Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-24T20:39:42.789Z Has data issue: false hasContentIssue false
  • English
  • Français

Uncovering Townsend’s wall-attached eddies in low-Reynolds-number wall turbulence

Published online by Cambridge University Press:  26 February 2020

Cheng Cheng ,
Weipeng Li Open the ORCID record for Weipeng Li [Opens in a new window] ,
Adrián Lozano-Durán Open the ORCID record for Adrián Lozano-Durán [Opens in a new window]  and
Hong Liu
Cheng Cheng
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai200240, PR China
Weipeng Li*
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai200240, PR China
Adrián Lozano-Durán
Affiliation:
Center for Turbulence Research, Stanford University, CA94305, USA
Hong Liu
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai200240, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A growing body of studies supports the existence of Townsend’s wall-attached eddies in wall turbulence under the condition of sufficiently high Reynolds numbers. In the present work, we uncover the signature of Townsend’s wall-attached eddies in low-Reynolds-number wall turbulence. To this end, we use a three-dimensional clustering methodology to identify the wall-attached structures of intense streamwise and spanwise velocity fluctuations in turbulent channel flows at four Reynolds numbers ($Re_{\unicode[STIX]{x1D70F}}=186$, 358, 547 and 934). The statistical properties of the structures, such as their geometric self-similarity, population density and statistical moments, are investigated and compared with the predictions of the attached-eddy model. Particular attention is paid to the asymmetries between high- and low-speed wall-attached streaky structures, and we show that the former are a closer representation of the wall-attached eddies. This observation is ascribed to the differences between the sweep and ejection events associated with the streaks. We also examine the Reynolds-number effects on the statistical properties of the structures, and find that the signature of attached eddies can be observed within the Reynolds-number range under scrutiny. Our approach paves the way to cost-efficient model development and flow prediction using computationally more affordable simulations at low Reynolds numbers.

