boundary layer flow is comprised of wall-attached eddies, but to extract the part of the flow whose statistical behaviours are well described by the AEH is not at all straightforward. The objective of this work is to extract the part of the flow that can be described by the AEH, and study the statistical behaviours of the other part, which cannot be described by the AEH. In this process, two types of eddies are identified in addition to the Kolmogorov-scale eddies, i.e. wall-attached eddies and wall-detached eddies. The statistical behaviours of the wall-attached eddies are shown to be very well described by the AEH, i.e. the eddies are wall-attached, self-similar and, importantly, Gaussian, whereas the wall-detached eddies cannot be modelled by the AEH. Specifically, a decomposition scheme is proposed following Townsend (The Structure of Turbulent Shear Flow, Cambridge University Press, 1976). We apply our decomposition scheme to three different flows, i.e. channel, boundary layer and atmospheric surface layer flows. The results are similar with only quantitative differences, suggesting possible universality in both the wall-attached eddies and the wall-detached eddies.

JFM classification

Boundary Layers: Boundary layer structure Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 885 , 25 February 2020 , A30
Copyright
© The Author(s), 2019. Published by Cambridge University Press

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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. Fluids Engng 126 (5), 835–843.CrossRefGoogle Scholar
Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.CrossRefGoogle Scholar
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.CrossRefGoogle Scholar
Agostini, L. & Leschziner, M. 2017 Spectral analysis of near-wall turbulence in channel flow at Re 𝜏 = 4200 with emphasis on the attached-eddy hypothesis. Phys. Rev. Fluids 2 (1), 014603.CrossRefGoogle Scholar
Agostini, L. & Leschziner, M. A. 2014 On the influence of outer large-scale structures on near-wall turbulence in channel flow. Phys. Fluids 26 (7), 075107.Google Scholar
Anderson, W. 2016 Amplitude modulation of streamwise velocity fluctuations in the roughness sublayer: evidence from large-eddy simulations. J. Fluid Mech. 789, 567–588.CrossRefGoogle Scholar
Baars, W. J., Hutchins, N. & Marusic, I. 2017a Reynolds number trend of hierarchies and scale interactions in turbulent boundary layers. Phil. Trans. R. Soc. Lond. A 375 (2089), 20160077.Google Scholar
Baars, W. J., Hutchins, N. & Marusic, I. 2017b Self-similarity of wall-attached turbulence in boundary layers. J. Fluid Mech. 823, R2.CrossRefGoogle Scholar
Baars, W. J. & Marusic, I. 2020a Data-driven decomposition of the streamwise turbulence kinetic energy in boundary layers. Part 1. Energy spectra. J. Fluid Mech. 882, A25.CrossRefGoogle Scholar
Baars, W. J. & Marusic, I. 2020b Data-driven decomposition of the streamwise turbulence kinetic energy in boundary layers. Part 2. Integrated energy and A 1. J. Fluid Mech. 882, A26.CrossRefGoogle Scholar
Baars, W. J., Talluru, K. M., Hutchins, N. & Marusic, I. 2015 Wavelet analysis of wall turbulence to study large-scale modulation of small scales. Exp. Fluids 56 (10), 188.CrossRefGoogle Scholar
Baidya, R.2016 Multicomponent velocity measurements in turbulent boundary layers. PhD thesis, The University of Melbourne.Google Scholar
Baidya, R., Philip, J., Hutchins, N., Monty, J. & Marusic, I. 2017 Distance-from-the-wall scaling of turbulent motions in wall-bounded flows. Phys. Fluids 29 (2), 020712.CrossRefGoogle Scholar
Balakumar, B. J. & Adrian, R. J. 2007 Large- and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. Lond. A 365 (1852), 665–681.CrossRefGoogle ScholarPubMed
Bandyopadhyay, P. R. & Hussain, A. K. M. F. 1984 The coupling between scales in shear flows. Phys. Fluids 27 (9), 2221–2228.CrossRefGoogle Scholar
