Turbulent channel flow perturbed by triangular ripples

  • Fernando David Cúñez
  • Gabriel Victor Gomes de Oliveira
  • Erick de Moraes FranklinEmail author
Technical Paper


This paper presents an experimental investigation of the perturbation of a turbulent closed-conduit flow by two-dimensional triangular ripples. Two ripple configurations were employed: one single asymmetric triangular ripple, and two consecutive asymmetric triangular ripples, all of them with the same geometry. Different water flows were imposed over either one or two ripples fixed to the bottom wall of a closed conduit, and the flow field was measured by particle image velocimetry (PIV). Reynolds numbers based on the channel height were moderate, varying between 27500 and 34700. The regime was hydraulically smooth, and the blockage ratio was significant. Experimental data for this specific case remain scarce, and the physics involved has yet to be fully elucidated. Using the instantaneous flow fields, the mean velocities and fluctuations were computed, and the shear stresses over the ripples were determined. The velocities and stresses obtained in this way for the single ripple and for the pair of ripples are compared, and the surface shear stress is discussed in terms of bed stability. Our results show that for the single and upstream ripples, the shear stress increases at the leading edge and decreases toward the crest, while for the downstream ripple it decreases monotonically between the reattachment point and the crest. The stress distribution over the downstream ripple, which is different from both the upstream and single ripples, is shown to sustain existing ripples over loose beds.


Closed-conduit flow Turbulent boundary layer Perturbation Ripples 


Roman symbols






Diameter (m)


Darcy friction factor


Local height of the ripple (m)


Channel height (m)

\(H_\text{ eff }\)

Distance between the PVC plates and the top wall of the channel (m)


Imaginary number


Wave number (m\(^{-1}\))


Ripple length (m)


Viscous length (m)


Turbulence production term (m\(^2\)/s\(^3\))

\(P_{\text {max}}\)

Maximum value of turbulence production (m\(^2\)/s\(^3\))


Volumetric flow rate (m\(^3\)/h)


Reynolds number based on the channel height

\(Re_{\text {dh}}\)

Reynolds number based on the hydraulic diameter


Time (s)


Longitudinal component of the velocity (m/s)


Cross-sectional mean velocity (m/s)


Velocity at the channel centerline (m/s)


Shear velocity (m/s)


Vertical component of the velocity (m/s)

\(\mathbf {V}\)

Velocity vector (m/s)


Horizontal coordinate (m)


Vertical coordinate (m)

Greek symbols


Perturbation field


von Kármán constant


Wavelength (m)


Dynamic viscosity (Pa s)


Kinematic viscosity (m\(^2\)/s)


Density (kg/m\(^3\))


Shear stress (N/m\(^2\))


Angle between the horizontal and the ripple surface (\(^o\))



Relative to the flat surface (unperturbed flow)


Relative to Blasius correlation


Relative to the displaced coordinate system


Relative to the hydraulic diameter


Relative to Fourier space


Maximum value


Relative to the viscous layer


Aligned with the ripple surface



Normalized by the viscous length \(l_v\) or by the shear velocity \(u_{*,0}\)

\(\overline{\quad }\)

Averaged in time



\(\hat{\quad }\)




Fernando David Cúñez Benalcázar is grateful to SENESCYT (Programa de Becas Convocatoria Abierta 2014 Segunda Fase) and to FAPESP (grant no. 2016/18189-0), and Gabriel Victor Gomes de Oliveira is grateful to FAPESP (grant no. 2015/15001-8) and to CAPES for providing financial support. Erick de Moraes Franklin would like to express his gratitude to FAPESP (grant nos. 2012/19562-6 and 2016/13474-9) and CNPq (grant no. 400284/2016-2) for the financial support they provided.


