Skip to main content
SpringerLink
Log in

A 3-D finite volume model for sediment transport in coastal waters

  • Published:
Ocean Dynamics Aims and scope Submit manuscript

Abstract

A 3-D model has been developed to simulate sediment transport and bed change induced by currents and waves in coastal waters. The currents are calculated with the 3-D phase-averaged shallow water flow equations, the wave characteristics are determined with a horizontal 2-D wave spectral transformation model, and multiple-sized non-cohesive suspended load and bed load are simulated using a non-equilibrium transport model. The classical mixing length model is modified to determine the horizontal and vertical eddy viscosity considering the effects of current, waves, and wave breaking. A new approach is proposed in the present 3-D model framework to calculate the bed grain shear stress, which is applied to determine the equilibrium bed-load transport rate and near-bed suspended-load concentration. The flow and sediment transport equations are numerically solved using an implicit finite volume method on a hexahedral mesh constructed with horizontal telescoping (quadtree) rectangular cells and vertical sigma coordinate. The difference in the near-bed cells for flow and suspended load calculations is avoided by adding the bed load to the suspended load in the first flow cell above the bed. The developed model has been tested in four laboratory and field cases. It reasonably well reproduces the measured water levels, flow velocities, sediment concentrations, and bed changes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Andrews DG, McIntyre ME (1978) An exact theory of nonlinear waves on a Lagrangian-mean flow. J Fluid Mech 89:609–646. https://doi.org/10.1017/S0022112078002773

    Article  Google Scholar 

  • Ardhuin F, Rascle N, Belibassakis KA (2008a) Explicit wave-averaged primitive equations using a generalized Lagrangian mean. Ocean Model 20:35–60. https://doi.org/10.1016/j.ocemod.2007.07.001

    Article  Google Scholar 

  • Ardhuin F, Jenkins AD, Belibassakis KA (2008b) Comments on “The three-dimensional current and surface wave equations”. J Phys Oceanogr 38:1340–1350. https://doi.org/10.1175/2007JPO3670.1

    Article  Google Scholar 

  • Battjes J (1975) Modeling of turbulence in the surf zone. Proc. Symp. Model Techniques, San Francisco, USA, pp 1050–1061

  • Beck TM, Kraus NC (2010) Shark River Inlet, New Jersey, entrance shoaling: report 2, Analysis with coastal modeling system. Technical Report ERDC/CHL-TR-10-4. U.S. Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, Vicksburg, MS. http://cirp.usace.army.mil/pubs/html/10-Beck-Kraus_TR-10-4.html

  • Bijvelds MDJP (2001) Numerical modelling of estuarine flow over steep topography. Doctoral Dissertation, Delft University of Technology, The Netherlands

  • Craik ADD, Leibovich S (1976) A rational model for Langmuir circulation. J Fluid Mech 73:401–426. https://doi.org/10.1017/S0022112076001420

    Article  Google Scholar 

  • DHI (2008) Mike 3 flow model. Scientific Documentation, Danish Hydraulic Institute

  • Ding Y, Wang SSY, Jia Y (2006) Development and validation of a quasi-three dimensional coastal area morphological model. J Waterw Port Coast Ocean Eng 132(6):462–476

    Article  Google Scholar 

  • Fortunato, A.B., Oliviera, A. (2007). Improving the stability of a morphodynamic modeling system. J Coast Res Spec Issue 50, 486–490

  • Gravens MB, Wang P (2007) Data report: laboratory testing of longshore sand transport by waves and currents; morphology change behind headland structures. Technical Report ERDC/CHL TR-07-8, U.S. Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, Vicksburg, Mississippi

  • Groeneweg J (1999) Wave-current interactions in a generalized Lagrangian mean formulation. Ph.D. Thesis, Delft Univ. of Technology, Delft, Netherlands

  • Hanson H, Kraus NC (1989) GENESIS: generalized model for simulating shoreline change, report 1: technical reference. Technical Report CERC-89-19, U.S. Army Engineer Waterways Experiment Station, Coastal Engineering Research Center, Vicksburg, Mississippi

