Hostname: page-component-784d4fb959-9bxm5 Total loading time: 0 Render date: 2025-07-15T23:08:25.271Z Has data issue: false hasContentIssue false
  • English
  • Français

Inter-scale energy transfer and interaction in a turbulent channel flow with randomly distributed wall roughness

Published online by Cambridge University Press:  14 July 2025

Guo-Zhen Ma ,
Chun-Xiao Xu Open the ORCID record for Chun-Xiao Xu [Opens in a new window] ,
Hyung Jin Sung Open the ORCID record for Hyung Jin Sung [Opens in a new window] ,
Hai-Ping Tian  and
Wei-Xi Huang Open the ORCID record for Wei-Xi Huang [Opens in a new window]
Guo-Zhen Ma
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China Institute of Applied Mechanics, Taiyuan University of Technology, Taiyuan 030024, PR China
Chun-Xiao Xu
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China State Key Laboratory of Advanced Space Propulsion, Tsinghua University, Beijing 100084, PR China
Hyung Jin Sung
Affiliation:
Department of Mechanical Engineering, KAIST, Daejeon 34141, Korea
Hai-Ping Tian
Affiliation:
Institute of Applied Mechanics, Taiyuan University of Technology, Taiyuan 030024, PR China
Wei-Xi Huang*
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China State Key Laboratory of Advanced Space Propulsion, Tsinghua University, Beijing 100084, PR China
*
Corresponding author: Wei-Xi Huang, hwx@tsinghua.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations are performed to explore the impact of surface roughness on inter-scale energy transfer and interaction in a turbulent open-channel flow over differently arranged rough walls. With friction Reynolds number approximately 540, six distinct configurations of roughness arrangements are examined. The results show that the clustered roughness arrangements yield notable changes in large-scale secondary-flow structures, which manifest in the profiles of dispersive stresses, predominantly near the roughness elements. They are marked by the presence of spanwise alternating high-momentum pathways and low-momentum pathways. From the outer peak in the spanwise energy spectra, the size and intensity of turbulent secondary flows are shown to be related to the spanwise spacing of the roughness heterogeneity. The emergence of turbulent secondary flows serves to suppress the original large-scale structures in the outer region of smooth-wall turbulence, paving the way for the development of new turbulent structures at the second harmonic scale. Furthermore, the spanwise triadic interaction analysis reveals the mutual energy exchange between the secondary harmonic scale and the secondary-flow scale. These findings elucidate the underlying mechanisms behind the attenuation of large-scale structures in the outer region influenced by roughness, offering new insights into the dynamic interplay of scale interactions in rough-wall turbulence.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulence simulation

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1015 , 25 July 2025 , A2
Check for updates
Copyright
© The Author(s), 2025. 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.)

