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Shoreface-connected ridges under the action of waves and currents

Published online by Cambridge University Press:  14 June 2007

EMILY M. LANE  and
JUAN M. RESTREPO
EMILY M. LANE
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095-1567, USA
JUAN M. RESTREPO
Affiliation:
Department of Mathematics and Department of Physics, University of Arizona, Tucson, AZ 85721, USA
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Abstract

Up-current-rotated, shoreface-connected ridges are found in various coastal areas around the world. An often-quoted conjecture is that these ridges form during storm conditions through free instabilities in the erodible bed. Under these conditions both waves and currents are expected to play a significant role in the hydrodynamics. Although some existing models have included the effects of waves parametrically in their bottom friction terms and sediment equations, the dynamical effects of wave–current interaction have not been explored. In this paper we begin to rectify this by considering the effects of wave–current interaction on the bed-form instabilities of a simple model. This raises the possibility of unsteady alongshore flows and questions about the roles of wave parameters and boundary conditions, which we address here. We show that the flow is stable under the wave forcing; however the waves do affect the bed-form instability. The main dynamical effect of the waves is in altering the shapes of the unstable modes. Under various conditions, however, waves may enhance or suppress the instability or introduce new unstable modes. They also affect the celerity of the ridges. In addition, we investigate the mechanisms whereby the waves affect the instability. We also show a potential problem with the parameterization in terms of wave orbital velocity.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 582 , 10 July 2007 , pp. 23 - 52
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Boyd, J. P. 1987 Orthogonal rational functions on a semi-infinite interval. J. Comput. Phys. 70, 63–88.CrossRefGoogle Scholar
Boyd, J. P. 1989 Chebyshev and Fourier Spectral Methods. Springer.CrossRefGoogle Scholar
Boyd, J. P. 1996 Traps and snares in eigenvalue calculations with applications to pseudospectral computations of ocean tides in a basin bounded by meridians. J. Comput. Phys. 126, 11–20.CrossRefGoogle Scholar
Boyd, J. P., Rangan, C. & Bucksbaum, P. H. 2003 Pseudospectral methods on a semi-infinite interval with application to the hydrogen atom: a comparison of the mapped Fourier-sine method with Laguerre series and rational Chebyshev expansions. J. Comput. Phys. 188, 56–74.CrossRefGoogle Scholar
Calvete, D., Falques, A., de Swart, H. E. & Dodd, N. 1999 Non-linear modeling of shoreface-connected sand ridges. In Proc. Coastal Sediments (ed. Kraus, N. C. & McDougal, W. G.), pp. 1123–1138. American Society of Civil Engineers.Google Scholar
Calvete, D., Falques, A., de Swart, H. E. & Walgreen, M. 2001 a Modelling the formation of shore connected sand ridges on storm dominated inner shelves. J. Fluid Mech. 441, 169–193.CrossRefGoogle Scholar
Calvete, D. & de Swart, H. E. 2003 A nonlinear model study on the long-term behaviour of shore-connected sand ridges. J. Geophys. Res. 108 (C5), 3169.Google Scholar
Calvete, D., de Swart, H. E. & Falques, A. 2002 Effect of depth dependent wave stirring on the final amplitude of shore-connected sand ridges. Continent. Shelf Res. 22, 2763–2776.CrossRefGoogle Scholar
Calvete, D., Walgreen, M., de Swart, H. E. & Falques, A. 2001 b A model for sand ridges on the shelf: Effect of tidal and steady currents. J. Geophys. Res. 106 (C5), 9311–9325.CrossRefGoogle Scholar
Csanady, G. T. 1982 Circulation in the Coastal Ocean. D. Reidel.CrossRefGoogle Scholar
