Numerical Investigation of Natural Rough-Bed Flow

  • Giancarlo Alfonsi
  • Domenico Ferraro
  • Agostino LauriaEmail author
  • Roberto Gaudio
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11974)


The turbulent flow in natural rough-bed watercourses is a rather complex phenomenon, still poorly investigated. The majority of the existing works on this subject is of experimental nature, while the numerical ones are mostly related to artificially and regularly-roughened beds. In the present work a numerical investigation is carried out, in which the fully turbulent flow in an open channel is simulated, where the channel bottom is constituted by natural-pebble layers. In the numerical simulations, the Large Eddy Simulation (LES) approach is used, in conjunction with the Wall-Adapting Local Eddy viscosity (WALE) Sub-Grid Scale (SGS) closure model at Reynolds number 46,500 and Froude number 0.186. The Finite-Volume discretized governing equations are solved numerically by means of the InterFOAM solver, embedded in the OpenFOAM C++ digital library. In order to take into account the free-surface dynamics, the Volume of Fluid (VoF) method has been used. The results of the simulations are compared with those obtained in a companion experiment, mainly in terms of turbulence statistics of different order, obtaining a rather good agreement.


Pebble bed flow Large Eddy Simulation Volume of Fluid 


  1. 1.
    Giménez-Curto, L.A., Lera, M.A.C.: Oscillating turbulent flow over very rough surfaces. J. Geophys. Res. Oceans 101, 20745–20758 (1996)CrossRefGoogle Scholar
  2. 2.
    Dittrich, A., Koll, K.: Velocity field and resistance of flow over rough surface with large and small relative submergence. Int. J. Sedim. Res. 12, 21–33 (1997)Google Scholar
  3. 3.
    Nikora, V., Goring, D., McEwan, I., Griffiths, G.: Spatially averaged open-channel flow over rough bed. ASCE J. Hydraul. Eng. 127, 123–133 (2001)CrossRefGoogle Scholar
  4. 4.
    Nikora, V., McEwan, I., McLean, S., Coleman, S., Pokrajac, D., Walters, R.: Double averaging concept for rough-bed open-channel and overland flows: theoretical background. ASCE J. Hydraul. Eng. 133, 873–883 (2007)CrossRefGoogle Scholar
  5. 5.
    Manes, C., Pokrajac, D., McEwan, I.: Double-averaged open-channel flows with small relative submergence. ASCE J. Hydraul. Eng. 133, 896–904 (2007)CrossRefGoogle Scholar
  6. 6.
    Aberle, J., Koll, K., Dittrich, A.: Form induced stresses over rough gravel-beds. Acta Geophys. 56, 584–600 (2008)CrossRefGoogle Scholar
  7. 7.
    Dey, S., Das, R.: Gravel-bed hydrodynamics: double-averaging approach. ASCE J. Hydraul. Eng. 138, 707–725 (2012)CrossRefGoogle Scholar
  8. 8.
    Ferraro, D., Servidio, S., Carbone, V., Dey, S., Gaudio, R.: Turbulence laws in natural bed flows. J. Fluid Mech. 798, 540–571 (2016)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Coscarella, F., Servidio, S., Ferraro, D., Carbone, V., Gaudio, R.: Turbulent energy dissipation rate in a tilting flume with a highly rough bed. Phys. Fluids 29, 085101 (2017)CrossRefGoogle Scholar
  10. 10.
    Cameron, S., Nikora, V., Stewart, M.: Very-large-scale motions in rough-bed open-channel flow. J. Fluid Mech. 814, 416–429 (2018)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Padhi, E., Penna, N., Dey, S., Gaudio, R.: Hydrodynamics of water-worked and screeded gravel beds: a comparative study. Phys. Fluids 30, 085105 (2018)CrossRefGoogle Scholar
  12. 12.
    Padhi, E., Penna, N., Dey, S., Gaudio, R.: Spatially averaged dissipation rate in flows over water-worked and screeded gravel beds. Phys. Fluids 30, 125106 (2018)CrossRefGoogle Scholar
  13. 13.