Article purchase

Temporarily unavailable

References

Barros, J.M. & Christensen, K.T. 2014 Observations of turbulent secondary flows in a rough-wall boundary layer. J. Fluid Mech. 748, R1.10.1017/jfm.2014.218CrossRefGoogle Scholar
Bhaganagar, K., Kim, J. & Coleman, G. 2004 Effect of roughness on wall-bounded turbulence. Flow Turbul. Combust. 72 (2), 463–492.10.1023/B:APPL.0000044407.34121.64CrossRefGoogle Scholar
Busse, A. & Jelly, T.O. 2023 Effect of high skewness and kurtosis on turbulent channel flow over irregular rough walls. J. Turbul. 24 (1–2), 57–81.10.1080/14685248.2023.2173761CrossRefGoogle Scholar
Chan, L., MacDonald, M., Chung, D., Hutchins, N. & Ooi, A. 2018 Secondary motion in turbulent pipe flow with three-dimensional roughness. J. Fluid Mech. 854, 5–33.10.1017/jfm.2018.570CrossRefGoogle Scholar
Cho, M., Hwang, Y. & Choi, H. 2018 Scale interactions and spectral energy transfer in turbulent channel flow. J. Fluid Mech. 854, 474–504.10.1017/jfm.2018.643CrossRefGoogle Scholar
Choi, Y.K., Hwang, H.G., Lee, Y.M. & Lee, J.H. 2020 Effects of the roughness height in turbulent boundary layers over rod- and cuboid-roughened walls. Intl J. Heat Fluid Flow 85, 108644.10.1016/j.ijheatfluidflow.2020.108644CrossRefGoogle Scholar
Chung, D., Chan, L., MacDonald, M., Hutchins, N. & Ooi, A. 2015 A fast direct numerical simulation method for characterising hydraulic roughness. J. Fluid Mech. 773, 418–431.10.1017/jfm.2015.230CrossRefGoogle Scholar
Chung, D., Hutchins, N., Schultz, M.P. & Flack, K.A. 2021 Predicting the drag of rough surfaces. Annu. Rev. Fluid Mech. 53 (1), 439–471.10.1146/annurev-fluid-062520-115127CrossRefGoogle Scholar
De Marchis, M., Milici, B. & Napoli, E. 2015 Numerical observations of turbulence structure modification in channel flow over 2D and 3D rough walls. Intl J. Heat Fluid Flow 56, 108–123.10.1016/j.ijheatfluidflow.2015.07.002CrossRefGoogle Scholar
Dunbar, D., Scandura, P. & O’Donoghue, T. 2023 An experimental and numerical study of turbulent oscillatory flow over an irregular rough wall. J. Fluid Mech. 955, A33.10.1017/jfm.2022.1090CrossRefGoogle Scholar
Flack, K.A., Schultz, M.P. & Shapiro, T.A. 2005 Experimental support for Townsend’s Reynolds number similarity hypothesis on rough walls. Phys. Fluids 17 (3), 035102.10.1063/1.1843135CrossRefGoogle Scholar
Flores, O. & Jimenez, J. 2006 Effect of wall-boundary disturbances on turbulent channel flows. J. Fluid Mech. 566, 357–376.10.1017/S0022112006001534CrossRefGoogle Scholar
Ge, M.W., Xu, C.X. & Cui, G.X. 2010 Direct numerical simulation of flow in channel with time-dependent wall geometry. Appl. Maths Mech. 31 (1), 97–108.10.1007/s10483-010-0110-xCrossRefGoogle Scholar
Hamilton, J.M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.10.1017/S0022112095000978CrossRefGoogle Scholar
Hong, J.R., Katz, J. & Schultz, M.P. 2011 Near-wall turbulence statistics and flow structures over three-dimensional roughness in a turbulent channel flow. J. Fluid Mech. 667, 1–37.10.1017/S0022112010003988CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. A: Math. Phys. Engng Sci. 365 (1852), 647–664.10.1098/rsta.2006.1942CrossRefGoogle ScholarPubMed
Hwang, H.G. & Lee, J.H. 2018 Secondary flows in turbulent boundary layers over longitudinal surface roughness. Phys. Rev. Fluids 3 (1), 014608.10.1103/PhysRevFluids.3.014608CrossRefGoogle Scholar
Jelly, T.O., Ramani, A., Nugroho, B., Hutchins, N. & Busse, A. 2022 Impact of spanwise effective slope upon rough-wall turbulent channel flow. J. Fluid Mech. 951, A1.10.1017/jfm.2022.823CrossRefGoogle Scholar
Jensen, R.M. & Forooghi, P. 2025 A study of turbulent flow over patchy roughness. J. Fluid Mech. 1006, A28.10.1017/jfm.2024.1095CrossRefGoogle Scholar
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36 (1), 173–196.10.1146/annurev.fluid.36.050802.122103CrossRefGoogle Scholar
