Ocean Dynamics

, Volume 65, Issue 4, pp 555–587 | Cite as

Mixed-sediment transport modelling in Scheldt estuary with a physics-based bottom friction law

  • Qilong BiEmail author
  • Erik A. Toorman
Part of the following topical collections:
  1. Topical Collection on the 12th International Conference on Cohesive Sediment Transport in Gainesville, Florida, USA, 21-24 October 2013


In this study, the main object is to investigate the performance of a few new physics-based process models by implementation into a numerical model for the simulation of the flow and morphodynamics in the Western Scheldt estuary. In order to deal with the complexity within the research domain, and improve the prediction accuracy, a 2D depth-averaged model has been set up as realistic as possible, i.e. including two-way hydrodynamic-sediment transport coupling, mixed sand–mud sediment transport (bedload transport as well as suspended load in the water column) and a dynamic non-uniform bed composition. A newly developed bottom friction law, based on a generalised mixing-length (GML) theory, is implemented, with which the new bed shear stress closure is constructed as the superposition of the turbulent and the laminar contribution. It allows the simulation of all turbulence conditions (fully developed turbulence, from hydraulic rough to hydraulic smooth, transient and laminar), and the drying and wetting of intertidal flats can now be modelled without specifying an inundation threshold. The benefit is that intertidal morphodynamics can now be modelled with great detail for the first time. Erosion and deposition in these areas can now be estimated with much higher accuracy, as well as their contribution to the overall net fluxes. Furthermore, Krone’s deposition law has been adapted to sand–mud mixtures, and the critical stresses for deposition are computed from suspension capacity theory, instead of being tuned. The model has been calibrated and results show considerable differences in sediment fluxes, compared to a traditional approach and the analysis also reveals that the concentration effects play a very important role. The new bottom friction law with concentration effects can considerably alter the total sediment flux in the estuary not only in terms of magnitude but also in terms of erosion and deposition patterns.


Sediment transport Mixed sediment Generalised mixing-length theory Bottom friction Near-bottom sediment transport Residual sediment transport 



This study has been supported by the EU FP7 projects THESEUS and FIELD_AC. The computational resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Hercules Foundation and the Flemish Government—department EWI.