JFM classification

Boundary Layers: Boundary layer structure Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 889 , 25 April 2020 , A29
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Agostini, L. & Leschziner, M. 2014 On the influence of outer large-scale structures on near-wall turbulence in channel flow. Phys. Fluids 26 (7), 075107.Google Scholar
Agostini, L. & Leschziner, M. 2016a On the validity of the quasi-steady-turbulence hypothesis in representing the effects of large scales on small scales in boundary layers. Phys. Fluids 28 (4), 045102.CrossRefGoogle Scholar
Agostini, L. & Leschziner, M. 2016b Predicting the response of small-scale near-wall turbulence to large-scale outer motions. Phys. Fluids 28 (1), 339–352.CrossRefGoogle Scholar
Agostini, L. & Leschziner, M. 2019 The connection between the spectrum of turbulent scales and the skin-friction statistics in channel flow at Re 𝜏 ≈ 1000. J. Fluid Mech. 871, 22–51.CrossRefGoogle Scholar
Alfredsson, P. H., Segalini, A. & Örlü, R. 2011 A new scaling for the streamwise turbulence intensity in wall-bounded turbulent flows and what it tells us about the outer peak. Phys. Fluids 23 (4), 041702.CrossRefGoogle Scholar
Baars, W. J., Hutchins, N. & Marusic, I. 2017 Self-similarity of wall-attached turbulence in boundary layers. J. Fluid Mech. 823, R2.CrossRefGoogle Scholar
Baars, W. J. & Marusic, I. 2020 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
Cheng, C., Li, W., Lozano-Durán, 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
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
Corrsin, S.1958 Local isotropy in turbulent shear flow. NACA Res. Memo. 58B11.Google 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
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
Deshpande, R., Monty, J. P. & Marusic, I. 2019 Streamwise inclination angle of large wall-attached structures in turbulent boundary layers. J. Fluid Mech. 877, R4.CrossRefGoogle Scholar
Dong, S., Lozano-Durán, A., Sekimoto, A. & Jiménez, J. 2017 Coherent structures in statistically stationary homogeneous shear turbulence. J. Fluid Mech. 816, 167–208.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
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.Google Scholar
Hu, R., Yang, X. I. A. & Zheng, X. 2020 Wall-attached and wall-detached eddies in wall-bounded turbulent flows. J. Fluid Mech. 885, A30.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
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, J. & Sung, H. J. 2019 Wall-attached clusters for the logarithmic velocity law in turbulent pipe flow. Phys. Fluids 31 (5), 055109.Google Scholar
Hwang, J. & Sung, H. J. 2017 Influence of large-scale motions on the frictional drag in a turbulent boundary layer. J. Fluid Mech. 829, 751–779.CrossRefGoogle Scholar
Hwang, Y. 2015 Statistical structure of self-sustaining attached eddies in turbulent channel flow. J. Fluid Mech. 767, 254–289.CrossRefGoogle Scholar
Hwang, Y. & Bengana, Y. 2016 Self-sustaining process of minimal attached eddies in turbulent channel flow. J. Fluid Mech. 795, 708–738.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
Klewicki, J., Fife, P. & Wei, T. 2009 On the logarithmic mean profile. J. Fluid Mech. 638, 73–93.CrossRefGoogle Scholar
Lee, M. & Moser, R. D. 2015 Direct numerical simulation of turbulent channel flow up to Re 𝜏 ≈ 5200. J. Fluid Mech. 774, 395–415.CrossRefGoogle Scholar
Lozano-Durán, A. & Bae, H. J. 2019 Characteristic scales of Townsend’s wall-attached eddies. J. Fluid Mech. 868, 698–725.CrossRefGoogle ScholarPubMed
Lozano-Durán, A. & Borrell, G. 2016 Algorithm 964: an efficient algorithm to compute the genus of discrete surfaces and applications to turbulent flows. ACM Trans. Math. Softw. 42 (4), 34:1–34:19.Google 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
Lozano-Durán, A. & Jiménez, J. 2014 Effect of the computational domain on direct simulations of turbulent channels up to Re 𝜏 = 4200. Phys. Fluids 26 (1), 011702.CrossRefGoogle Scholar
Lozano-Durán, A. & Jiménez, J. 2014 Time-resolved evolution of coherent structures in turbulent channels: characterization of eddies and cascades. J. Fluid Mech. 759, 432–471.CrossRefGoogle Scholar
Marusic, I., Baars, W. J. & Hutchins, N. 2017 Scaling of the streamwise turbulence intensity in the context of inner–outer interactions in wall turbulence. Phys. Rev. Fluids 2 (10), 100502.CrossRefGoogle Scholar
Marusic, I. & Kunkel, G. J. 2003 Streamwise turbulence intensity formulation for flat-plate boundary layers. Phys. Fluids 15 (8), 2461–2464.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., Marusic, I., Chernyshenko, S. I. & Hutchins, N. 2013 Estimating wall-shear-stress fluctuations given an outer region input. J. Fluid Mech. 715, 163–180.CrossRefGoogle Scholar
Mehrez, A., Philip, J., Yamamoto, Y. & Tsuji, Y. 2019 Pressure and spanwise velocity fluctuations in turbulent channel flows: logarithmic behavior of moments and coherent structures. Phys. Rev. Fluids 4 (4), 044601.CrossRefGoogle Scholar
Meneveau, C. & Marusic, I. 2013 Generalized logarithmic law for high-order moments in turbulent boundary layers. J. Fluid Mech. 719, R11.CrossRefGoogle Scholar
Mizuno, Y. & Jiménez, J. 2011 Mean velocity and length-scales in the overlap region of wall-bounded turbulent flows. Phys. Fluids 23 (8), 085112.CrossRefGoogle Scholar
Moisy, F. & Jiménez, J. 2004 Geometry and clustering of intense structures in isotropic turbulence. J. Fluid Mech. 513, 111–133.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
Osawa, K. & Jiménez, J. 2018 Intense structures of different momentum fluxes in turbulent channels. Phys. Rev. Fluids 3, 084603.CrossRefGoogle Scholar
Perry, A. & 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
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119 (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
Sillero, J. A., Jiménez, J. & Moser, R. D. 2013 One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to 𝛿+ ≈ 2000. Phys. Fluids 25 (10), 105102.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Wallace, J. M. 2016 Quadrant analysis in turbulence research: history and evolution. Annu. Rev. Fluid Mech. 48, 131–158.CrossRefGoogle Scholar
Wang, W., Pan, C. & Wang, J. 2018 Quasi-bivariate variational mode decomposition as a tool of scale analysis in wall-bounded turbulence. Exp. Fluids 59 (1), 1.CrossRefGoogle Scholar
Wang, W., Pan, C. & Wang, J. 2019 Multi-component variational mode decomposition and its application on wall-bounded turbulence. Exp. Fluids 60 (6), 95.CrossRefGoogle Scholar
Woodcock, J. D. & Marusic, I. 2015 The statistical behaviour of attached eddies. Phys. Fluids 27 (1), 97–120.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, Q., Willis, A. P. & Hwang, Y. 2019 Exact coherent states of attached eddies in channel flow. J. Fluid Mech. 862, 1029–1059.CrossRefGoogle Scholar
Yang, X., 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. 2016 Moment generating functions and scaling laws in the inertial layer of turbulent wall-bounded flows. J. Fluid Mech. 791, R2.CrossRefGoogle Scholar
Yoon, M., Hwang, J., Yang, J. & Sung, H. J. 2020 Wall-attached structures of streamwise velocity fluctuations in an adverse-pressure-gradient turbulent boundary layer. J. Fluid Mech. 885, A12.CrossRefGoogle Scholar