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Grain sorting effects on the formation of tidal sand waves

Published online by Cambridge University Press:  15 June 2009

TOMAS VAN OYEN  and
PAOLO BLONDEAUX
TOMAS VAN OYEN
Affiliation:
Department of Civil, Environmental and Architectural Engineering, University of Genoa, Via Montallegro 1, 16145 Genova, Italy
PAOLO BLONDEAUX*
Affiliation:
Department of Civil, Environmental and Architectural Engineering, University of Genoa, Via Montallegro 1, 16145 Genova, Italy
*
†Email address for correspondence: [email protected]
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Abstract

A model is developed to investigate the process which leads to the formation of sand waves in shallow tidal seas characterized by a heterogeneous sea bed composition. The main goal of the analysis is the evaluation of the effects that a graded sediment has on the formation of the bottom forms and the investigation of the sorting process induced by the growth of the bottom forms. The analysis is based on the study of the stability of the flat bed configuration, i.e. small amplitude perturbations are added to the flat bottom and a linear analysis of their time development is made. For an oscillatory tidal current dominated by one tidal constituent, the results show that the graded sediment can stabilize or destabilize the flat bottom configuration with respect to the uniform sediment case, depending on the standard deviation σ* of the grain size distribution and on the ratio between the horizontal tidal excursion and the water depth. For moderate values of , i.e. values just larger than the critical value for which the sediment is moved and sand waves appear, the presence of a sand mixture stabilizes the flat bed. On the other hand, for large values of , the mixture has a destabilizing effect. In both cases the effect that a sand mixture has on the stability of the flat bed configuration is relatively small. Moreover, for moderate values of , the fine fraction of the mixture tends to pile up at the crests of the bottom forms while the coarse fraction moves towards the troughs. For large values of , the grain size distribution depends on the value of σ*. The results are physically interpreted and provide a possible explanation of the apparently conflicting field observations of the grain size distribution along the sand wave profile, carried out in the North Sea.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 629 , 25 June 2009 , pp. 311 - 342
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Antia, E. E. 1996 Shoreface-connected ridges in German and US mid-Atlantic bights: similarities and contrasts. J. Coast. Res. 12, 141–146.Google Scholar
Ashida, K. & Michiue, M. 1972 Study on hydraulic resistance and bedload transport rate in alluvial streams. Japan Soc. Civ. Engng 206, 59–69.Google Scholar
van den Berg, J. & Van Damme, R. M. J. 2005 Sand wave simulation on large domains. In Proc. RCEM'05 (ed. Parker, G. & Garcia, M. H.). Taylor & Francis/Balkema.Google Scholar
Besio, G., Blondeaux, P., Brocchini, M., Hulscher, S. J. M. H., Idier, D., Knaapen, M. A. P., Nemeth, A. A., Roos, P. C. & Vittori, G. 2008 The morphodynamics of tidal sand waves: a model overview. The morphodynamics of tidal sand waves: a model overview 55 (7–8), 657–670.Google Scholar
Besio, G., Blondeaux, P. & Frisina, P. 2003 A note on tidally generated sand waves. J. Fluid Mech. 485, 171–190.CrossRefGoogle Scholar
Besio, G., Blondeaux, P. & Vittori, G. 2006 On the formation of sand waves and sand banks. J. Fluid Mech. 557, 1–27CrossRefGoogle Scholar
