INFLUENCE OF NON-LINEAR WAVES AND UNDERTOW IN SANDBAR DEVELOPMENT

Tiago Abreu, Francisco Sancho, Paulo A. Silva

Abstract


As waves propagate from deep into shallow waters, they begin to interact with the sea floor and undergo through several changes due to non-linear effects. These interactions cause the waves to transform and become non-linear as they decelerate and finally break. These local nonlinearities are reflected on the near-bed oscillatory flow and are inextricably linked to sediment transport, causing erosion-accretion patterns and bar migration. In this work the ability of a practical transport model that includes the effects of velocity and acceleration skewness in the time-varying bed shear stress (Abreu et al., 2011) is assessed to predict sediment transport rates under oscillatory flows and currents. The results are compared with two different data sets obtained under sheet flow conditions, showing a good agreement with the measurements. Moreover, its performance to the undertow and to non-linear characteristics is further assessed. The practical sediment transport model is coupled to a simple bed-evolution model, enabling to evidence the relative strength of mechanisms associated with the wave and current induced sand transports. The results show that the formation of the bar and its migration is affected by a new term introduced in the bed shear stress predictor. This time-varying term accounts for the shape of the wave and is described through two non-linear parameters recently proposed in Abreu et al. (2010).This work provides further insights in the correct prediction of sediment transport modeling and sandbar developments, due to the combined influence of non-linear waves with undertow currents.

Keywords


non-linear waves; skewness; asymmetry; undertow; sandbar

References


Abreu, T. 2011. Coastal sediment dynamics under asymmetric waves and currents: measurements and simulations. PhD thesis, University of Coimbra, 255 pp.

Abreu, T., Silva, P.A., Sancho, F. and A. Temperville. 2010. Analytical approximate wave form for asymmetric waves, Coastal Engineering, 57, 656-667.http://dx.doi.org/10.1016/j.coastaleng.2010.02.005

Abreu, T., van der A, D.A., Silva, P.A., Sancho, F. and H. Michallet. 2011a. New bed shear stress estimator for net sand transport rate predictions under non-linear waves, Journal of Coastal Research, SI 64, 2007-2011.

Abreu, T., Silva, P.A. and F. Sancho. 2011b. Asymmetrical waves in barred beaches, Revista de Gestão Costeira Integrada / Journal of Integrated Coastal Zone Management, 11(3), 297-306, (in Portuguese).

Airy, G.B. 1841. Tides and waves, Encyclopaedia Metropolitana, 396 pp.

Bruun, P. 1954, Coast erosion and the development of beach profiles, Beach erosion board technical memorandum, 44, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.

Davies, A.G., van Rijn, L.C., Damgaard, J.S., van de Graaff, J. and J.S. Ribberink. 2002. Intercomparison of research and practical sand transport models, Coastal Engineering, 46, 1 –23http://dx.doi.org/10.1016/S0378-3839(02)00042-X

De Vriend, H.J., J. Zyserman, J. Nicholson, J.A. Roelvink, P. Pechon, and H.N. Southgate. 1993. Medium-term 2DH coastal area modeling, Coastal Engineering, 21, 193-224.http://dx.doi.org/10.1016/0378-3839(93)90050-I

Dean, R.G. and R.A. Dalrymple. 1991. Water wave mechanics for engineers and scientists, Advanced Series on Ocean Engineering, 2. World Scientific, 353 pp.

Dibajnia, M., Moriya, T. and A. Watanabe. 2001. A representative wave model for estimation of nearshore local transport rate, Coastal Engineering Journal, 43(1), 1-38.http://dx.doi.org/10.1142/S0578563401000256

Doering, J.C. and A.J. Bowen. 1995. Parametrization of orbital velocity asymmetries of shoaling and breaking waves using bispectral analysis, Coastal Engineering, 26(1-2), 15-33.http://dx.doi.org/10.1016/0378-3839(95)00007-X

Drake, T.G. and J. Calantoni. 2001. Discrete particle model for sheet flow sediment transport in the nearshore, Journal of Geophysical Research,106, C9, 19859-19868.http://dx.doi.org/10.1029/2000JC000611

Elfrink, B., Hanes, D.M. and B.G. Ruessink. 2006. Parameterization and simulation of near bed orbital velocities under irregular waves in shallow water, Coastal Engineering, 53, 915-927.http://dx.doi.org/10.1016/j.coastaleng.2006.06.002

Elgar, S.L. and R.T. Guza. 1985. Observations of bispectra of shoaling surface gravity waves, Journal of Fluid Mechanics,167, 425-448.http://dx.doi.org/10.1017/S0022112085003007

Hoefel, F. and S. Elgar. 2003. Wave-induced sediment transport and sandbar migration, Science 299, 1885–1887.http://dx.doi.org/10.1126/science.1081448

PMid:12649479

Long, W., J.T. Kirby and Z. Shao, 2008. A numerical scheme for morphological bed level calculations, Coastal Engineering, 55, 167-180.http://dx.doi.org/10.1016/j.coastaleng.2007.09.009

Malarkey, J. and A.G. Davies. 2012. Free-stream velocity descriptions under waves with skewness and asymmetry, Coastal Engineering, 68, 78-95.http://dx.doi.org/10.1016/j.coastaleng.2012.04.009

McCowan, J. 1984. On the highest wave of permanent type, Philosophical Magazine, 38, pp. 351-358.