  1. Amoudry L (2008) A review on coastal sediment transport modelling. POL Internal Document No.189, Proudman Oceanographic Laboratory, Liverpool, 44Google Scholar
  2. Backers J, Hindryckx K (2010) RV Belgica: rapport van de RV Belgica meetcampagnes en verankering van meetsystemen MOMO—2009. Beheerseenheid Mathematisch Model Noordzee. Meetdienst Oostende: Oostende, different pagination + data CD-ROM (in Dutch)Google Scholar
  3. Baeyens W, Adam Y, Mommaerts JP, Pichot G (1981) Numerical simulations of salinity, turbidity and sediment accumulation in the Scheldt estuary. Elsevier Oceanography Ser 32:319–332CrossRefGoogle Scholar
  4. Baeyens W, Van Eck G, Lambert C, Wollast R, Goeyens L (1998) General description of the Scheldt estuary. Hydrobiologia 366:1–14CrossRefGoogle Scholar
  5. Bolle A, Bing Wang Z, Amos C, De Ronde J (2010) The influence of changes in tidal asymmetry on residual sediment transport in the Western Scheldt. Cont Shelf Res 30(8):871–882CrossRefGoogle Scholar
  6. Cancino L, Neves R (1994) 3D-numerical modelling of cohesive suspended sediment in the Western Scheldt estuary (The Netherlands). Neth J Aquat Ecol 28(3–4):337–345CrossRefGoogle Scholar
  7. Cancino L, Neves R (1999a) Hydrodynamic and sediment suspension modelling in estuarine systems: part I: description of the numerical models. J Mar Syst 22(2):105–116CrossRefGoogle Scholar
  8. Cancino L, Neves R (1999b) Hydrodynamic and sediment suspension modelling in estuarine systems: part II: application to the western Scheldt and Gironde estuaries. J Mar Syst 22(2):117–131CrossRefGoogle Scholar
  9. Cellino M (1998) Experimental study of suspension flow in open channels. PhD dissertation, No. 1824, Ecole Polytechnique Fédérale de LausanneGoogle Scholar
  10. Cleveringa J (2013) Grootschalige sedimentbalans van de Westerschelde. VNSC Basisrapport grootschalige ontwikkeling G-2. Report 076945827:0.4, Arcadis Nederland, Arnhem (NL), 81 ppGoogle Scholar
  11. Da Silva PA, Temperville A, Seabra Santos F (2006) Sand transport under combined current and wave conditions: a semi-unsteady, practical model. Coast Eng 53(11):897–913CrossRefGoogle Scholar
  12. Dam G, Bliek AJ (2013) Using a sand–mud model to hindcast the morphology near Waarde, The Netherlands. In: Proceedings of the Institution of Civil Engineer. Mar Eng 166 (2):63–75Google Scholar
  13. Dam G, Cleveringa J (2013) De rol van het slib in de sedimentbalans van de Westerschelde. VNSC Basisrapport grootschalige ontwikkeling G-3. Report G3; 1630/U12376/C/GD, Svasek Hydraulics, Rotterdam (NL), 35 ppGoogle Scholar
  14. Dam G, Bliek AJ, Labeur RJ, Ides S, Plancke Y (2007) Long term process-based morphological model of the Western Scheldt Estuary. In: Dohmen-Janssen CM, Hulscher SJMH (eds) Proceedings of 5th IAHR Symposium of the River, Coastal and Estuarine Morphodynamics Conference, Enschede, The Netherlands, Vol. 2. Taylor & Francis, Leiden, The Netherlands, pp 1077–1084Google Scholar
  15. De Brye B, de Brauwere A, Gourgue O, Kärnä T, Lambrechts J, Comblen R, Deleersnijder E (2010) A finite-element, multi-scale model of the Scheldt tributaries, river, estuary and ROFI. Coast Eng 57(9):850–863CrossRefGoogle Scholar
  16. De Ruijter, W, Huber, K, Backhaus, J (1987) North Sea circulation. In: Report of the Ocanography Subroup. Second International Conference on the Protection of the North Sea, Scientific and Technical Working Group, pp. 19–36 (Chapter 4)Google Scholar
  17. Elghobashi S (1994) On predicting particle-laden turbulent flows. Appl Sci Res 52:309–329CrossRefGoogle Scholar
  18. Fettweis M, Van den Eynde D (2003) The mud deposits and the high turbidity in the Belgian–Dutch coastal zone, southern bight of the north Sea. Cont Shelf Res 23(7):669–691CrossRefGoogle Scholar
  19. Fettweis M, Sas M, Monbaliu J (1998) Seasonal, neap-spring and tidal variation of cohesive sediment concentration in the Scheldt Estuary, Belgium. Estuar Coast Shelf Sci 47(1):21–36CrossRefGoogle Scholar
  20. Fettweis M, Nechad B, Van den Eynde D (2007) An estimate of the suspended particulate matter (SPM) transport in the southern north Sea using SeaWiFS images, in situ measurements and numerical model results. Cont Shelf Res 27(10):1568–1583CrossRefGoogle Scholar
  21. Fokkink RJ (1998) Morphodynamic network simulations of the Western Scheldt. WL| Delft Hydraulics, Report Z, 919Google Scholar
  22. Gourgue O, Baeyens W, Chen MS, de Brauwere A, de Brye B, Deleersnijder E, Elskens M, Legat V (2013) A depth-averaged two-dimensional sediment transport model for environmental studies in the Scheldt Estuary and tidal river network. J Mar Syst 128:27–39CrossRefGoogle Scholar