Bernardini, M. & Pirozzoli, S. 2011 Inner/outer layer interactions in turbulent boundary layers: a refined measure for the large-scale amplitude modulation mechanism. Phys. Fluids 23 (6), 061701.CrossRefGoogle Scholar
Brown, G. L. & Thomas, A. S. W. 1977 Large structure in a turbulent boundary layer. Phys. Fluids 20 (10), S243–S252.CrossRefGoogle Scholar
Cantwell, B. J. 1981 Organized motion in turbulent flow. Annu. Rev. Fluid Mech. 13 (1), 457–515.CrossRefGoogle Scholar
Chen, X., Hussain, F. & She, Z.-S. 2018 Quantifying wall turbulence via a symmetry approach. Part 2. Reynolds stresses. J. Fluid Mech. 850, 401–438.CrossRefGoogle Scholar
Cheng, C., Li, W., Lozano-Duran, A. & Liu, H. 2019 Identity of attached eddies in turbulent channel flows with bidimensional empirical mode decomposition. J. Fluid Mech. 870, 1037–1071.CrossRefGoogle ScholarPubMed
Christensen, K. T. & Adrian, R. J. 2001 Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433–443.CrossRefGoogle Scholar
Chung, D., Marusic, I., Monty, J. P., Vallikivi, M. & Smits, A. J. 2015 On the universality of inertial energy in the log layer of turbulent boundary layer and pipe flows. Exp. Fluids 56 (7), 141.CrossRefGoogle Scholar
Chung, D. & McKeon, B. J. 2010 Large-eddy simulation of large-scale structures in long channel flow. J. Fluid Mech. 661, 341–364.CrossRefGoogle Scholar
Davidson, P. A., Nickels, T. B. & Krogstad, P.-Å. 2006 The logarithmic structure function law in wall-layer turbulence. J. Fluid Mech. 550, 51–60.CrossRefGoogle Scholar
De Silva, C. M., Hutchins, N. & Marusic, I. 2016 Uniform momentum zones in turbulent boundary layers. J. Fluid Mech. 786, 309–331.CrossRefGoogle Scholar
De Silva, C. M., Marusic, I., Woodcock, J. D. & Meneveau, C. 2015 Scaling of second-and higher-order structure functions in turbulent boundary layers. J. Fluid Mech. 769, 654–686.CrossRefGoogle Scholar
Del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144.CrossRefGoogle Scholar
Del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2006 Self-similar vortex clusters in the turbulent logarithmic region. J. Fluid Mech. 561, 329–358.CrossRefGoogle Scholar
Deng, S., Pan, C., Wang, J. & He, G. 2018 On the spatial organization of hairpin packets in a turbulent boundary layer at low-to-moderate Reynolds number. J. Fluid Mech. 844, 635–668.CrossRefGoogle Scholar
Dogan, E., Hanson, R. E. & Ganapathisubramani, B. 2016 Interactions of large-scale free-stream turbulence with turbulent boundary layers. J. Fluid Mech. 802, 79–107.CrossRefGoogle Scholar
Dogan, E., Örlü, R., Gatti, D., Vinuesa, R. & Schlatter, P. 2019 Quantification of amplitude modulation in wall-bounded turbulence. Fluid Dyn. Res. 51 (1), 011408.CrossRefGoogle Scholar
Duvvuri, S. & McKeon, B. J. 2015 Triadic scale interactions in a turbulent boundary layer. J. Fluid Mech. 767, R4.CrossRefGoogle Scholar
Ganapathisubramani, B. 2018 Law of the wall for small-scale streamwise turbulence intensity in high-Reynolds-number turbulent boundary layers. Phys. Rev. Fluids 3 (10), 104607.CrossRefGoogle Scholar
Ganapathisubramani, B., Hutchins, N., Monty, J. P., Chung, D. & Marusic, I. 2012 Amplitude and frequency modulation in wall turbulence. J. Fluid Mech. 712, 61–91.CrossRefGoogle Scholar
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 35–46.CrossRefGoogle Scholar
Ge, M.-W., Yang, X. I. A. & Marusic, I. 2019 Velocity probability distribution scaling in wall-bounded flows at high Reynolds numbers. Phys. Rev. Fluids 4, 034101.CrossRefGoogle Scholar
Graham, J., Kanov, K., Yang, X. I. A., Lee, M., Malaya, N., Lalescu, C. C., Burns, R., Eyink, G., Szalay, A., Moser, R. D. et al. 2016 A web services accessible database of turbulent channel flow and its use for testing a new integral wall model for LES. J. Turbul. 17 (2), 181–215.CrossRefGoogle Scholar
Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542.CrossRefGoogle Scholar
Guala, M., Metzger, M. & McKeon, B. J. 2011 Interactions within the turbulent boundary layer at high Reynolds number. J. Fluid Mech. 666, 573–604.CrossRefGoogle Scholar
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.CrossRefGoogle Scholar
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297–338.CrossRefGoogle Scholar
Hellström, L. H. O., Marusic, I. & Smits, A. J. 2016 Self-similarity of the large-scale motions in turbulent pipe flow. J. Fluid Mech. 792, R1.CrossRefGoogle Scholar
Howland, M. F. & Yang, X. I. A. 2018 Dependence of small-scale energetics on large scales in turbulent flows. J. Fluid Mech. 852, 641–662.CrossRefGoogle Scholar
Hu, R. & Zheng, X. 2018 Energy contributions by inner and outer motions in turbulent channel flows. Phys. Rev. Fluids 3 (8), 084607.CrossRefGoogle Scholar
Hultmark, M., Vallikivi, M., Bailey, S. C. C. & Smits, A. J. 2012 Turbulent pipe flow at extreme Reynolds numbers. Phys. Rev. Lett. 108 (9), 094501.CrossRefGoogle ScholarPubMed
Hutchins, N. & Marusic, I. 2007a Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365 (1852), 647–664.CrossRefGoogle Scholar
Hutchins, N., Nickels, T. B., Marusic, I. & Chong, M. S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103–136.CrossRefGoogle Scholar
Hwang, J. & Sung, H. J. 2018 Wall-attached structures of velocity fluctuations in a turbulent boundary layer. J. Fluid Mech. 856, 958–983.CrossRefGoogle Scholar
Hwang, Y. 2015 Statistical structure of self-sustaining attached eddies in turbulent channel flow. J. Fluid Mech. 767, 254–289.CrossRefGoogle Scholar
Jiménez, J. 2012 Cascades in wall-bounded turbulence. Annu. Rev. Fluid Mech. 44, 27–45.CrossRefGoogle Scholar
Jiménez, J. 2018 Coherent structures in wall-bounded turbulence. J. Fluid Mech. 842, P1.CrossRefGoogle Scholar
Jiménez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215–236.CrossRefGoogle Scholar
Jiménez, J. & Moser, R. D. 2007 What are we learning from simulating wall turbulence? Phil. Trans. R. Soc. Lond. A 365 (1852), 715–732.CrossRefGoogle ScholarPubMed
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.CrossRefGoogle Scholar
Katul, G. & Vidakovic, B. 1996 The partitioning of attached and detached eddy motion in the atmospheric surface layer using Lorentz wavelet filtering. Boundary-Layer Meteorol. 77 (2), 153–172.CrossRefGoogle Scholar
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417–422.CrossRefGoogle Scholar
Kovasznay, L. S. G., Kibens, V. & Blackwelder, R. F. 1970 Large-scale motion in the intermittent region of a turbulent boundary layer. J. Fluid Mech. 41 (2), 283–325.CrossRefGoogle Scholar
Laval, J. P., Vassilicos, J. C., Foucaut, J. M. & Stanislas, M. 2017 Comparison of turbulence profiles in high-Reynolds-number turbulent boundary layers and validation of a predictive model. J. Fluid Mech. 814, R2.CrossRefGoogle Scholar
Lee, J. H. & Sung, H. J. 2011 Very-large-scale motions in a turbulent boundary layer. J. Fluid Mech. 673, 80–120.CrossRefGoogle Scholar
Lee, M. K., Malaya, N. & Moser, R. D. 2013 Petascale direct numerical simulation of turbulent channel flow on up to 786k cores. In 2013 International Conference for High Performance Computing, Networking, Storage and Analysis. IEEE Computer Society.Google Scholar
Lee, M. K. & Moser, R. D. 2015 Direct numerical simulation of turbulent channel flow up to Re 𝜏 ≈ 5200. J. Fluid Mech. 774, 395–415.CrossRefGoogle Scholar
Lee, M. K. & Moser, R. D. 2019 Spectral analysis of the budget equation in turbulent channel flows at high Reynolds number. J. Fluid Mech. 860, 886–938.CrossRefGoogle Scholar
Liu, H., Bo, T. & Liang, Y. 2017 The variation of large-scale structure inclination angles in high Reynolds number atmospheric surface layers. Phys. Fluids 29 (3), 035104.CrossRefGoogle Scholar