Jiménez, J. 2018 Coherent structures in wall-bounded turbulence. J. Fluid Mech. 842, P1.10.1017/jfm.2018.144CrossRefGoogle Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.10.1017/S0022112099005066CrossRefGoogle Scholar
Kaminaris, I.K., Balaras, E., Schultz, M.P. & Volino, R.J. 2023 Secondary flows in turbulent boundary layers developing over truncated cone surfaces. J. Fluid Mech. 961, A23.10.1017/jfm.2023.241CrossRefGoogle Scholar
Kevin, K., Monty, J.P., Bai, H.L., Pathikonda, G., Nugroho, B., Barros, J.M., Christensen, K.T. & Hutchins, N. 2017 Cross-stream stereoscopic particle image velocimetry of a modified turbulent boundary layer over directional surface pattern. J. Fluid Mech. 813, 412–435.10.1017/jfm.2016.879CrossRefGoogle Scholar
Lee, J.H., Seena, A., Lee, S.H. & Sung, H.J. 2012 Turbulent boundary layers over rod- and cube-roughened walls. J. Turbul. 13 (1), N40.10.1080/14685248.2012.716157CrossRefGoogle Scholar
Lee, J.H., Sung, H.J. & Krogstad, P.Å. 2011 Direct numerical simulation of the turbulent boundary layer over a cube-roughened wall. J. Fluid Mech. 669, 397–431.10.1017/S0022112010005082CrossRefGoogle Scholar
Lee, M. & Moser, R.D. 2015 Spectral analysis on Reynolds stress transport equation in high Re wall-bounded turbulence. In Proceedings of the 9th International Symposium on Turbulence and Shear Flow Phenomena (TSFP9), Melbourne, Australia, art. no. 4A-3. Available at: http://www.tsfp-conference.org/proceedings/2015/v2/4A-3.pdf.Google Scholar
Lee, S.H. & Sung, H.J. 2007 Direct numerical simulation of the turbulent boundary layer over a rod-roughened wall. J. Fluid Mech. 584, 125–146.10.1017/S0022112007006465CrossRefGoogle Scholar
Ma, G.Z., Xu, C.X., Sung, H.J. & Huang, W.X. 2020 Scaling of rough-wall turbulence by the roughness height and steepness. J. Fluid Mech. 900, R7.10.1017/jfm.2020.542CrossRefGoogle Scholar
Ma, G.Z., Xu, C.X., Sung, H.J. & Huang, W.X. 2023 Outer-layer similarity and energy transfer in a rough-wall turbulent channel flow. J. Fluid Mech. 968, A18.10.1017/jfm.2023.425CrossRefGoogle Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193–196.10.1126/science.1188765CrossRefGoogle ScholarPubMed
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.10.1017/S0022112009006946CrossRefGoogle Scholar
Medjnoun, T., Vanderwel, C. & Ganapathisubramani, B. 2018 Characteristics of turbulent boundary layers over smooth surfaces with spanwise heterogeneities. J. Fluid Mech. 838, 516–543.10.1017/jfm.2017.849CrossRefGoogle Scholar
Narayanan, C., Singh, J.S., Nauer, S., Belt, R., Palermo, T. & Lakehal, D. 2024 Direct numerical simulation of turbulent flow over irregular rough surfaces. Phys. Fluids 36 (6), 065166.10.1063/5.0209338CrossRefGoogle Scholar
Nikitin, N.V., Popelenskaya, N.V. & Stroh, A. 2021 Prandtl’s secondary flows of the second kind. Problems of description, prediction, and simulation. Fluid Dyn. 56 (4), 513–538.10.1134/S0015462821040091CrossRefGoogle Scholar
Nikora, V., Goring, D., McEwan, I. & Griffiths, G. 2001 Spatially averaged open-channel flow over rough bed. J. Hydraul. Engng 127 (2), 123–133.10.1061/(ASCE)0733-9429(2001)127:2(123)CrossRefGoogle Scholar
Nikora, V., McEwan, I., McLean, S., Coleman, S., Pokrajac, D. & Walters, R. 2007 Double-averaging concept for rough-bed open-channel and overland flows: theoretical background. J. Hydraul. Engng 133 (8), 873–883.10.1061/(ASCE)0733-9429(2007)133:8(873)CrossRefGoogle Scholar
Nilsen, C., Andersson, H.I. & Zhao, L.H. 2013 A Voronoï analysis of preferential concentration in a vertical channel flow. Phys. Fluids 25 (11), 115108.10.1063/1.4830435CrossRefGoogle Scholar
Orlandi, P. & Leonardi, S. 2006 DNS of turbulent channel flows with two- and three-dimensional roughness. J. Turbul. 7 (53), N73.10.1080/14685240600827526CrossRefGoogle Scholar
Orlandi, P. & Leonardi, S. 2008 Direct numerical simulation of three-dimensional turbulent rough channels: parameterization and flow physics. J. Fluid Mech. 606, 399–415.10.1017/S0022112008001985CrossRefGoogle Scholar