  1. 1.
    Jackson PS, Hunt JCR (1975) Turbulent wind flow over a low hill. Quart J R Meteorol Soc 101:929–955CrossRefGoogle Scholar
  2. 2.
    Hunt JCR, Leibovich S, Richards KJ (1988) Turbulent shear flows over low hills. Quart J R Meteorol Soc 114:1435–1470CrossRefGoogle Scholar
  3. 3.
    Belcher SE, Hunt JCR (1998) Turbulent flow over hills and waves. Ann Rev Fluid Mech 30:507–538MathSciNetCrossRefGoogle Scholar
  4. 4.
    Poggi D, Katul G, Albertson J, Ridolfi L (2007) An experimental investigation of turbulent flows over a hilly surface. Phys Fluids 19(3):036601CrossRefzbMATHGoogle Scholar
  5. 5.
    Carruthers DJ, Hunt JCR (1990) Fluid mechanics of airflows over hills: turbulence, fluxes, and waves in the boundary layer. Atmospheric processes over complex terrain, vol 23. American Meteorological Society, Boston, pp 83–108CrossRefGoogle Scholar
  6. 6.
    Weng MS, Hunt JCR, Carruthers DJ, Warren A, Wiggs GFS, Livingstone I, Castro I (1991) Air flow and sand transport over sand-dunes. Acta Mech 1–21Google Scholar
  7. 7.
    Kroy K, Sauermann G, Herrmann HJ (2002) Minimal model for aeolian sand dunes. Phys Rev E 66:031302CrossRefGoogle Scholar
  8. 8.
    Kroy K, Sauermann G, Herrmann HJ (2002) Minimal model for sand dunes. Phys Rev Lett 88:054301CrossRefGoogle Scholar
  9. 9.
    Andreotti B, Claudin P, Douady S (2002) Selection of dune shapes and velocities. Part 1: dynamics of sand, wind and barchans. Eur Phys J B 28:321–329CrossRefGoogle Scholar
  10. 10.
    Andreotti B, Claudin P, Douady S (2002) Selection of dune shapes and velocities. Part 2: a two-dimensional model. Eur Phys J B 28:341–352CrossRefGoogle Scholar
  11. 11.
    Howard AD, Morton JB, Gad-El Hak M, Pierce DB (1978) Sand transport model of barchan dune equilibrium. Sedimentology 25(3):307–338CrossRefGoogle Scholar
  12. 12.
    Wiggs GFS, Livingstone A, Warren A (1996) The role of streamline curvature in sand dune dynamics: evidence from field and wind tunnel measurements. Geomorphology 17:29–46CrossRefGoogle Scholar
  13. 13.
    Sauermann G (2001) Modeling of wind blown sand and desert dunes. Ph.D. thesis Modeling of wind blown sand and desert dunes. Universität StuttgartGoogle Scholar
  14. 14.
    Sauermann G, Andrade JS, Maia LP, Costa UMS, Araújo AD, Herrmann HJ (2003) Wind velocity and sand transport on a barchan dune. Geomorphology 54:245–255CrossRefGoogle Scholar
  15. 15.
    Marquillie M, Laval JP, Dolganov R (2008) Direct numerical simulation of a separated channel flow with a smooth profile. J Turbul 9:N1CrossRefGoogle Scholar
  16. 16.
    Marquillie M, Ehrenstein U, Laval JP (2011) Instability of streaks in wall turbulence with adverse pressure gradient. J Fluid Mech 681:205–240CrossRefzbMATHGoogle Scholar
  17. 17.
    Franklin EM, Charru F (2011) Subaqueous barchan dunes in turbulent shear flow. Part 1: Dune motion. J Fluid Mech 675:199–222CrossRefzbMATHGoogle Scholar
  18. 18.
    Charru F, Franklin EM (2012) Subaqueous barchan dunes in turbulent shear flow. Part 2: fluid flow. J Fluid Mech 694:131–154CrossRefzbMATHGoogle Scholar
  19. 19.
    Franklin EM, Ayek GA (2013) The perturbation of a turbulent boundary layer by a two-dimensional hill. J Braz Soc Mech Sci 35:337–346CrossRefGoogle Scholar
  20. 20.
    Walker IJ, Nickling WG (2003) Simulation and measurement of surface shear stress over isolated and closely spaced transverse dunes in a wind tunnel. Earth Surf Process Landforms 28:1111–1124CrossRefGoogle Scholar
  21. 21.
    Florez JEC, Franklin EM (2016) The formation and migration of sand ripples in closed conduits: experiments with turbulent water flows. Exp Therm Fluid Sci 71:95–102CrossRefGoogle Scholar
  22. 22.
    Coleman SE, Nikora VI, McLean SR, Clunie TM, Schlicke T, Schlicke BW (2006) Equilibrium hydrodynamics concept for developing dunes. Phys Fluids 18:105104CrossRefGoogle Scholar
  23. 23.
    Mendez MA, Raiola M, Masullo A, Discetti S, Ianiro A, Theunissen R, Buchlin JM (2017) POD-based background removal for particle image velocimetry. Exp Therm Fluid Sci 80:181–192CrossRefGoogle Scholar
  24. 24.
    Franklin EM (2015) Formation of sand ripples under a turbulent liquid flow. Appl.Math Model 39(23):7390–7400MathSciNetCrossRefGoogle Scholar
  25. 25.
    Schlichting H (2000) Boundary-layer theory. SpringerGoogle Scholar
  26. 26.
    Engelund F, Fredsoe J (1982) Sediment ripples and dunes. Ann Rev Fluid Mech 14:13–37CrossRefzbMATHGoogle Scholar
  27. 27.
    Charru F (2006) Selection of the ripple length on a granular bed sheared by a liquid flow. Phys Fluids 18:121508CrossRefzbMATHGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.School of Mechanical EngineeringUniversity of Campinas-UNICAMPCampinasBrazil

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