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wave-current interaction
sediment transport
seabed evolution

How to Cite

Coutinho, T. N., de Jesus, L. C., & Chacaltana, J. T. A. (2017). WAVE-CURRENT INTERACTION, SEDIMENT TRANSPORT AND SEABED EVOLUTION IN THE PIRAQUÊ-AÇU/PIRAQUÊ MIRIM ESTUARY (BRAZIL). Coastal Engineering Proceedings, 1(35), sediment.32. https://doi.org/10.9753/icce.v35.sediment.32


The medium-term seabed evolution of Piraquê-Açú/Piraquê-Mirim estuary (ES/Brazil) is studied numerically in this work. The hydrodynamics is induced by the tide, the river discharges, and the incident water wave. The wave-tide-current interactions are obtained by coupling the shallow water equations with the radiation stress tensor introduced by Longuet-Higgins & Stewart (1960). In this way, the influence of both the tidal current and the current induced by gravity waves on the sediment transport are taken into account. We utilized the Exner (1925) equation, based on the conservation of seabed sediment mass, to calculate the morphological evolution. Seabed morphological changes are accelerated by introducing a time scale factor. Four bedload sediment transport formulations were tested and compared. We found an excellent agreement when numerical results are compared with currents measured in the upper estuary and with sediment transport rates measured at the river's mouth when using the Engelund and Hansen (1967) sediment transport formulation. We also found that the main morphological changes occurring at the estuary mouth are due to the action of gravity waves. Between the head and mouth of the estuary, the sediment transport rate and morphological seabed changes are controlled exclusively by the tidal currents and the river discharge. In this latter case, we found that the large sandbank located at the estuary mouth is responsible for the absence of wave.


Ariathurai, C. R. 1974. A finite element model for sediment transport in estuaries. Ph.D Thesis, University of California, Davis.

Bertin, X., A. Oliveira, and A.B. Fortunato. 2009. Simulating morphodynamics with unstructured grids: description and validation of a modeling system for coastal applications, Ocean Modelling, 28 (1-3), 75-87.

Brière, C., P.C. Roos, E. Garel and S.J.M.H. Hulscher. 2010. Modelling the morphodynamics of the Kwinte Bank, subject to sand extraction. Journal of Coastal Research, 51, 117-126.

Cayocca, F. 2001. Long-term morphological modeling of a tidal inlet: the Arcachon Basin, France, Coastal Engineering, 42 (2), 115-142.

Chen, F. 2014. Analysis of the effects of process variations on delta morphology and stratigraphy in Delft3D computational models. Thesis of master degree. Faculty of Civil Engineering and Geosciences. Delft University of Tecnology. Delft.

da Silva, A., V. da Silva Quaresma, and A. Bastos. 2013. Sedimentological Sectorization of an Estuarine System In A Regressive Coast, Southeast Brazil. Journal of Sedimentary Research, 83(11), 994-1003.

Ding, Y. and S.S.Y Wang. 2006. Development and validation of a quasi-three-dimensional coastal area morphological model, Journal of waterway, port, coastal, and ocean engineering, 132, 462-476.

Dissanayake, D., A. Wurpts, M. Miani, H. Knaack, H. Niemeyer, and J. Roelvink. 2012. Modelling morphodynamic response of a tidal basin to an anthropogenic effect: Ley Bay, East Frisian Wadden Sea - applying tidal forcing only and different sediment fractions, Coastal Engineering, 67, 14-28.

Dissanayake, D., J. Roelvink, and M. van der Wegen. 2009. Modelled channel patterns in a schematized tidal inlet, Coastal Engineering, 56, 1069-1083.

Engelund, F. and F. Hansen. 1967. A Monograph of Sediment Transport in Alluvial Channels. Teknisk Forlag, Copenhagen.

Exner, F. M. 1925. Über die Wechselwirkung zwischen Wasser und Geschiebe in Flussen (On the interaction between water and sediment in streams), Sitzungsber. Akad. Wiss. Wien Math. Naturwiss., Abt. 2A, 134, 165-205.