Duane, D. B., Field, M. E., Miesberger, E. P. & Swift, D. J. P. 1972 Linear shoals on the Atlantic continental shelf, Florida to {Long Island. In Shelf Sediment Transport: Process and Pattern (ed. Swift, D. J. P., Duane, D. B. & Pikey, O. H.), pp. 447–498. Van Nostrand Reinhold.Google Scholar
Falques, A., Calvete, D. & Montoto, A. 1998 a Bed-flow instabilities of coastal currents. In Physics of Estuaries and Coastal Seas, pp. 417–424. A. A. Balkema.Google Scholar
Falques, A., Calvete, D., de Swart, H. E. & Dodd, N. 1998 b Morphodynamics of shoreface-connected ridges. In Coastal Engineering (ed. Dronkers, J. & Scheffers, M.), pp. 2851–2864. A. A. Balkema.Google Scholar
Huthnance, J. M. 1982 On the mechanism forming linear sand bars. Estuarine, Coast. Shelf Sci. 14, 79–99.CrossRefGoogle Scholar
Iranzo, V. & Falques, A. 1992 Some spectral approximations for differential equations in unbounded domains. Computer Method. Appl. Mech. Engng 98, 105–126.CrossRefGoogle Scholar
Lane, E. M., Restrepo, J. M. & McWilliams, J. C. 2007 Wave-current interaction: A comparison of radiation-stress and vortex-force representations. J. Phys. Oceanogr. (in press).Google Scholar
Lentz, S. J. 2001 The influence of stratification on the wind-driven cross-shelf circulation over the North Carolina shelf. J. Phys. Oceanogr. 31, 2749–2760.2.0.CO;2>CrossRefGoogle Scholar
McClennen, C. E. & McMaster, R. L. 1971 Probable Holocene transgressive effects on the geomorphic features of the continental shelf off {New Jersey}, {United States}. Mar. Sediments 7, 67–72.Google Scholar
McWilliams, J. C. & Restrepo, J. M. 1999 The wave-driven ocean circulation. J. Phys. Oceanogr. 29, 2523–2540.2.0.CO;2>CrossRefGoogle Scholar
McWilliams, J. C., Restrepo, J. M. & Lane, E. M. 2004 Interaction of waves and currents in coastal waters: An asymptotic theory for the interaction of waves and currents in shallow coastal waters. J. Fluid Mech. 511, 135–178.CrossRefGoogle Scholar
van der Meene, J. W. H. 1996 Sediment structures of combined flow deposits from shoreface-connected rodgs along the central Dutch coast. Mar. Geol. 131, 151–175.CrossRefGoogle Scholar
Mei, C. C. 1989 The Applied Dynamics of Ocean Surface Waves. World Scientific.Google Scholar
Off, T. 1960 Rhythmic sand bodies caused by tidal currents. Bull. Am. Assoc. Petrol. Geologists 47, 324–341.Google Scholar
Parker, G., Lanfredi, N. W. & Swift, D. J. P. 1982 Seafloor response to flow in the southern hemisphere sand-ridge field: Argentina inner shelf. Sediment Geol. 33, 195–216.CrossRefGoogle Scholar
Restrepo, J. M. 2001 Sediment dynamics and wave–current interactions. Continent. Shelf Res. 21, 1331–1360.CrossRefGoogle Scholar
Swift, D. J. P., Duane, D. B. & McKinney, T. F. 1973 Ridge and swale topography of the Middle Atlantic Bight, North America: secular response to the Holocene hydraulic regime. Mar. Geol. 15, 227–247.CrossRefGoogle Scholar
Swift, D. J. P., Holliday, B., Avignone, N. & Schideler, G. 1972 Anatomy of a shoreface ridge system, False Cape, Virginia. Mar. Geol. 12, 59–84.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. Estuarine Coast. Mar. Sci. 7, 257–273.CrossRefGoogle Scholar
Trowbridge, J. H. 1995 A mechanism for the formation and maintenance of shore-oblique sand ridges on storm dominated shelves. J. Geophys. Res. 100 (C8), 16071–16086.CrossRefGoogle Scholar
Walgreen, M., Calvete, D. & de Swart, H. E. 2002 Growth of large-scale bed forms due to storm driven and tidal currents: a model approach. Continent. Shelf Res. 22, 2777–2793.CrossRefGoogle Scholar
Walgreen, M., de Swart, H. E. & Calvete, D. 2003 Effect of grain size sorting on the formation of shoreface-connected sand ridges. J. Geophys. Res. 108 (C3), 3063S.Google Scholar
Walgreen, M., de Swart, H. E. & Calvete, D. 2004 A model for grain-size sorting over tidal sand ridges. Ocean Dyn. 54, 374–384.CrossRefGoogle Scholar