Environmental Fluid Mechanics

, Volume 13, Issue 2, pp 169–187 | Cite as

Numerical study of coastal sandbar migration, by hydro-morphodynamical coupling

  • Abdellatif Ouahsine
  • Hassan Smaoui
  • Khouane Meftah
  • Philippe Sergent
  • François Sabatier
Original Article


We present a numerical model based on the hydro-morphodynamical coupling to study coastal sandbar migration. In order to improve both nonlinear and dispersive wave processes in relatively shallow water, we developed a finite element model based on the Legendre polynomials and on the Extended Boussinesq model. This model reproduces the propagation of wave trains with a high degree of accuracy on a greater range of depths than the standard Boussinesq models. We also implemented the Total Variation Diminishing schemes to improve the quality of the computed hydrodynamic fields, especially in areas where sharp flow gradients occurred. The coupled morpho-hydrodynamical model is then used to simulate the migration of real sandbars observed at Rousty beach (Mediterranean French coast). For verification the model results are compared with field measurements obtained from a small-scale field campaign carried out over two years at Rousty beach, and the results of this comparison are thoroughly discussed and analyzed.


Nonlinear waves Boussinesq Legendre polynomials TVD scheme Underwater sandbars Morphodynamics Spectral 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bailard J (1981) Identification of intense intermittent coherent motions under shoaling and breaking waves. J Geophys Res 86(C11): 10938–10954CrossRefGoogle Scholar
  2. 2.
    Carrier GF, Greenspan HP (1957) Water waves of finite amplitude on a sloping beach. J Fluid Mech 4: 97–109CrossRefGoogle Scholar
  3. 3.
    Dingemans MW (1994) Comparison of computations with Boussinesq-like models and laboratory measurements. MAST G8-M, Report H1684.12. Delft Hydraulics, DelftGoogle Scholar
  4. 4.
    Grand WD, Madsen OS (1979) Combined wave and current interaction with a rough bottom. J Geophys Res 84(C4): 1798–1808Google Scholar
  5. 5.
    Harten A (1983) High-resolution schemes for hyperbolic conservation laws. J Comput Phys 49: 357–393CrossRefGoogle Scholar
  6. 6.
    Hibbert S, Peregrine DH (1979) Surf and runup on a beach: a uniform bore. J Fluid Mech 95: 323–345CrossRefGoogle Scholar
  7. 7.
    Kroon A (1998) International bar dynamics. In: Geographical developments in coastal morphodynamics. A tribute to Joost Terwindt. Utrecht University, Utrecht, pp 169–184Google Scholar
  8. 8.
    Lynett PJ, Wu TR, Liu PLF (2002) Modeling wave runup with depth-integrated equations. Coast Eng 46: 89–107CrossRefGoogle Scholar
  9. 9.
    Madsen PA, Schäffer HA (1998) Higher order Boussinesq-type equations for surface gravity waves: derivation and analysis. Philos Trans R Soc Lond 356: 3123–3184CrossRefGoogle Scholar
  10. 10.
    Meftah K (1998) Modélisation tridimensionnelle de l’hydrodynamique et du transport par suspension. PhD Thesis. Université de Technologie de Compiègne, Compiègne Cedex, p 196Google Scholar
  11. 11.
    Meftah K, Sergent P, Gomi P (2004) Linear analysis of a new type of extended Boussinesq model. Coast Eng 51(2): 185–206CrossRefGoogle Scholar
  12. 12.
    Ouahsine A, Smaoui H (1999) Flux-limiter schemes for oceanic tracers: application to the English channel tidal model. Comput Methods Appl Mech Eng 179(3–4): 307–325CrossRefGoogle Scholar
  13. 13.