Fortunato, A., A. Nahon, G. Dodet, A. Rita Pires, M. Conceição Freitas, N. Bruneau, A. Azevedo, X. Bertin, P. Benevides, C. Andrade, and Oliveira. 2014. Morphological evolution of an ephemeral tidal inlet from opening to closure: The Albufeira inlet, Portugal, Continental Shelf Research, 73, 49-63.

Hassanzadeh, H., S. Faiznia, M.S. Bajestan, and A. Motamed. 2011. Estimate of sediment transport rate at Karkheh River in Iran using selected transport formulas. World Applied Sciences Journal, 13 (2), 376-384.

Hibma, A., H.J. de Vriend, and M.J.F. Stive. 2003. Numerical modelling of shoal pattern formation in well-mixed elongated estuaries. Estuarine coastal and shelf science, 57, 981-991.

Holthuijsen, L.H., N. Booij and R.C. Ris. 1993. A spectral wave model for the coastal zone, 2nd International Symposium on Ocean Wave Measurement and Analysis, New York, 630-641.

Kleinhans, M. G., and B.T. Grasmeijer. 2006. Bed load transport on the shoreface by currents and waves. Coastal Engineering, 53, 983-996.

Kuang, C., X. Liu, J. Gu, Y. Guo, S. Huang, S. Liu, W. Yu, J. Huang, and B. Sun. 2013. Numerical prediction of medium-term tidal flat evolution in the Yangtze Estuary: Impacts of the Three Gorges project, Continental Shelf Research, 52, 12-26.

Lesser, G. R., J.A Roelvink, J.A.T.M. Kester, and G.S. Stelling. 2004. Development and validation of a three-dimensional morphological model, Coastal Engineering, 51, 883-915.

Longuet-Higgins M.S. and Stwart R. W. (1960) Changes in the form of short gravity waves on long waves and tidal currents, Jounal of Fluid Mechanics, 8, 565-583.

MacMahan, J., E. Thornton, A. Reniers, T. Stanton, and G. Symonds. 2008. Low-Energy Rip Currents Associated With Small Bathymetric Variations. Marine Geology, 255(3-4), 156-164.

Olabarrieta, M., W.R. Geyer, and N. Kumar 2014. The role of morphology and wave-current interaction at tidal inlets: An idealized modeling analysis. Journal of Geophysical Research, Oceans, 119(12), 8818-8837.

Partheniades, E. 1965. Erosion and deposition of cohesive soils. Journal of the Hydraulics Division Proceedings of the ASCE, 9, 105-139.

Soulsby, R., 1997. Dynamics of marine sands. Thomas Telford, UK, 249p.

Van Der Vegt, M., H.M. Schuttelaars, H.E. De Swart. 2006. Modelling the equilibrium of tide-dominated ebb-tidal deltas. Journal of Geophysical Research, 111, F02013.

Van Rijn V. 1993. Principles of sediment transport in rivers, estuaries and coastal seas. Aqua Publicantions, Amsterdam, 700p.

van Rijn, L.C. 2007. Unified view of sediment transport by currents and waves. I: initiation of motion, bed roughness, and bed-load transport, Journal of Hydraulic Engineering, 133, 649-667.

Verboom, G. K., and A. Slob. 1984. Weakly-reflective boundary conditions for two-dimensional shallow water flow problems. Advance Water Resources, 7, 1693-1708.

Wang, Z., T. Louters, and H. de Vriend. 1995. Morphodynamic modelling for a tidal inlet in the Wadden Sea, Marine Geology, 126(1-4), 289-300.

Xie, D., S. Gao, Z. Wang, and C. Pan. 2013. Numerical modeling of tidal currents, sediment transport and morphological evolution in Hangzhou Bay, China. International Journal of Sediment Research, 28, 316-328.

Zhou, Z., G. Coco, M. Jiménez, M. Olabarrieta, M. van der Wegen, and I. Townend. 2014. Morphodynamics of river-influenced back-barrier tidal basins: The role of landscape and hydrodynamic settings. Water Resources Research, 50(12), 9514-9535.

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