    Stoesser, T., Nikora, V.I.: Flow structure over square bars at intermediate submergence: large eddy simulation study of bar spacing effect. Acta Geophys. 56, 876–893 (2008)CrossRefGoogle Scholar
  14. 14.
    Bomminayuni, S., Stoesser, T.: Turbulence statistics in an open-channel flow over rough bed. ASCE J. Hydraul. Eng. 137, 1347–1358 (2008)CrossRefGoogle Scholar
  15. 15.
    Fang, H., Han, X., He, G., Dey, S.: Influence of permeable beds on hydraulically macro-rough flow. J. Fluid Mech. 847, 552–590 (2018)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Omidyeganeh, M., Piomelli, U.: Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. Part 1. Turbulence statistics. J. Fluid Mech. 721, 454–483 (2013)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Omidyeganeh, M., Piomelli, U.: Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. Part 2. Flow structures. J. Fluid Mech. 734, 509–534 (2013)CrossRefGoogle Scholar
  18. 18.
    Hardy, R.J., Lane, S.N., Ferguson, R.I., Parsons, D.R.: Emergence of coherent flow structures over a gravel surface: a numerical experiment. Water Resour. Res. 43, Article no. W03422 (2007)Google Scholar
  19. 19.
    Hardy, R.J., Best, J.L., Lane S.N., Carbonneau, P.E.: Coherent flow structures in a depth-limited flow over a gravel surface: the role of near-bed turbulence and influence of Reynolds number. J. Geophys. Res. Earth Surf. 114, Article no. F011003 (2009)Google Scholar
  20. 20.
    Stoesser, T.: Physically-realistic roughness closure scheme to simulate turbulent channel flow over rough beds within the framework of LES. ASCE J. Hydraul. Eng. 136, 812–819 (2010)CrossRefGoogle Scholar
  21. 21.
    Nicoud, F., Ducros, F.: Subgrid-scale stress modelling based on the square of the velocity-gradient tensor. Flow Turbul. Combust. 62, 183–200 (1999)CrossRefGoogle Scholar
  22. 22.
    Goring, D.G., Nikora, V.I.: Despiking acoustic Doppler velocimeter data. ASCE J. Hydraul. Eng. 128, 117–126 (2002)CrossRefGoogle Scholar
  23. 23.
    Issa, R.I.: Solution of the implicitly discretized fluid flow equations by operator splitting. J. Comput. Phys. 62, 40–65 (1986)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Hirt, C.W., Nichols, B.D.: Volume of fluid (VoF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201–225 (1981)CrossRefGoogle Scholar
  25. 25.
    Calomino, F., et al.: Experimental and numerical study of free-surface flows in a corrugated pipe. Water 10, 638 (2018)CrossRefGoogle Scholar
  26. 26.
    Alfonsi, G., Lauria, A., Primavera, L.: Proper orthogonal flow modes in the viscous-fluid wave diffraction case. J. Flow Vis. Image Process. 24, 227–241 (2013)CrossRefGoogle Scholar
  27. 27.
    Alfonsi, G., Lauria, A., Primavera, L.: The field of flow structures generated by a wave of viscous fluid around vertical circular cylinder piercing the free surface. Procedia Eng. 116, 103–110 (2015)CrossRefGoogle Scholar
  28. 28.
    Alfonsi, G., Lauria, A., Primavera, L.: Recent results from analysis of flow structures and energy modes induced by viscous wave around a surface-piercing cylinder. Math. Probl. Eng. 2017, Article no. 5875948 (2017)Google Scholar
  29. 29.
    Alfonsi, G., Lauria, A., Primavera, L.: On evaluation of wave forces and runups on cylindrical obstacles. J. Flow Vis. Image Process. 20, 269–291 (2013)CrossRefGoogle Scholar
  30. 30.
    Frisch, U.: Turbulence. Cambridge University Press, Cambridge (1995)CrossRefGoogle Scholar
  31. 31.
    Alfonsi, G., Ferraro, D., Lauria, A., Gaudio, R.: Large-eddy simulation of turbulent natural-bed flow. Phys. Fluids 31(8), 085105 (2019)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Civil EngineeringUniversity of CalabriaRendeItaly

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