  • Hsu SA (1988) Coastal meteorology. In: Academic Press. San Diego, California

    Google Scholar 

  • Johnson HK, Zyserman JA (2002) Controlling spatial oscillations in bed level update schemes. Coast Eng 46(2):109–126

    Article  Google Scholar 

  • Johnson BD, Kobayashi N, Gravens MB (2012) Cross-shore numerical model CSHORE for waves, currents, sediment transport, and beach profile evolution. Technical Report ERDC/CHL TR-12-22, U.S. Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, Vicksburg, Mississippi

  • Kaihatu JM, Shi F, Kirby JT, Svendsen IA (2002) Incorporation of random wave effects into a quasi-3D nearshore circulation model. Naval Research laboratory, Oceanography Division, 1002 Balch Boulevard, Stennis Space Center, MS, USA

  • Kraus NC, Larson M (1991) NMLONG—numerical model for simulating the longshore current, report 1: model development and tests. Technical Report DRP-91-1, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS, USA

  • Kubatko EJ, Westerlink JJ, Dawson C (2006) An unstructured grid morphodynamic model with a discontinuous Galerkin method for bed evolution. Ocean Model 15(1–2):71–89

    Article  Google Scholar 

  • Larson M, Kraus NC (1989) SBEACH: numerical model for simulating storm-induced beach change. Technical Report CERC-89-9, Waterways Experiment Station, Coastal Engineering Research Center, Vicksburg, Mississippi

  • Lesser G, Roelvink J, van Kester J, Stelling G (2004) Development and validation of a three-dimensional morphological model. Coast Eng 51(8–9):883–915

    Article  Google Scholar 

  • Lin L, Demirbilek Z, Mase H, Zheng J, Yamada F (2008) CMS-Wave: a nearshore spectral wave processes model for coastal inlets and navigation projects. Technical Report ERDC/CHL TR-08-13. U.S. Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, Vicksburg, Mississippi

  • Longuet-Higgins MS, Stewart RW (1962) Radiation stress and mass transport in gravity waves with application to “surf beats”. J Fluid Mech 13:481–504. https://doi.org/10.1017/S0022112062000877

    Article  Google Scholar 

  • Longuet-Higgins MS, Stewart RW (1964) Radiation stresses in water waves; a physical discussion with applications. Deep-Sea Res 11:529–562

    Google Scholar 

  • Marsooli R, Wu W (2014) Three-dimensional finite-volume model of dam-break flows with sediment transport over movable beds. J Hydraul Eng, ASCE, 04014066, 1–12, https://doi.org/10.1061/(ASCE)HY.1943-7900.0000947

  • Mase H (2001) Multidirectional random wave transformation model based on energy balance equation. Coastal Eng Journal 43(4):317–337

    Article  Google Scholar 

  • Mase H, Oki K, Hedges TS, Li HJ (2005) Extended energy-balance-equation wave model for multidirectional random wave transformation. Ocean Eng 32(8–9):961–985

    Article  Google Scholar 

  • McWilliams JC, Restrepo JM, Lane EM (2004) An asymptotic theory for the interaction of waves and currents in coastal waters. J Fluid Mech 511:135–178. https://doi.org/10.1017/S0022112004009358

    Article  Google Scholar 

  • Mellor GL (2003) The three-dimensional current and surface wave equations. J Phys Oceanogr 33:1978–1989

    Article  Google Scholar 

  • Mellor GL (2008) The depth-dependent current and wave interaction equations: a revision. J Phys Oceanogr 38:2587–2596

    Article  Google Scholar 

  • Nairn RB, Southgate HN (1993) Deterministic profile modelling of nearshore processes. Part 2. Sediment transport and beach profile development. Coast Eng 19(1–2):57–96

    Article  Google Scholar 

  • Newberger PA, Allen JS (2007) Forcing a three-dimensional, hydrostatic, primitive-equation model for application in the surf zone: I. Formulation. J Geophys Res 112:C08018. https://doi.org/10.1029/2006JC003472

