Skip to main content Accessibility help

Secondary motion in turbulent pipe flow with three-dimensional roughness

  • L. Chan (a1), M. MacDonald (a1), D. Chung (a1), N. Hutchins (a1) and A. Ooi (a1)...


The occurrence of secondary flows is investigated for three-dimensional sinusoidal roughness where the wavelength and height of the roughness elements are systematically altered. The flow spanned from the transitionally rough regime up to the fully rough regime and the solidity of the roughness ranged from a wavy, sparse roughness to a dense roughness. Analysing the time-averaged velocity, secondary flows are observed in all of the cases, reflected in the coherent stress profile which is dominant in the vicinity of the roughness elements. The roughness sublayer, defined as the region where the coherent stress is non-zero, scales with the roughness wavelength when the roughness is geometrically scaled (proportional increase in both roughness height and wavelength) and when the wavelength increases at fixed roughness height. Premultiplied energy spectra of the streamwise velocity turbulent fluctuations show that energy is reorganised from the largest streamwise wavelengths to the shorter streamwise wavelengths. The peaks in the premultiplied spectra at the streamwise and spanwise wavelengths are correlated with the roughness wavelength in the fully rough regime. Current simulations show that the spanwise scale of roughness determines the occurrence of large-scale secondary flows.


Corresponding author

Email address for correspondence:


Hide All
Anderson, W., Barros, J. M., Christensen, K. T. & Awasthi, A. 2015 Numerical and experimental study of mechanisms responsible for turbulent secondary flows in boundary layer flows over spanwise heterogeneous roughness. J. Fluid Mech. 768, 316347.
Andreopoulos, J. & Bradshaw, P. 1981 Measurements of turbulence structure in the boundary layer on a rough surface. Boundary-Layer Meteorol. 20, 201213.
Antonia, R. A. & Krogstad, P.-Å. 2001 Turbulence structure in boundary layers over different types of surface roughness. Fluid Dyn. Res. 28, 139157.
Antonia, R. A. & Luxton, R. E. 1971 The response of a turbulent boundary layer to a step change in surface roughness. Part 1. Smooth to rough. J. Fluid Mech. 48 (4), 721761.
Barros, J. M. & Christensen, K. T. 2014 Observations of turbulent secondary flows in a rough-wall boundary layer. J. Fluid Mech. 748, R1.
Barros, J. M., Schultz, M. P. & Flack, K. A. 2017 Measurements of skin-friction of systematically generated surface roughness. In Proc. of the 10th International Symposium on Turbulence and Shear Flow Phenomena (TSFP10), Chicago, USA.
Bhaganagar, K., Kim, J. & Coleman, G. 2004 Effect of roughness on wall-bounded turbulence. Flow Turbul. Combust. 72, 463492.
Brundrett, E. & Baines, W. D. 1964 The production and diffusion of vorticity in duct flow. J. Fluid Mech. 19, 375394.
Busse, A. E., Lützner, M. & Sandham, N. D. 2015 Direct numerical simulation of turbulent flow over a rough surface based on a surface scan. Comput. Fluids 116, 129147.
Chan, L., MacDonald, M., Chung, D., Hutchins, N. & Ooi, A. 2014 Numerical simulation of a rough-wall pipe from the transitionally rough regime to the fully rough regime. In Proc. of the 19th Australasian Fluid Mechanics Conference, Melbourne, Australia.
Chan, L., MacDonald, M., Chung, D., Hutchins, N. & Ooi, A. 2015 A systematic investigation of roughness height and wavelength in turbulent pipe flow in the transitionally rough regime. J. Fluid Mech. 771, 743777.
Chau, L. & Bhaganagar, K. 2012 Understanding turbulent flow over ripple-shaped random roughness in a channel. Phys. Fluids 24, 115102.
Chin, C., Ooi, A., Marusic, I. & Blackburn, H. M. 2010 The influence of pipe length on turbulence statistics computed from direct numerical simulation data. Phys. Fluids 22, 115107.
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, 418431.
Coceal, O. & Belcher, S. E. 2004 A canopy model of mean winds through urban areas. Q. J. R. Meteorol. Soc. 130, 13491372.
Coceal, O., Thomas, T. G., Castro, I. P. & Belcher, S. E. 2006 Mean flow and turbulence statistics over groups of urban-like cubical obstacles. Boundary-Layer Meteorol. 121, 491519.
Colebrook, C. F. 1939 Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws. J. Inst. Civ. Engrs 11, 133156.
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, 108123.
Finnigan, J. J. 1985 Turbulent transport in flexible plant canopies. In The Forest-Atmosphere Interaction, pp. 443480. Springer.
Finnigan, J. J. 2000 Turbulence in plant canopies. Annu. Rev. Fluid Mech. 32, 519571.
Flack, K. A. & Schultz, M. P. 2010 Review of hydraulic roughness scales in the fully rough regime. J. Fluids Engng 132, 041203.
Flack, K. A. & Schultz, M. P. 2014 Roughness effects on wall-bounded turbulent flows. Phys. Fluids 26, 101305.
Flack, K. A., Schultz, M. P. & Shapiro, T. A. 2005 Experimental support for Townsends Reynolds number similarity hypothesis on rough walls. Phys. Fluids 17, 035102.
Forooghi, P., Stroh, A., Magagnato, F., Jakirlić, S. & Frohnapfel, B. 2017 Towards a universal roughness correlation. J. Fluids Engng 139, 121201.
Goldstein, D. B. & Tuan, T.-C. 1998 Secondary flow induced by riblets. J. Fluid Mech. 363, 115151.
Ham, F. & Iaccarino, G.2004 Energy conservation in collocated discretization schemes on unstructured meshes, In Annual Research Briefs 2004. Center for Turbulence Research Stanford University/ NASA Ames.
Hinze, J. O. 1967 Secondary currents in wall turbulence. Phys. Fluids 10, S122S125.
Hutchins, N. & Marusic, I. 2007 Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365 (1852), 647664.
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173196.
Kevin, 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, 412435.
Krogstad, P.-Å. & Antonia, R. A. 1994 Structure of turbulent boundary layers on smooth and rough walls. J. Fluid Mech. 277, 121.
Krogstad, P.-Å. & Antonia, R. A. 1999 Surface roughness effects in turbulent boundary layers. Exp. Fluids 27, 450460.
Krogstad, P.-Å., Antonia, R. A. & Browne, L. W. B. 1992 Comparison between rough- and smooth-wall turbulent boundary layers. J. Fluid Mech. 245, 599617.
Leonardi, S. & Castro, I. P. 2010 Channel flow over large cube roughness a direct numerical simulation study. J. Fluid Mech. 651, 519539.
MacDonald, M., Chan, L., Chung, D., Hutchins, N. & Ooi, A. 2016 Turbulent flow over transitionally rough surfaces with varying roughness densities. J. Fluid Mech. 804, 130161.
MacDonald, M., Chung, D., Hutchins, N., Chan, L., Ooi, A. & Garca-Mayoral, R. 2017 The minimal-span channel for rough-wall turbulent flows. J. Fluid Mech. 816, 542.
Mahesh, K., Constantinescu, G. & Moin, P. 2004 A numerical method for large-eddy simulation in complex geometries. J. Comput. Phys. 197, 215240.
Medjnoun, T., Vanderwel, C. & Ganapathisubramani, B. 2018 Characteristics of turbulent boundary layers over smooth surfaces with spanwise heterogeneities. J. Fluid Mech. 838, 516543.
Mejia-Alvarez, R. & Christensen, K. T. 2010 Low-order representations of irregular surface roughness and their impact on a turbulent boundary layer. Phys. Fluids 22, 015106.
Mejia-Alvarez, R. & Christensen, K. T. 2013 Wall-parallel stereo particle-image velocimetry measurements in the roughness sublayer of turbulent flow overlying highly irregular roughness. Phys. Fluids 25, 115109.
Mignot, E., Barthelemy, E. & Hurther, D. 2009 Double-averaging analysis and local flow characterization of near-bed turbulence in gravel-bed channel flows. J. Fluid Mech. 618, 279303.
Napoli, E., Armenio, V. & De Marchis, M. 2008 The effect of the slope of irregularly distributed roughness elements on turbulent wall-bounded flows. J. Fluid Mech. 613, 385394.
Nikora, V., Goring, D., McEwan, I. & Griffiths, G. 2001 Spatially averaged open-channel flow over rough bed. ASCE J. Hydraul. Engng 127, 123133.
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. ASCE J. Hydraul. Engng 133, 873883.
Nugroho, B., Hutchins, N. & Monty, J. P. 2013 Large-scale spanwise periodicity in a turbulent boundary layer induced by highly ordered and directional surface roughness. Intl J. Heat Fluid Flow 41, 90102.
Orlandi, P. & Leonardi, S. 2006 DNS of turbulent channel flows with two- and three-dimensional roughness. J. Turbul. 7, N73.
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44, 125.
Raupach, M. R. & Shaw, R. H. 1982 Averaging procedures for flow within vegetation canopies. Boundary-Layer Meteorol. 22, 7990.
Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54, 263288.
Sadique, J., Yang, X. I. A., Meneveau, C. & Mittal, R. 2016 Aerodynamic properties of rough surfaces with high aspect-ratio roughness elements: effect of aspect ratio and arrangements. Boundary-Layer Meteorol. 163, 122.
Schultz, M. P. & Flack, K. A. 2005 Outer layer similarity in fully rough turbulent boundary layers. Exp. Fluids 38, 328340.
Schultz, M. P. & Flack, K. A. 2009 Turbulent boundary layers on a systematically varied rough wall. Phys. Fluids 21, 015104.
Scotti, A. 2006 Direct numerical simulation of turbulent channel flows with boundary roughened with virtual sandpaper. Phys. Fluids 18, 031701.
Squire, D. T., Morrill-Winter, C., Hutchins, N., Schultz, M. P., Klewicki, J. C. & Marusic, I. 2016 Comparison of turbulent boundary layers over smooth and rough surfaces up to high Reynolds numbers. J. Fluid Mech. 795, 210240.
Tachie, M. F., Bergstrom, D. J. & Balachandar, R. 2000 Rough wall turbulent boundary layers in shallow open channel flow. J. Fluids Engng 122, 533541.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.
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.
Volino, R. J., Schultz, M. P. & Flack, K. A. 2011 Turbulence structure in boundary layers over periodic two-and three-dimensional roughness. J. Fluid Mech. 676, 172190.
Willingham, D., Anderson, W., Christensen, K. T. & Barros, J. M. 2014 Turbulent boundary layer flow over transverse aerodynamic roughness transitions: induced mixing and flow characterization. Phys. Fluids 26, 025111.
Yang, J. & 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, 117.
Yang, X. I. A., Sadique, J., Mittal, R. & Meneveau, C. 2016 Exponential roughness layer and analytical model for turbulent boundary layer flow over rectangular-prism roughness elements. J. Fluid Mech. 789, 127165.
Yuan, J. & Piomelli, U. 2014 Estimation and prediction of the roughness function on realistic surfaces. J. Turbul. 15, 350365.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Secondary motion in turbulent pipe flow with three-dimensional roughness

  • L. Chan (a1), M. MacDonald (a1), D. Chung (a1), N. Hutchins (a1) and A. Ooi (a1)...


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.