Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 15 6 2008 10.5194/npg-15-943-2008 http://www.nonlin-processes-geophys.net/15/943/2008/ http://www.nonlin-processes-geophys.net/15/943/2008/npg-15-943-2008.html http://www.nonlin-processes-geophys.net/15/943/2008/npg-15-943-2008.pdf 943 955 2008-12-08 Patch behaviour and predictability properties of modelled finite-amplitude sand ridges on the inner shelf N. C. Vis-Star H. E. de Swart h.e.deswart@uu.nl D. Calvete Institute for Marine and Atmospheric research, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands Dept. de Física Aplicada, Universitat Politècnica de Catalunya, Campus Nord, Jordi Girona, 08034 Barcelona, Spain The long-term evolution of shoreface-connected sand ridges is investigated with a nonlinear spectral model which governs the dynamics of waves, currents, sediment transport and the bed level on the inner shelf. Wave variables are calculated with a shoaling-refraction model instead of using a parameterisation. The spectral model describes the time evolution of amplitudes of known eigenmodes of the linearised system. Bottom pattern formation occurs if the transverse bottom slope of the inner shelf, β, exceeds a critical value βc. For fixed model parameters the sensitivity of the properties of modelled sand ridges to changes in the number (N−1) of resolved subharmonics (of the initially fastest growing mode) is investigated. For any N the model shows the growth and subsequent saturation of the height of the sand ridges. The saturation time scale is several thousands of years, which suggests that observed sand ridges have not reached their saturated stage yet. The migration speed of the ridges and the average longshore spacing between successive crests in the saturated state differ from those in the initial state. Analysis of the potential energy balance of the ridges reveals that bed slope-induced sediment transport is crucial for the saturation process. In the transient stage the shoreface-connected ridges occur in patches. The overall characteristics of the bedforms (saturation time, final maximum height, average longshore spacing, migration speed) hardly vary with N. However, individual time series of modal amplitudes and bottom patterns strongly depend on N, thereby implying that the detailed evolution of sand ridges can only be predicted over a limited time interval. Additional experiments show that the critical bed slope βc increases with larger offshore angles of wave incidence, larger offshore wave heights and longer wave periods, and that the corresponding maximum height of the ridges decreases whilst the saturation time increases. Ashton, A D. and Murray, A B.: High-angle wave instability and emergent shoreline shapes: 1. Modeling of sand waves, flying spits, and capes, J. Geophys. Res., 111, 1–19, F04011, \doi10.1029/2005JF000422, 2006. Bruun, P.: Coast erosion and the development of beach profiles, Technical Memorandum, vol. 44, Beach Erosion Board, Corps of Engineers, 1954. Bruun, P.: Sea-level rise as a cause of shore erosion, in: Proceedings of the American Society of Civil Engineers, Journal of the Waterways and Harbors Division, 88, 117–130, 1962. Calvete, D. and De Swart, H E.: A nonlinear model study on the long-term behavior of shore face-connected sand ridges, J. Geophys. Res., 108, 3169, \doi10.1029/2001JC001091, 2003. Calvete, D., Falqués, A., De Swart, H E., and Walgreen, M.: Modelling the formation of shoreface-connected sand ridges on storm-dominated inner shelves, J. Fluid Mech., 441, 169–193, 2001a. Coco, G., Burnet, T K., Werner, B T., and Elgar, S.: The role of tides in beach cusp development, J. Geophys. Res., 109, C04011, \doi10.1029/2003JC002154, 2004. Cooper, J. A G. and Pilkey, O H.: Sea-level rise and shoreline retreat: time to abandon the Bruun Rule, Global and planetary change, 43, 157–171, 2004. Duane, D B., Field, M E., Miesberger, E P., Swift, D. J P., and Williams, S J.: Linear shoals on the Atlantic continental shelf, Florida to Long Island, in: Shelf Sediment Transport: Process and Pattern, edited by: Swift, D. J P., Duane, D B., and Pilkey, O H., 447–498, Dowden, Hutchinson and Ross, Stroudsburg, Pa., 1972. Dyer, K R. and Huntley, D A.: The origin, classification and modelling of sand banks and ridges, Cont. Shelf Res., 19, 1285–1330, 1999. Garnier, R., Calvete, D., Falqués, A., and Caballeria, M.: Generation and nonlinear evolution of shore-oblique/transverse sand bars, J. Fluid Mech., 567, 327–360, 2006. Harrison, S E., Locker, S D., Hine, A C., Edwards, J H., Naar, D F., and Twichell, D C.: Sediment-starved sand ridges on a mixed carbonate/siliciclastic inner shelf off west-central Florida, Mar. Geol., 200, 171–194, 2003. Huntley, D A., Coco, G., Bryan, K R., and Murray, A B.: Influence of "defects" on sorted bedform dynamics, Geophys. Res. Lett., 35, L02601, \doi10.1029/2007GL030512, 2008. Karniadakis, G E., Israeli, M., and Orszag, S A.: High-order splitting methods for the incompressible Navier-Stokes equations, J. Comput. Phys., 97, 414–443, 1991. Lane, E M. and Restrepo, J M.: Shoreface-connected ridges under the action of waves and currents, J. Fluid. Mech., 582, 23–52, \doi10.1017/S0022112007005794, 2007. Masetti, R., Fagherazzi, S., and Montanari, A.: Application of a barrier island translation model to the millennial-scale evolution of Sand Key, Florida, Cont. Shelf Res., 28, 1116–1126, 2008. McBride, R A. and Moslow, T F.: Origin, evolution, and distribution of shoreface sand ridges, Atlantic inner shelf, USA, Mar. Geol., 97, 57–85, 1991. Murray, A B. and Thieler, E R.: A new hypothesis and exploratory model for the formation of large-scale inner-shelf sediment sorting and "rippled scour depressions", Cont. Shelf Res., 24, 295–315, 2004. Swift, D. J P. and Field, M E.: Evolution of a classic sand ridge field: Maryland sector, North American inner shelf, Sedimentology, 28, 461–482, 1981. Trowbridge, J H.: A mechanism for the formation and maintenance of the shore oblique sand ridges on storm-dominated shelves, J. Geophys. Res., 100(C8), 16 071–16 086, 1995. Van de Meene, J. W H. and Van Rijn, L C.: The shoreface-connected ridges along the central Dutch coast. Part 1: field observations, Cont. Shelf Res., 20, 2295–2323, 2000. Vis-Star, N C., De Swart, H E., and Calvete, D.: Effect of wave-topography interactions on the formation of sand ridges on the shelf, J. Geophys. Res., 112, C06012, \doi10.1029/2006JC003844, 2007. Vis-Star, N C., De Swart, H E., and Calvete, D.: Finite amplitude dynamics of shoreface-connected ridges: Role of waves, in: River, Coastal and Estuarine Modeling, edited by: Dohmen-Janssen, M. and Hulscher, S. J. M H., 691–698, Taylor & Francis, 2008.