Liu, H., Wang, G. & Zheng, X. 2019 Amplitude modulation between multi-scale turbulent motions in high-Reynolds-number atmospheric surface layers. J. Fluid Mech. 861, 585–607.CrossRefGoogle Scholar
Lozano-Durán, A., Flores, O. & Jiménez, J. 2012 The three-dimensional structure of momentum transfer in turbulent channels. J. Fluid Mech. 694, 100–130.CrossRefGoogle Scholar
Marusic, I., Chauhan, K. A., Kulandaivelu, V. & Hutchins, N. 2015 Evolution of zero-pressure-gradient boundary layers from different tripping conditions. J. Fluid Mech. 783, 379–411.CrossRefGoogle Scholar
Marusic, I. & Heuer, W. D. C. 2007 Reynolds number invariance of the structure inclination angle in wall turbulence. Phys. Rev. Lett. 99 (11), 114504.CrossRefGoogle ScholarPubMed
Marusic, I., McKeon, B. J., Monkewitz, P. A., Nagib, H. M., Smits, A. J. & Sreenivasan, K. R. 2010 Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22 (6), 065103.CrossRefGoogle Scholar
Marusic, I. & Monty, J. P. 2019 Attached eddy model of wall turbulence. Annu. Rev. Fluid Mech. 51, 49–74.CrossRefGoogle Scholar
Marusic, I., Monty, J. P., Hultmark, M. & Smits, A. J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.CrossRefGoogle Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.CrossRefGoogle Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2011a A predictive inner-outer model for streamwise turbulence statistics in wall-bounded flows. J. Fluid Mech. 681, 537–566.CrossRefGoogle Scholar
Mathis, R., Marusic, I., Hutchins, N. & Sreenivasan, K. R. 2011b The relationship between the velocity skewness and the amplitude modulation of the small scale by the large scale in turbulent boundary layers. Phys. Fluids 23 (12), 121702.CrossRefGoogle Scholar
McKeon, B. J. & Sharma, A. S. 2010 A critical-layer framework for turbulent pipe flow. J. Fluid Mech. 658, 336–382.CrossRefGoogle Scholar
Meneveau, C. & Marusic, I. 2013 Generalized logarithmic law for high-order moments in turbulent boundary layers. J. Fluid Mech. 719, R1.CrossRefGoogle Scholar
Monkewitz, P. A. & Nagib, H. M. 2015 Large-Reynolds-number asymptotics of the streamwise normal stress in zero-pressure-gradient turbulent boundary layers. J. Fluid Mech. 783, 474–503.CrossRefGoogle Scholar
Monty, J. P., Hutchins, N., Ng, H. C. H., Marusic, I. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431–442.CrossRefGoogle Scholar
Mouri, H. 2017 Two-point correlation in wall turbulence according to the attached-eddy hypothesis. J. Fluid Mech. 821, 343–357.CrossRefGoogle Scholar
Mouri, H., Morinaga, T. & Haginoya, S. 2019 Unlikely existence of k x-1 spectral law in wall turbulence: an observation of the atmospheric surface layer. Phys. Fluids 31 (3), 035103.CrossRefGoogle Scholar
Nickels, T. B., Marusic, I., Hafez, S. & Chong, M. S. 2005 Evidence of the k 1-1 law in a high-Reynolds-number turbulent boundary layer. Phys. Rev. Lett. 95 (7), 074501.CrossRefGoogle Scholar
Pathikonda, G. & Christensen, K. T. 2017 Inner–outer interactions in a turbulent boundary layer overlying complex roughness. Phys. Rev. Fluids 2 (4), 044603.CrossRefGoogle Scholar
Pathikonda, G. & Christensen, K. T. 2019 Investigation of inner-outer interactions in a turbulent boundary layer using high-speed particle image velocimetry. Phys. Rev. Fluids 4 (3), 034607.CrossRefGoogle Scholar
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173–217.CrossRefGoogle Scholar
Perry, A. E., Henbest, S. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163–199.CrossRefGoogle Scholar
Perry, A. E. & Marusic, I. 1995 A wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis. J. Fluid Mech. 298, 361–388.CrossRefGoogle Scholar