  23. Hartsuiker G (2004) 2Dh NEVLA Scheldemodel: Bouw en afregeling stromingsmode (in Dutch). Report MOD 753. Antwerp, Belgium, Flanders Hydraulics ResearchGoogle Scholar
  24. Herman PMJ, Heip CHR (1999) Biochemistry of the maximum turbidity zone of estuaries (MATURE): some conclusions. J Mar Syst 22:89–104CrossRefGoogle Scholar
  25. Hervouet JM (2007) Hydrodynamics of free surface flows: modelling with the finite element method. Wiley, ChichesterCrossRefGoogle Scholar
  26. Hervouet JM, Bates P (2000) The telemac modelling system. Hydrol Process 14(13), Special IssueGoogle Scholar
  27. Hoffmann M, Meire P (1997) De oevers langs de Zeeschelde: inventarisatie van de huidige oeverstructuren. Water 95:131–137Google Scholar
  28. Hoogduin L, Stive MJF, Wang ZB, Uijttewaal WSJ, Hibma, A, & Eelkema, M (2009) Sediment transport through the Eastern Scheldt storm surge barrier. Delft University of TechnologyGoogle Scholar
  29. International Marine and Dredging Consultants et al. (2010) Langdurige metingen Deurganckdok: opvolging en analyse aanslibbing: deelrapport 1.23. Sedimentbalans 01/01/2009 - 31/03/2009. Versie 2.0. Waterbouwkundig Laboratorium: Antwerpen. IV, 28 + annexes (in Dutch)Google Scholar
  30. Janssens J, Delgado R, Verwaest T, Mostaert F (2012) Morfologische trends op middellange termijn van strand, vooroever en kustnabije zone langsheen de Belgische kust: Deelrapport in het kader van het Quest4D-project. Versie 1_0. WL Rapporten, 814_02. Waterbouwkundig Laboratorium: Antwerpen, BelgiëGoogle Scholar
  31. Jeuken MCJL (2000) On the morphologic behaviour of tidal channels in the Westerschelde estuary. Nederlandse geografische studies (Netherlands)Google Scholar
  32. Krone RB (1962) Flume studies of the transport of sediment in estuarial shoaling processes: Final Report. Hydraulic Engineering Laboratory and Sanitary Engineering Research Laboratory, University of California, 118 ppGoogle Scholar
  33. Kuijper C, Steijn R, Roelvink D, van der Kaaij T, Olijslagers P (2004) Report: Morphological modelling of the Western Scheldt: validation of Delft3D. Deltares (WL). Chapter 2, 1–2Google Scholar
  34. Lee BJ, Toorman E, Fettweis M (2014) Flocculation of fine-grained cohesive sediments developing multimodal particle size distributions: field investigation and mathematical modeling. Ocean Dyn 64:429–441CrossRefGoogle Scholar
  35. Malherbe B (1991) A case study of dumping in open seas. Terra et Aqua 45, 5 – 32Google Scholar
  36. Maximova T, Ides S, De Mulder T, Mostaert F (2009a) Verbetering 2D randvoorwaardenmodel. Deelrapport 4: Extra aanpassingen Zeeschelde (in Dutch). WL Rapporten, 753_09. Antwerp, Belgium, Flanders Hydraulics ResearchGoogle Scholar
  37. Maximova T, Ides S, Vanlede J, De Mulder T, Mostaert F (2009b) Verbetering 2D randvoorwaardenmodel. Deelrapport 3: Calibratie bovenlopen (in Dutch). WL Rapporten, 753_09. Antwerp, Belgium, Flanders Hydraulics ResearchGoogle Scholar
  38. Meire P, Ysebaert T, Van Damme S, Van den Bergh E, Maris T, Struyf E (2005) The Scheldt estuary: a description of a changing ecosystem. Hydrobiologia 540(1–3):1–11CrossRefGoogle Scholar
  39. Mitchener H, Torfs H (1996) Erosion of mud/sand mixtures. Coast Eng 29:1–25CrossRefGoogle Scholar
  40. Mulder HP, Udink C (1990) Modelling of cohesive sediment transport. A case study: the western Scheldt estuary. Coastal Engineering Proceedings, 1(22)Google Scholar
  41. Nihoul JCJF, Ronday F, Peters JJ, Sterling A (1978) Hydrodynamics of the Scheldt estuary. In: Nihoul JCJF (ed) Hydrodynamics of estuaries and fjords. Elsevier, Amsterdam, pp 27–53CrossRefGoogle Scholar
  42. Nikuradse J (1933) Laws of flow in rough pipes. NACA Tech. Mem., No.1292 (translation, 1950), Washington, 62 pp.Google Scholar
  43. Panagiotopoulos I, Voulgaris G, Collins MB (1997) The influence of clay on the threshold of movement of fine sandy beds. Coast Eng 32(1):19–43CrossRefGoogle Scholar
  44. Peters (1975) Les mechanismes de mélange des eaux dans l’estuaire de l’Escaut. Tijdschrift der Openbare Werken van België 2, pp. 101–119Google Scholar
  45. Portela LI, Neves R (1994) Numerical modelling of suspended sediment transport in tidal estuaries: a comparison between the Tagus (Portugal) and the Scheldt (Belgium–The Netherlands). Neth J Aquat Ecol 28(3–4):329–335CrossRefGoogle Scholar
  46. Prandtl L (1925) Bericht über untersuchungen zur ausgebildeten turbulenz. ZAMM 5:136–139Google Scholar