    Google Scholar 

  • Nezu I (2005) Open-channel flow turbulence and its research prospect in the 21st century. J Hydraul Eng ASCE 131(4):229–246. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:4(229

    Article  Google Scholar 

  • Pelnard-Considere R (1956) Essai de theorie de l’Evolution des forms de rivages en plage de sable et de galets, Fourth Journees de l’Hydrolique, les energies de la Mer, Question III, Rapport No. 1, 289–298

  • Powell MD, Vickery PJ, Reinhold TA (2003) Reduced drag coefficient for high wind speeds in tropical cyclones. Nature 422:279–283

    Article  Google Scholar 

  • Prandtl L (1925) Über die ausgebildete Turbulenz. ZAMM 5:136–139

    Article  Google Scholar 

  • Raudkivi AJ (1998) Loose boundary hydraulics. A.A. Balkema, Rotterdam 496p

    Google Scholar 

  • Rhie TM, Chow A (1983) Numerical study of the turbulent flow past an isolated airfoil with trailing-edge separation. AIAA J 21:1525–1532

    Article  Google Scholar 

  • Rodi W (1993) Turbulence models and their applications in hydraulics, 3rd edn. IAHR Monograph, Rotterdam, p 104

    Google Scholar 

  • Roelvink D, Reniers A (2012) A guide to modeling coastal morphology. Advances in coastal and ocean engineering, World Scientific, Vol 12, p 274

  • Roland A, Cucco A, Ferrarin C, Hsu T, Liau J, Ou S, Umgiesser G, Zanke U (2009) On the development and verification of a 2-D coupled wave-current model on unstructured meshes. J Mar Syst 78:S244–S254. https://doi.org/10.1016/j.jmarsys.2009.01.026

    Article  Google Scholar 

  • Ruessink BG, Miles JR, Feddersen F, Guza RT, Elgar S (2001) Modeling the alongshore current on barred beaches. J Geophys Res 106(C10):22451–22464

    Article  Google Scholar 

  • Saad Y (1993) A flexible inner-outer preconditioned GMRES algorithm. SIAM J Sci Comput 14:461–469

    Article  Google Scholar 

  • Saad Y (1994) ILUT: a dual threshold incomplete ILU factorization. Numerical Linear Algebra Appl 1:387–402

    Article  Google Scholar 

  • Sanchez A, Wu W, Beck TM (2016) A depth-averaged 2-D model of flow and sediment transport in coastal waters. Ocean Dyn 66:1475–1495. https://doi.org/10.1007/s10236-016-0994-3

    Article  Google Scholar 

  • Satkevich (Саткевич), А.А. (1934) Theoretical foundations of hydro-aerodynamics (Теоретические основи гидроазродинамики), Т. 2, Dynamics of Liquid Bodies (Динамика жидких тел)

  • Sheng YP, Liu T (2011) Three-dimensional simulation of wave-induced circulation: comparison of three radiation stress formulations. J Geophys Res 116:C05021. https://doi.org/10.1029/2010JC006765

    Article  Google Scholar 

  • Soulsby RL (1997) Dynamics of marine sands, a manual for practical applications. H.R. Wallingford, Thomas Telford

    Google Scholar 

  • Soulsby R, Whitehouse R (2005) Prediction of ripple properties in shelf seas: mark 1, predictor. Technical Report TR 150, HR Wallingford, UK

  • Spalding DB (1972) A novel finite-difference formulation for differential expressions involving both first and second derivatives. Int J Numer Methods Eng 4:551–559. https://doi.org/10.1002/nme.1620040409

    Article  Google Scholar 

  • Stelling GS, Van Kester JATM (1994) On the approximation of horizontal gradients in sigma coordinates for bathymetry with steep bottom slopes. Int J Numer Methods Fluids 18(10):915–935

    Article  Google Scholar 

  • Stive MJF, de Vriend HJ (1994) Shear stresses and mean flow in shoaling and breaking waves. Proc. the 24th Coastal Engineering International Conference, Kobe, Japan. American Society of Civil Engineers, New York, pp 594–608

