Volume 15, Issue 1 - March 2015


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Revista de Gestão Costeira Integrada
Volume 15, Número 1, Março 2015, Páginas 21-33

DOI: 10.5894/rgci530
* Submission: 25 JUN 2014; Peer review: 19 AUG 2014; Revised: 2 MAR 2015; Accepted: 3 MAR 2015; Available on-line: 5 MAR 2015

Model of the evolution of mounds placed in the nearshore *  

Magnus Larson@, a; Hans Hansona

@ - Corresponding author, to whom correspondence should be addressed.
a - Lund University, Department of Water Resources Engineering, Box 118, S-221 00 Lund, Sweden. E-mails: Larson [email protected]; Hanson <[email protected]>   

A one-dimensional mathematical model is presented that describes the cross-shore evolution of a long linear mound of noncohesive sediment placed in the nearshore and exposed to non-breaking waves. The equation for the transport rate accounts for wave asymmetry and gravity, and the net rate is expressed by reference to an equilibrium profile shape. Simplifications reduce the governing equation for mound evolution to the diffusion equation, for which analytical solutions are available for various initial shapes of the mound. Temporal and spatial dependencies governing mound evolution are obtained from the analytic solutions; for example, a doubling of the wave height implies a certain mound response in 1/8 of the time compared to the original conditions. The governing equation is also solved numerically in order to avoid schematization of the forcing, initial, and boundary conditions. Both the analytical and numerical models are compared with data on mound evolution from several sites around the world. Model predictions agree with trends in measurements of four mounds at widely different sites. An example is given concerning the application of the analytical model for preliminary mound design. The formulation presented also applies to infilling of dredged trenches with lengths much greater than their widths.

Keywords: sediment transport, dredging, profile evolution, beach nourishment, mound design.   

Model of the evolution of mounds placed in the nearshore

A evolução morfodinâmica de um banco de areia existente na zona costeira do oceano antes da zona de rebentação é descrita recorrendo a um matemático unidimensional. As taxas de transporte sedimentar são calculadas relativamente a um perfil de equilíbrio e têm em conta a assimetria das ondas e o termo gravitacional. A equação de balanço que rege a evolução da morfologia do fundo, sob certas hipóteses, reduz-se a uma equação de difusão que tem solução analítica conhecida para diferentes condições iniciais. Para condições mais gerais, a equação é resolvida numericamente. Os resultados numéricos obtidos descrevem a tendência das observações efetuadas em quatro bancos de areia distintos. O modelo analítico desenvolvido é aplicado para estudar a configuração inicial de um banco de areia. A formulação apresentada pode também ser aplicada para estudar a evolução da morfologia de escavações resultantes de dragagens com uma configuração em que o seu comprimento é maior do que a sua largura.
Palavras-chave: transporte de sedimentos, dragagem, evolução de perfil, alimentação artificial, projeto de banco de areia. 


Andrassy, C.J. (1991) - Monitoring of a nearshore disposal mound at Silver Strand State Park. Proceedings Coastal Sediments ‘91, ASCE, 1970-1984.

Barnard, P.L.; Hanes, D.M.; Lescinski, J.; Elias, E. (2007) - Monitoring and modeling nearshore dredge disposal for indirect beach nourishment, Ocean Beach, San Francisco. Proceedings 30th Coastal Engineering Conference, ASCE, 4192-4204.

Beck, T.M.; Rosati, J.D.; Rosati, J. (2012) - An update on nearshore berms in the Corps of Engineers: Recent projects and future needs. CHETN-XIV-10, Coastal and Hydraulics Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS.

Bruun, P. (1954) - Coast erosion and the development of beach profiles. Technical Memorandum No. 44, Beach Erosion Board, U.S. Army Corps of Engineers.

Carslaw, H.; Jaeger, J. (1959) - Conduction of heat in solids. Clarendon
Press, Oxford.

Crank, J. (1973) - The Mathematics of Diffusion. 2nd ed., Clarendon Press, Oxford.

Dally, W.R. (1992) - Random breaking waves: Field verification of a wave-by-wave algorithm for engineering application. Coastal
Engineering, 16, 369-397.

Dally, W.R.; Osiecki, D.A. (2006) - Development & validation of hindcast-driven nearshore wave information. 9th International
Workshop on Wave Hindcasting and Forecasting, Victoria, Canada, 24-29 September.

Dean, R.G. (1977) - Equilibrium beach profiles: U.S. Atlantic and Gulf coasts. Department of Civil Engineering, Ocean Engineering Report No. 12, Univ. of Delaware, Newark, DE.

Dean, R.G. (1987) - Coastal sediment processes: Toward engineering
solutions. Proceedings of Coastal Sediments '87, ASCE, 1-24.