  47. Smagorinsky J (1963) General circulation experiments with the primitive equations: I. The basic experiment. Mon Weather Rev 91(3):99–164CrossRefGoogle Scholar
  48. Toorman EA (2000) Numerical simulation of turbulence damping in sediment-laden flow. Part 2. Suspension capacity of uniform turbulent shear flows. Report HYD/ET/00/COSINUS4, Hydraulics Laboratory, K.U.Leuven, 23 ppGoogle Scholar
  49. Toorman EA (2002) Modelling of turbulent flow with cohesive sediment. In: Winterwerp JC, Kranenburg C (eds) Proceedings in Marine Science, vol 5: Fine sediment dynamics in the marine environment. Elsevier Science, Amsterdam, pp 155–169Google Scholar
  50. Toorman EA (2003) Validation of macroscopic modelling of particle-laden turbulent flows. Proceedings 6th Belgian National Congress on Theoretical and Applied Mechanics (Gent, 26–27 May 2003), CD Rom, 7 ppGoogle Scholar
  51. Toorman E A (2011) Low-Reynolds modelling of high-concentrated near-bottom suspended sediment transport. IAHR Symposium on Two-phase Modelling for Sediment Dynamics in Geophysical Flows (THESIS-2011, Paris, April 26–28, 2011), Abstract, 4 ppGoogle Scholar
  52. Toorman E, Bi Q (2011) Dealing with benthic high-concentrated layers and fluid mud in cohesive sediment transport modeling. INTERCOH’11. Book of Abstracts. Int. Conf. on Cohesive Sediment Transport Processes. Shanghai, China, 18–21 October 2011, 85–86Google Scholar
  53. Toorman E, Bi Q (2012) Section 2.4, EU FP7 FIELD_AC Report D3.3. In: Liste M, Monbaliu J (Eds) Improvements to sea-bed boundary conditions (pp. 19–31)Google Scholar
  54. Toorman E, Bi Q (2013a). Hybrid two-phase/mixture modelling of sediment transport. Abstracts THESIS-2013 (CDRom). Symposium on Two-phase Modelling for Sediment Dynamics. Chatou (France), 10–12 June 2013, 4 ppGoogle Scholar
  55. Toorman E, Bi Q (2013b) A practical model for drag modulation by suspended sediment, with application to the Scheldt estuary. INTERCOH2013 Book of Abstracts. Int. Conf. on Cohesive Sediment Transport. Gainesville, Florida, 20–24 October 2013, 7–8Google Scholar
  56. Toorman E, Bi Q (2013c). Hybrid two-phase/mixture modelling of sediment transport as a tool for large-scale morphological model development. Advances in Water Resources (SI THESIS2013)Google Scholar
  57. Van Driest ER (1956) On turbulent flow near a wall. J. Aeronautical Science, 23, 1007-1011 + 1136Google Scholar
  58. Van Kessel T, Vanlede J (2010) Impact of harbour basins on mud dynamics Scheldt estuary in the framework of LTV. Delft, Deltares, p 29Google Scholar
  59. Van Kessel T, Vanlede J, & Bruens A (2006) Development of a mud transport model for the Scheldt estuary in the framework of LTV. Report Z4210 WL| Delft Hydraulics and Flanders Hydraulics Research, DelftGoogle Scholar
  60. Van Kessel T, Vanlede J, de Kok J (2011) Development of a mud transport model for the Scheldt estuary. Cont Shelf Res 31:S165–S181CrossRefGoogle Scholar
  61. Van Rijn LC (1984) Sediment transport, part I: bed load transport. J Hydraul Eng 110(10):1431–1456CrossRefGoogle Scholar
  62. Van Rijn LC (1993) Principles of sediment transport in rivers, estuaries and coastal seas, vol 2, no 3. Aqua publications, Amsterdam, p 4Google Scholar
  63. Verbeek H, Jansen, MHP, & Wouters CAH (1998) Adaptation of 2D sediment transport patterns using 3D hydrodynamic modelling. In OCEANS’98 Conference Proceedings (Vol. 1, 444–448), IEEEGoogle Scholar
  64. Verlaan PAJ, Donze M, Kuik P (1998) Marine vs fluvial suspended matter in the Scheldt estuary. Estuar Coast Shelf Sci 46(6):873–883CrossRefGoogle Scholar
  65. Waeles B (2005) Detachment and transport of slay sand gravel mixtures by channel flows. PhD thesis. University of Caen Caen, FranceGoogle Scholar
  66. Waeles B, Le Hir P, Lesueur P, Delsinne N (2007) Modelling sand/mud transport and morphodynamics in the Seine river mouth (France): an attempt using a process-based approach. Hydrobiologia 588(1):69–82CrossRefGoogle Scholar
  67. Wartel S. & van Eck, GTM (2000) Slibhuishouding van de Schelde. Report, Koninklijk Belgisch Instituut voor Natuurwetenschappen (Brussels) & Rijksinstituut der Kust en Zee (Middelburg, NL), 66 pp. (in Dutch)Google Scholar
  68. Widera P, Toorman E, Lacor C (2009) Large eddy simulation of sediment transport in open-channel flow. J Hydraul Res 47(3):291–298CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Hydraulics Laboratory, Department of Civil EngineeringKU LeuvenLeuvenBelgium

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