  • Svendsen IA (2006) Introduction to nearshore hydrodynamics. World Scientific, p 722

  • Uchiyama Y, McWilliams JC, Shchepetkin AF (2010) Wave-current interaction in an oceanic circulation model with a vortex-force formalism: application to the surf zone. Ocean Model 34:16–35. https://doi.org/10.1016/j.ocemod.2010.04.002

    Article  Google Scholar 

  • van der Salm GLS (2013) Coastline modelling with UNIBEST: areas close to structures. M.S. Thesis. Delft University of Technology, The Netherlands

  • van Doormal JP, Raithby GD (1984) Enhancements of the SIMPLE method for predicting incompressible fluid flows. Num Heat Transfer 7:147–163

    Google Scholar 

  • van Rijn LC (1986) Sedimentation of dredged channels by currents and waves. J Waterw Port Coast Ocean Eng 112(5):541–559

    Article  Google Scholar 

  • van Rijn LC (1993) Principles of sediment transport in rivers, estuaries and coastal seas. Aqua Publications, The Netherlands

    Google Scholar 

  • van Rijn LC, Havinga FJ (1995) Transport of fine sands by currents and waves. J Waterw Port Coast Ocean Eng 121(2):123–133

    Article  Google Scholar 

  • Warner JC, Sherwood CR, Signell RP, Harris CK, Arango HG (2008) Development of a three-dimensional, regional, coupled wave, current, and sediment-transport model. Comput Geosci 34:1284–1306

    Article  Google Scholar 

  • Wu W (2004) Depth-averaged 2-D numerical modeling of unsteady flow and nonuniform sediment transport in open channels. J Hydraul Eng ASCE 130(10):1013–1024

    Article  Google Scholar 

  • Wu W (2007) Computational river dynamics. Taylor & Francis, Abingdon, p 494

    Book  Google Scholar 

  • Wu W (2014) A 3-D phase-averaged model for shallow water flow with waves in vegetated water. Ocean Dyn 64(7):1061–1071. https://doi.org/10.1007/s10236-014-0739-0

    Article  Google Scholar 

  • Wu W (2015) 3-D numerical modeling of undertow current and sediment transport in surf zone. Proc. 2015 International Conference on Coastal Sediments, San Diego, CA

  • Wu W, Lin Q (2014) Nonuniform sediment transport under non-breaking waves and currents. Coast Eng 90:1–14. https://doi.org/10.1016/j.coastaleng.2014.04.0060378-3839

  • Wu W, Lin Q (2015) An implicit 3-D finite-volume model of shallow water flows. Adv Water Resour 83:263–276. https://doi.org/10.1016/j.advwatres.2015.06.008

    Article  Google Scholar 

  • Wu W, Rodi W, Wenka T (2000a) 3-D numerical modeling of water flow and sediment transport in open channels. J Hydraul Eng ASCE 126(1):4–15

    Article  Google Scholar 

  • Wu W, Wang SSY (2006) Formulas for sediment porosity and settling velocity. J Hydraul Eng ASCE 132(8):858–862

    Article  Google Scholar 

  • Wu W, Wang SSY, Jia Y (2000b) Nonuniform sediment transport in alluvial rivers. J Hydraul Res IAHR 38(6):427–434

    Article  Google Scholar 

  • Xia H, Xia Z, Zhu L (2004) Vertical variation in radiation stress and wave-induced current. Coast Eng 51:309–321. https://doi.org/10.1016/j.coastaleng.2004.03.003

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Clarkson University, Potsdam, NY, 13699, USA

    Weiming Wu

  2. Microsoft, Redmond, WA, 98052, USA

    Qianru Lin

Authors
  1. Weiming Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qianru Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Weiming Wu.

Additional information

Responsible Editor: Eric Deleersnijder

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, W., Lin, Q. A 3-D finite volume model for sediment transport in coastal waters. Ocean Dynamics 69, 561–580 (2019). https://doi.org/10.1007/s10236-019-01261-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10236-019-01261-7

Keywords

Search

Navigation