Raupach, M.R. & Shaw, R.H. 1982 Averaging procedures for flow within vegetation canopies. Boundary-Layer Meteorol. 22 (1), 79–90.10.1007/BF00128057CrossRefGoogle Scholar
Sarakinos, S. & Busse, A. 2019 Influence of spatial distribution of roughness elements on turbulent flow past a biofouled surface. In Proceedings of the 11th International Symposium on Turbulence and Shear Flow Phenomena (TSFP11), Southampton, UK. Available at: http://www.tsfp-conference.org/proceedings/2019/238.pdf.Google Scholar
Sarakinos, S. & Busse, A. 2022 Investigation of rough-wall turbulence over barnacle roughness with increasing solidity using direct numerical simulations. Phys. Rev. Fluids 7 (6), 064602.10.1103/PhysRevFluids.7.064602CrossRefGoogle Scholar
Sarakinos, S. & Busse, A. 2024 Reynolds number dependency of wall-bounded turbulence over a surface partially covered by barnacle clusters. Flow Turbul. Combust. 112 (1), 85–103.10.1007/s10494-023-00495-2CrossRefGoogle Scholar
Seddighi, M., He, S., Pokrajac, D., O’Donoghue, T. & Vardy, A.E. 2015 Turbulence in a transient channel flow with a wall of pyramid roughness. J. Fluid Mech. 781, 226–260.10.1017/jfm.2015.488CrossRefGoogle Scholar
Stroh, A., Schäfer, K., Frohnapfel, B. & Forooghi, P. 2020 Rearrangement of secondary flow over spanwise heterogeneous roughness. J. Fluid Mech. 885, R5.10.1017/jfm.2019.1030CrossRefGoogle Scholar
Thakkar, M., Busse, A. & Sandham, N. 2017 Surface correlations of hydrodynamic drag for transitionally rough engineering surfaces. J. Turbul. 18 (2), 138–169.10.1080/14685248.2016.1258119CrossRefGoogle Scholar
Townsend, A.A. 1976 The Structure of Turbulent Shear Flow. 2nd edn. Cambridge University Press.Google Scholar
Vanderwel, C. & Ganapathisubramani, B. 2015 Effects of spanwise spacing on large-scale secondary flows in rough-wall turbulent boundary layers. J. Fluid Mech. 774, R2.10.1017/jfm.2015.292CrossRefGoogle Scholar
Volino, R.J., Schultz, M.P. & Flack, K.A. 2009 Turbulence structure in a boundary layer with two-dimensional roughness. J. Fluid Mech. 635, 75–101.10.1017/S0022112009007617CrossRefGoogle Scholar
Wang, L.H., Zhang, W.Y., Hao, X.T., Huang, W.X., Shen, L., Xu, C.X. & Zhang, Z.S. 2020 Surface wave effects on energy transfer in overlying turbulent flow. J. Fluid Mech. 893, A21.10.1017/jfm.2020.246CrossRefGoogle Scholar
Wangsawijaya, D.D., Baidya, R., Chung, D., Marusic, I. & Hutchins, N. 2020 The effect of spanwise wavelength of surface heterogeneity on turbulent secondary flows. J. Fluid Mech. 894, A7.10.1017/jfm.2020.262CrossRefGoogle Scholar
Womack, K.M., Volino, R.J., Meneveau, C. & Schultz, M.P. 2022 Turbulent boundary layer flow over regularly and irregularly arranged truncated cone surfaces. J. Fluid Mech. 933, A38.10.1017/jfm.2021.946CrossRefGoogle Scholar
Wu, Y. & Christensen, K.T. 2007 Outer-layer similarity in the presence of a practical rough-wall topography. Phys. Fluids 19 (8), 085108.10.1063/1.2741256CrossRefGoogle Scholar
Yang, J.Z. & Anderson, W. 2018 Numerical study of turbulent channel flow over surfaces with variable spanwise heterogeneities: topographically-driven secondary flows affect outer-layer similarity of turbulent length scales. Flow Turbul. Combust. 100 (1), 1–17.10.1007/s10494-017-9839-5CrossRefGoogle Scholar
Yuan, J. & Piomelli, U. 2014 Roughness effects on the Reynolds stress budgets in near-wall turbulence. J. Fluid Mech. 760, R1.10.1017/jfm.2014.608CrossRefGoogle Scholar
Zampiron, A., Cameron, S. & Nikora, V. 2020 Secondary currents and very-large-scale motions in open-channel flow over streamwise ridges. J. Fluid Mech. 887, A17.10.1017/jfm.2020.8CrossRefGoogle Scholar
Zhang, W.Y., Huang, W.X. & Xu, C.X. 2019 Very large-scale motions in turbulent flows over streamwise traveling wavy boundaries. Phys. Rev. Fluids 4 (5), 054601.10.1103/PhysRevFluids.4.054601CrossRefGoogle Scholar