Blondeaux, P. & Vittori, G. 2005 a Flow and sediment transport induced by tide propagation. Part 1. The flat bottom case. J. Geophys. Res. 110 (C7), C07020, doi:10.1029/2004JC002532.Google Scholar
Blondeaux, P. & Vittori, G. 2005 b Flow and sediment transport induced by tide propagation. Part 2. The wavy bottom case. J. Geophys. Res. 110 (C8), C08003, doi:10.1029/2004JC002545.Google Scholar
Blondeaux, P. & Vittori, G. 2009 The formation of tidal sand waves: steady versus unsteady approaches. The formation of tidal sand waves: steady versus unsteady approaches 47 (2), 213–222.Google Scholar
Boon, J. G. & Gerritsen, H. 1997 Modelling of suspended particulate matter (SPM) in the North Sea: a detailed orthogonal boundary-fitted modelling approach (PROMISE). Res Rep. Z2025. Delft Hydraulics, Delft, The Netherlands.Google Scholar
Brownlie, W. R. 1981 Prediction of flow depth and sediment discharge in open channel. Res Rep. KH-R-43A. W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, CA.Google Scholar
Cherlet, J., Besio, G., Blondeaux, P., Van Lancker, V., Verfaillie, E. & Vittori, G. 2007 Modelling sand wave characteristics in Belgian continental shelf and in the Calais-Dover strait. J. Geophys. Res. 112, C06002, doi:10.1029/2007JC004089.Google Scholar
Colombini, M. 2004 Revisiting the linear theory of sand dune formation. J. Fluid Mech. 502, 1–16.CrossRefGoogle Scholar
Dean, R. B. 1974 AERO Report 74-11. Imperial College, London.Google Scholar
Egiazaroff, I. V. 1965 Calculation of non-uniform sediment concentrations. Calculation of non-uniform sediment concentrations 91 (4), 225–248.Google Scholar
Foti, E. & Blondeaux, P. 1995 a Sea ripple formation: the turbulent boundary layer case. Coast. Engng 25 (3–4), 227–236.CrossRefGoogle Scholar
Foti, E. & Blondeaux, P. 1995 b Sea ripple formation: the heterogenous sediment case. Coast. Engng 25 (3–4), 237–253.CrossRefGoogle Scholar
Fredsøe, J. & Deigaard, R. 1992 Mechanics of coastal sediment transport. In Advanced Series on Ocean Engineering. World Scientific.Google Scholar
Gao, S., Collins, M. B., Lanckneus, J., De Moor, G. & Van Lancker, V. 1994 Grain-size trends associated with net sediment transport patterns: an example from the Belgian continental shelf. Mar. Geol. 121, 171–185.CrossRefGoogle Scholar
Gerkema, T. 2000 A linear stability analysis of tidally generated sand waves. J. Fluid Mech. 417, 303–322.CrossRefGoogle Scholar
Hirano, M. 1971 On river bed degradation with armoring. Trans. Japan Soc. of Civil Eng. 3 (2), 194–195.Google Scholar
Houthuys, R., Trentesaux, A. & De Wolf, P. 1994 Storm influences on a tidal sandbank's surface (Middelkerke Bank, southern North Sea). Mar. Geol. 121, 23–41.CrossRefGoogle Scholar
Hulscher, S. J. M. H. 1996 Tidal-induced large-scale regular bed form patterns in a three-dimensional shallow water model. Tidal-induced large-scale regular bed form patterns in a three-dimensional shallow water model 101 (C9), 20727–20744.Google Scholar
Hydrographer of the Navy. 1992 Spurn, East Anglia: associated British Ports, Thames estuary. Taunton, England, UK.Google Scholar
Kovacs, A. & Parker, G. 1994 A new vectorial bedload formulation and its application to the time evolution of straight river channels. J. Fluid Mech. 267, 153–183.CrossRefGoogle Scholar
Lanckneus, J., De Moor, G. & Stolk, A. 1994 Environmental setting, morphology and volumetric evolution of the Middelkerke Bank (southern North Sea). Mar. Geol. 121, 1–21.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. A. 345, 535–581.Google Scholar
Lyne, W. H. 1971. Unsteady viscous flow over a wavy wall. J. Fluid Mech. 50, 33–48.CrossRefGoogle Scholar