Meyer-Peter, E. and R. Müller. 1948. Formulas for bed-load transport. IAHR, 2nd Meeting of the International Association for Hydraulic Structures Research, Stockholm, Sweden, 39-64.

Nielsen, P. 1992. Coastal Bottom Boundary Layers and Sediment Transport, Advanced Series on Ocean Engineering, 4, World Scientific, 324 pp.

Nielsen, P. 2002. Shear stress and sediment transport calculations for swash zone modelling, Coastal Engineering, 45(1), 53-60.http://dx.doi.org/10.1016/S0378-3839(01)00036-9

Nielsen, P. 2006. Sheet flow sediment transport under waves with acceleration skewness and boundary layer streaming, Coastal Engineering, 53(9), 749-758.http://dx.doi.org/10.1016/j.coastaleng.2006.03.006

Nielsen, P. and D.P. Callaghan. 2003. Shear stress and sediment transport calculations for sheet flow under waves, Coastal Engineering, 47(3), 347-354.http://dx.doi.org/10.1016/S0378-3839(02)00141-2

O'Donoghue, T., Doucette, J.S., van der Werf, J.J. and Ribberink, J.S., 2006. The dimensions of sand ripples in full-scale oscillatory flows, Coastal Engineering, 53(12), 997-1012.http://dx.doi.org/10.1016/j.coastaleng.2006.06.008

Rattanapitikon, W. and T. Shibayama. 2000. Simple model for undertow profile, Coastal Engineering Journal, 42(1), 1-30.http://dx.doi.org/10.1142/S057856340000002X

Richtmyer, R.D., 1962. A survey of difference methods for nonsteady fluid dynamics, Natl. Cent. Atmos. Res. Tech., Note 63-2.

Ruessink, B.G., van den Berg, T.J.J. and L.C. van Rijn. 2009. Modeling sediment transport beneath skewed asymmetric waves above a plane bed, Journal of Geophysical Research, 114(C11), C11021.http://dx.doi.org/10.1029/2009JC005416

Ruessink, B.G., Ramaekers, G. and L.C. van Rijn. 2012. On the parameterization of the free-stream non-linear wave orbital motion in nearshore morphodynamic models, Coastal Engineering, 65, 56–63.http://dx.doi.org/10.1016/j.coastaleng.2012.03.006

Sancho, F., Abreu, T., D'Alessandro, F., Tomasicchio, G.R. and P.A. Silva. 2011. Surf hydrodynamics in front of collapsing coastal dunes. Journal of Coastal Research, SI 64: 144-148.

Shapiro, R. 1975. Linear filtering. Mathematics of computation, 29 (132), 1094-1097.http://dx.doi.org/10.1090/S0025-5718-1975-0389356-X

Silva, P.A., Temperville, A. and F. Seabra Santos. 2006. Sand transport under combined current and wave conditions: A semi-unsteady, practical model. Coastal Engineering, 53(11), pp. 897-913.http://dx.doi.org/10.1016/j.coastaleng.2006.06.010

Silva, P.A., Abreu, T., van der A, D.A., Sancho, F., Ruessink, B.G., van der Werf, J.J. and J.S. Ribberink. 2011. Sediment transport in non-linear skewed oscillatory flows: Transkew experiments. Journal of Hydraulic Research, 49, sup1 : 72-80.

Stokes, G. G. 1847. On the theory of oscillatory waves, Trans. Cambridge Philos. Soc., 8, 441-455.

Svendsen, I.A., Madsen, P.A. and J.B. Hansen. 1978. Wave characteristics in the surf zone, 16th International Conference on Coastal Engineering, 520-539.

Thornton, E.B., Humiston, R.T. and W. Birkemeier. 1996. Bar/trough generation on a natural beach, Journal of Geophysical Research, 101(C5), 12097-12110.http://dx.doi.org/10.1029/96JC00209

Terrile, E., Reniers, A.J.H.M. and M.J.F. Stive. 2009. Acceleration and Skewness Effects on the Instantaneous Bed-Shear Stresses in Shoaling Waves, Journal of Waterway, Port, Coastal, and Ocean Engineering, 135(5), 228-234.http://dx.doi.org/10.1061/(ASCE)0733-950X(2009)135:5(228)

van der A, D.A., O'Donoghue, T. and J.S. Ribberink. 2010. Measurements of sheet flow transport in acceleration-skewed oscillatory flow and comparison with practical formulations, Coastal Engineering, 57(3), 331-342.http://dx.doi.org/10.1016/j.coastaleng.2009.11.006


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