    Ouahsine A, Sergent P, Hadji S (2008) Modelling of non-linear waves by an extended Boussinesq model. Eng Appl Comput Fluid Mech 2(1): 11–21Google Scholar
  14. 14.
    Peregrine DH (1967) Long waves on a beach. J Fluid Mech 27(4): 815–827CrossRefGoogle Scholar
  15. 15.
    Roe PL (1981) Approximate Riemann solvers, parameter vectors and difference schemes. J Comput Phys 43: 357–372CrossRefGoogle Scholar
  16. 16.
    Roe PL (1985) Some contributions to the modeling of discontinous flows. Lect Notes Appl Math 22: 163–193Google Scholar
  17. 17.
    Roe PL, Sidilkover D (1992) Optimum positive linear schemes for advection in two and three dimensions. SIAM J Numer Anal 29: 1542–1568CrossRefGoogle Scholar
  18. 18.
    Sabatier F (2003) outils et conceptions d’un système de gestion des plages sableuses. In: Rousty beach survey 2000–2001 report. Liteau Program AMATE, CEREGE, report 0309sab. University of Provence Aix, Marseille Cédex, p 12Google Scholar
  19. 19.
    Smaoui H, Zouhri L, Ouahsine A (2008) Flux limiting techniques for simulation of pollutant transport in porous media: application to ground water management. J Math Comput Model 47: 47–59CrossRefGoogle Scholar
  20. 20.
    Smaoui H, Ouahsine A (2012) Extension of the skin shear stress Li’s relationship to the flat bed. J Environ Fluid Mech 12(3): 201–207CrossRefGoogle Scholar
  21. 21.
    Smaoui H, Ouahsine A (2008) Analysis and design of a class of limiter schemes in presence of physical diffusion. Int J Comput Methods Eng Sci Mech 9: 180–188CrossRefGoogle Scholar
  22. 22.
    Sørensen OR, Schäffer HA, Madsen PA (1998) Surf zone dynamics simulated by a Boussinesq type model. III. Wave-induced horizontal nearshore circulations. Coast Eng 33: 155–176CrossRefGoogle Scholar
  23. 23.
    Sweby PK (1984) High resolution schemes using flux limiters for hyberbolic conservation laws. SIAM J Numer Anal 21(5): 995–1011CrossRefGoogle Scholar
  24. 24.
    Van Leer B (1974) Towards the ULTIMATE conservation difference scheme. II. Monotonicity and conservation combined in a second order scheme. J Comput Phys 14: 361–370CrossRefGoogle Scholar
  25. 25.
    Van Leer B (1977) Towards the ULTIMATE conservation difference scheme. IV. A new approach to numerical convection. J Comput Phys 23: 276–299CrossRefGoogle Scholar
  26. 26.
    Vasquez JA, Steffler PM, Millar RG (2008) Modeling bed-changes in meandering rivers using triangular finite elements. JJ Hydraul Eng ASCE 134(9): 1348–1352CrossRefGoogle Scholar
  27. 27.
    Vincent S, Caltagirone JP, Bonneton P (2001) Numerical modelling of bore propagation and run-up on sloping beaches using a MacCormack TVD scheme. J Hydraul Res 39(1): 41–49CrossRefGoogle Scholar
  28. 28.
    Wright LD, Short AD (1984) Morphodynamic variability of surf zones and beaches: a synthesis. Mar Geol 56: 93–118CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Abdellatif Ouahsine
    • 1
  • Hassan Smaoui
    • 1
    • 2
  • Khouane Meftah
    • 3
  • Philippe Sergent
    • 2
  • François Sabatier
    • 4
  1. 1.Université de Technologie de Compiègne, Laboratoire Roberval, UMR-CNRS 7337, Centre de recherches de RoyallieuCompiègne CedexFrance
  2. 2.Centre d’Études Techniques Maritimes Et Fluviales (CETMEF) 2, Bd GambettaCompiègne CedexFrance
  3. 3.Faculté de Technologie de Tlemcen, Département Génie MécaniqueChetouane, TlemcenAlgeria
  4. 4.Centre Européen de Recherche et d’Enseignement des Géosciences de l’Environnement (CEREGE), UMR 6635 CNRS Europôle Méditérrannèen de l’ArboisAix en Provence Cedex 04France

Personalised recommendations