Dean, R.G. (1991) - Principles of beach nourishment. In: Komar, P.D. (editor), Handbook of Coastal Processes and Erosion, CRC Press, Boca Raton, FL, 217-231.

DRP (1994) - Tidal constituents database – East Coast, Gulf of Mexico, and Carribean Sea. Dredging Research Technical Notes, DRP-1-13. Coastal Engineering Research Center, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.

Foster, G.A.; Healy, T.R.; De Lange, W.P. (1996) - Presaging beach
nourishment from a nearshore dredge dump mound, Mt. Maunganui
Beach, New Zealand. Journal of Coastal Research, 12(2), 395-405.

Grunnet, N.M.; Ruessink, B.G.; Walstra, D.J.R. (2005) - The influence of tides, wind and waves on the redistribution of nourished sediment at Terschelling, The Netherlands. Coastal Engineering, 52(7), 617-631.

Hands, E.B.; Allison, M.C. (1991) - Mound migration in deeper water and methods of characterizing active and stable berms. Proceedings Coastal Sediments ’91, ASCE, 195-1999.

Kobayashi, N. (1982) - Sediment transport on a gentle slope due to
waves. Journal of Waterway, Port, Coastal and Ocean Engineering,
108(WW3), 254-271.

Larson, M. (1996) - Model of beach profile change under random waves. Journal of Waterway, Port, Coastal, and Ocean Engineering, 122(4), 172-181.

Larson, M.; Kraus, N.C. (1989) - SBEACH: Numerical Model for Simulating Storm-Induced Beach Change. Report 1: Empirical Foundation and Model Development. Technical Report CERC-89-9, Coastal Engineering Research Center, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.

Larson, M.; Kraus, N.C. (1992) - Analysis of cross-shore movement of natural longshore bars and material placed to create longshore bars. Technical Report DRP-92-5, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.

Larson, M.; Kraus, N.C.; Hanson, H. (1987) - Analytical solutions of the one-line model of shoreline change. Technical Report CERC-87-15, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.

Larson, M.; Kraus, N.C.; Wise, R.A. (1999) - Equilibrium beach profiles
under breaking and non-breaking waves. Coastal Engineering, 36(1), 59-85.

Madsen, O.S., (1991) - Mechanics of cohesionless sediment transport
in coastal waters. Proceedings of Coastal Sediments '91, ASCE,
pp 15-27.

Madsen, O.S. (1993) - Sediment transport on the shelf. Sediment
Transport Workshop DRP TA1, 8-9 June, Coastal Engineering Research
Center, Vicksburg, MS.

McLellan, T.N. (1990) - Nearshore mound construction using dredged material. Journal of Coastal Research, SI 7, 99-107.

Niedoroda, A.W.; Reed, C.W.; Swift, D.J.P; Arato, H.; Hoyanagi, K. (1995) - Modeling shore-normal large-scale coastal evolution. Marine Geology, 126, 181-199.

Otay, E.N. (1995) - Monitoring results of a nearshore disposal berm.
Proceedings Coastal Dynamics ’95, ASCE, 546-558.

Rosati, J.D.; Wise, R.A.; Kraus, N.C.; Larson, M. (1993) - SBEACH: Numerical model for simulating storm-induced beach change. Report 3: User's manual. Instruction Report CERC-93-2, Coastal Engineering Research Center, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.

Smith, E.R.; Gailani, J.Z. (2005) - Nearshore placed mound physical model experiment. DOER Technical Notes Collection (ERDC TN-DOER-D3), U.S. Army Engineer Research and Development Center, Vicksburg, MS.

Van Duin, M.J.P.; Wiersma, N.R.; Walstra, D.J.R: Van Rijn, L.C.; Stive, M.J.F. (2004) - Nourishing the shoreface: observations and hindcasting of the Egmond case, The Netherlands. Coastal Engineering, 51(8-9), 813-837.

Walstra, D.J.R.; Hoekstra, R.; Tonnon, P.K.; Ruessink, B.G. (2013)
- Input reduction for long-term morphodynamic simulations in wave-dominated coastal settings. Coastal Engineering, 77, 57-70. doi:10.1016/j.coastaleng.2013.02.001

Work, P.A.; Otay, E.N. (1996) - Influence of nearshore berm on beach nourishment. Proceedings 25th Coastal Engineering Conference, ASCE, 3722-3735.

Zwamborn, J.A.; Fromme, G.A.W.; FitzPatrick, J.B. (1970) - Underwater
mound for the protection of Durban’s beaches. Proceedings 12th Coastal Engineering Conference, ASCE, 975-994.


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