Meyer-Peter, E. & Muller, R. 1948 Formulas for bed-load transport. In Proceedings of the Second Congress I.A.H.R., Stockholm, pp. 39–64.Google Scholar
Parker, G. 2007 Transport of gravel and sediment mixtures. Private communication.CrossRefGoogle Scholar
Passchier, S. & Kleinhans, M. G. 2005 Observations of sand waves, megaripples and hummocks in the Dutch coastal area and their relation to currents and combined flow conditions. J. Geophys. Res. 110, F04S15, doi:10.1029/2004JF000215.Google Scholar
Rayleigh, L. 1884 On the circulation of air observed in Kundt's tubes, and on some allied acoustical problems. Phil. Trans. R. Soc. 175, 1–21.Google Scholar
Rijks Geologische Dienst. 1984 Geological Charts of the North Sea: Indefatigable, Flemish Bight, Ostend. Haarlem.Google Scholar
Roos, P. C., Hulscher, S. J. M. H., van der Meer, F., Van Dijk, T. A. G. P., Wientjes, I. G. M. & van den Berg, J. 2007 a Grain sorting over offshore sandwaves: observations and modelling. In Fifth IAHR Symp. on River, Coastal and Estuarine Morphodynamics, 17–21 September 2007, University of Twente, The Netherlands.Google Scholar
Roos, P. C., Wemmenhove, R., Hulscher, S. J. M. H., Hoeijmakers, H. W. M. & Kruyt, N. O. 2007 b Modeling the effect of non-uniform sediment on the dynamics of offshore tidal sand banks. J. Geophys. Res. 112, F02011, doi:10.1029/2005JF000376.Google Scholar
Schüttenhelm, R. T. E. 2002 Grain-sorting variability and crest stability of a North Sea sand wave in space and time. TNO Rep. 02-219-B. Netherlands Institute of Apllied Geosciences, Utrecht, The Netherlands.Google Scholar
Seminara, G. 1998 Stability and morphodynamics. Meccanica 33, 59–99.CrossRefGoogle Scholar
Soulsby, R. L. & Whitehouse, J. S. 2005 Prediction of ripple properties in shelf seas Tech. Rep. 154. Wallingford Ltd.Google Scholar
Stuart, J. T. 1966 Double boundary layers in oscillatory viscous flow. J. Fluid Mech. 24, 673–687.CrossRefGoogle Scholar
Swift, D. J. P., Parker, G., Lanfredi, N. W., Perillo, G. & Figge, K. 1978 Shoreface-connected sand ridges on American and European shelves: a comparison. Estur. Coast. Mar. Sci. 7, 257–273.CrossRefGoogle Scholar
Ten Brummelhuis, P. G. J., Gerritsen, H. & Van der Kaay, T. 1997 Sensitivity analysis and calibration of the orthogonal boundary-fitted coordinate model PROMISE for tidal flow: the use of adjoint modelling techniques. Res. Rep. Z2025. Delft Hydraulics, Delft, The Netherlands.Google Scholar
Terwindt, J. H. J. 1971 Sand waves in the Southern bight of the North Sea. Mar. Geology. 10, 51–67.CrossRefGoogle Scholar
Van Lancker, V. R. M. & Jacobs, P. 2000 The dynamical behaviour of shallow marine dunes. In International Workshop on Marine Sandwave Dynamics, 23–24 March (ed. Trentesaux, A. & Garlan, T.), University of Lille I.Google Scholar
Van Lancker, V. R. M. 1999 Sediment and morphodynamics of a siliciclastic near coastal area, in relation to hydrodynamical and meteorological conditions: Belgian continental shelf. PhD thesis, Gent University, Belgium.Google Scholar
Van Rijn, L. C. 1991 Sediment transport in combined waves and currents. In Proceedings of Euromech 262, Balkema.Google Scholar
van der Veen, H. H. 2008 Natural and human induced seabed evolution. PhD thesis, University of Twente, The Netherlands.Google Scholar
Vincent, C. E., Stolk, A. & Porter, C. F. C. 1998 Sand suspension and transport on the Middelkerke Bank (southern North Sea) by storms and tidal currents. Mar. Geol. 150, 113–129.CrossRefGoogle Scholar
Walgreen, M., De Swart, H. E. & Calvete, D. 2004 A model for grain-sorting over tidal sand ridges. Ocean Dyn. 54, 374–384.CrossRefGoogle Scholar