Philip, J., Baidya, R., Hutchins, N., Monty, J. & Marusic, I. 2013 Spatial averaging of streamwise and spanwise velocity measurements in wall-bounded turbulence using v- and x-probes. Meas. Sci. Technol. 24, 115302.Google Scholar
Pullin, D. I., Inoue, M. & Saito, N. 2013 On the asymptotic state of high Reynolds number, smooth-wall turbulent flows. Phys. Fluids 25 (1), 015116.CrossRefGoogle Scholar
Rao, K. N., Narasimha, R. & Narayanan, M. A. B. 1971 The bursting phenomenon in a turbulent boundary layer. J. Fluid Mech. 48 (2), 339–352.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.CrossRefGoogle Scholar
Schlatter, P. & Örlü, R. 2010 Quantifying the interaction between large and small scales in wall-bounded turbulent flows: a note of caution. Phys. Fluids 22 (5), 051704.CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.CrossRefGoogle Scholar
Sharma, A. S. & McKeon, B. J. 2013 On coherent structure in wall turbulence. J. Fluid Mech. 728, 196–238.CrossRefGoogle Scholar
Smits, A. J., McKeon, B. J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.CrossRefGoogle Scholar
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37–74.CrossRefGoogle Scholar
Townsend, A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Vallikivi, M., Hultmark, M. & Smits, A. J. 2015 Turbulent boundary layer statistics at very high Reynolds number. J. Fluid Mech. 779, 371–389.CrossRefGoogle Scholar
Vassilicos, J. C., Laval, J.-P., Foucaut, J.-M. & Stanislas, M. 2015 The streamwise turbulence intensity in the intermediate layer of turbulent pipe flow. J. Fluid Mech. 774, 324–341.CrossRefGoogle Scholar
Vincenti, P., Klewicki, J., Morrill-Winter, C., White, C. M. & Wosnik, M. 2013 Streamwise velocity statistics in turbulent boundary layers that spatially develop to high Reynolds number. Exp. Fluids 54 (12), 1629.CrossRefGoogle Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9 (4), 883–900.CrossRefGoogle Scholar
Wang, C., Gao, Q., Wang, J., Wang, B. & Pan, C. 2019 Experimental study on dominant vortex structures in near-wall region of turbulent boundary layer based on tomographic particle image velocimetry. J. Fluid Mech. 874, 426–454.CrossRefGoogle Scholar
Wang, G. & Zheng, X. 2016 Very large scale motions in the atmospheric surface layer: a field investigation. J. Fluid Mech. 802, 464–489.CrossRefGoogle Scholar
Woodcock, J. D. & Marusic, I. 2015 The statistical behaviour of attached eddies. Phys. Fluids 27 (1), 015104.CrossRefGoogle Scholar
Yamamoto, Y. & Tsuji, Y. 2018 Numerical evidence of logarithmic regions in channel flow at Re 𝜏 = 8000. Phys. Rev. Fluids 3 (1), 012602.Google Scholar
Yang, H. & Bo, T. 2018 Scaling of wall-normal turbulence intensity and vertical eddy structures in the atmospheric surface layer. Bound.-Layer Meteor. 166, 199–216.CrossRefGoogle Scholar
Yang, X. I. A., Baidya, R., Johnson, P., Marusic, I. & Meneveau, C. 2017 Structure function tensor scaling in the logarithmic region derived from the attached eddy model of wall-bounded turbulent flows. Phys. Rev. Fluids 2 (6), 064602.CrossRefGoogle Scholar
Yang, X. I. A., Baidya, R., Lv, Y. & Marusic, I. 2018 Hierarchical random additive model for the spanwise and wall-normal velocities in wall-bounded flows at high Reynolds numbers. Phys. Rev. Fluids 3 (12), 124606.CrossRefGoogle Scholar
Yang, X. I. A., Marusic, I. & Meneveau, C. 2016a Hierarchical random additive process and logarithmic scaling of generalized high order, two-point correlations in turbulent boundary layer flow. Phys. Rev. Fluids 1 (2), 024402.CrossRefGoogle Scholar
Yang, X. I. A., Marusic, I. & Meneveau, C. 2016b Moment generating functions and scaling laws in the inertial layer of turbulent wall-bounded flows. J. Fluid Mech. 791, R2.CrossRefGoogle Scholar
Yang, X. I. A. & Meneveau, C. 2019 Hierarchical random additive model for wall-bounded flows at high Reynolds numbers. Fluid Dyn. Res. 51 (1), 011405.CrossRefGoogle Scholar