Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T06:50:54.161Z Has data issue: false hasContentIssue false
  • English
  • Français

On beach cusp formation

Published online by Cambridge University Press:  01 February 2008

NICHOLAS DODD ,
ADAM M. STOKER ,
DANIEL CALVETE  and
ANURAK SRIARIYAWAT
NICHOLAS DODD
Affiliation:
School of Civil Engineering, University of Nottingham, Nottingham, NG7 2RD, UK
ADAM M. STOKER
Affiliation:
School of Civil Engineering, University of Nottingham, Nottingham, NG7 2RD, UK
DANIEL CALVETE
Affiliation:
Dept. de Fisica Aplicada, Univeristat Politecnica de Catalunya, Barcelona, Spain
ANURAK SRIARIYAWAT
Affiliation:
School of Civil Engineering, University of Nottingham, Nottingham, NG7 2RD, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

A system of shallow water equations and a bed evolution equation are used to examine the evolution of perturbations on an erodible, initially plane beach subject to normal wave incidence. Both a permeable (under Darcy's law) and an impermeable beach are considered. It is found that alongshore-periodic morphological features reminiscent of swash beach cusps form after a number of incident wave periods on both beaches. On the permeable (impermeable) beach these patterns are accretional (erosional). In both cases flow is ‘horn divergent’. Spacings of the cusps are consistent with observations, and are close to those provided by a standing synchronous linear edge wave. An analysis of the processes leading to bed change is presented. Two physical mechanisms are identified: concentration gradient and flow divergence, which are dominant in the lower and upper swash respectively, and their difference over a wave cycle leads to erosion or deposition on an impermeable beach. Infiltration enters this balance in the upper swash. A bed wave of elevation is shown to advance up the beach at the tip of the uprush, with a smaller wave of depression on the backwash. It is found that cusp horns can grow by a positive feedback mechanism stemming from decreased (increased) backwash on positive (negative) bed perturbations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 597 , 25 February 2008 , pp. 145 - 169
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Baldock, T. E. & Holmes, P. 1999 Simulation and prediction of swash oscillations on a steep beach. Coastal Engng 36, 219–242.CrossRefGoogle Scholar
Butt, T., Russell, P., Puleo, J., Miles, J. & Masselink, G. 2004 The influence of bore turbulence on sediment transport in swash and inner surf zones. Continent. Shelf Res. 24, 757–771.CrossRefGoogle Scholar
Calvete, D., Dodd, N., Falques, A. & Van Leeuwen, S. M. 2005 Morphological development of rip channel systems: normal and near normal wave incidence. J. Geophys. Res. 110 (C10), C10007, doi:10.1029/2004JC002803.CrossRefGoogle Scholar
Chow, V. T., Maidment, D. R. & Mays, L. W. 1988 Applied Hydrology. McGraw-Hill.Google Scholar
Ciriano, Y., Coco, G., Bryan, K. & Elgar, S. 2005 Field observations of swash zone infrgravity motions and beach cusp evolution. J. Geophys. Res. 110 (C02018), doi:10.1029/2004JC002485.CrossRefGoogle Scholar
Coco, G., Burnet, T. K., Werner, B. T. & Elgar, S. 2003 Test of self-organization in beach cusp formation. J. Geophys. Res. 108 (C3) (3101), doi:10.1029/2002JC001492.CrossRefGoogle Scholar
Coco, G., Huntley, D. A. & O'Hare, T. J. 2000 Investigation into a self-organization model for beach cusp formation. J. Geophys. Res. 105 (C9), 21991–22002.CrossRefGoogle Scholar
Coco, G., O'Hare, T. J. & Huntley, D. A. 1999 Beach cusps: A comparison of data and theories for their formation. J. Coastal Res. 15, 741–749.Google Scholar
Dicker, D. 1969 Transient free surface flow in porous media. In Flow through Porous Media (ed. DeWiest, R. J. M.), pp. 293–330. Academic.Google Scholar
Dyer, K. R. 1986 Estuarine and Coastal Sediment Dynamics. Wiley.Google Scholar
Falqués, A., Coco, G. & Huntley, D. A. 2000 A mechanism for the generation of wave driven rhythmic patterns in the surf zone. J. Geophys. Res. 105 (C10), 24071–24087.CrossRefGoogle Scholar
Guza, R. T. & Bowen, A. J. 1981 On the amplitude of beach cusps. J. Geophys. Res. 86, 4125–4132.CrossRefGoogle Scholar
Guza, R. T. & Inman, D. L. 1975 Edge waves and beach cusps. J Geophys. Res 80, 2997–3012.CrossRefGoogle Scholar
Hsu, T. & Raubenheimer, B. 2006 A numerical and field study on inner-surf and swash sediment transport. Continent. Shelf Res. 26, 589–598.CrossRefGoogle Scholar
Hubbard, M. E. & Dodd, N. 2002 A 2-d numerical model of wave run-up and overtopping. Coastal Engng 47 (1) , 1–26.CrossRefGoogle Scholar
Hudson, J., Damgaard, J. S., Dodd, N., Cooper, A. J. & Chesher, T. J. 2005 Approaches to 1d morphodynamical modelling in coastal engineering. Coastal Engng 52 (8), 691–707.CrossRefGoogle Scholar
Hudson, J. & Sweby, P. K. 2003 Formulations for numerically approximating hyperbolic systems governing sediment transport. J. Sci. Comp. 19, 225–252.CrossRefGoogle Scholar
Inman, D. L. & Guza, R. T. 1982 The origin of swash cusps on beaches. Mar. Geol. 49, 133–148.CrossRefGoogle Scholar
Kaneko, A. 1983 A numerical experiment on nearshore circulation in standing edge waves. Coastal Engng 7, 271–284.CrossRefGoogle Scholar
Karambas, T. V. 2003 Modelling of infiltration-exfiltration effects of cross-shore sediment transport in the swash zone. Coastal Engng J. 45 (1), 63–82.CrossRefGoogle Scholar
Komar, P. D. & Holman, R. A. 1986 Coastal processes and the development of shoreline erosion. Annu. Rev. Earth Planet. Sci. 14, 237–265.CrossRefGoogle Scholar
Masselink, G. & Li, L. 2001 The role of swash infiltration in determining the beachface gradient: a numerical study. Mar. Geol. 176, 139–156.CrossRefGoogle Scholar
Masselink, G. & Pattiaratchi, C. B. 1998 Morphological evolution of beach cusps and associated swash circulation. Mar. Geol. 146, 93–113.CrossRefGoogle Scholar
Masselink, G., Russell, P., Coco, G. & Huntley, D. 2004 Test of edge wave forcing during formation of rhythmic beach morphology. J. Geophys. Res. 109 (C06003), doi:10.1029/2004JC002339.CrossRefGoogle Scholar
Mei, C. C. 1990 The Applied Dynamics of Ocean Surface Waves, 2nd edn. World Scientific.Google Scholar
Packwood, A. R. 1983 The influence of beach porosity on wave uprush and backwash. Coastal Engng 7 (1), 29–40.CrossRefGoogle Scholar
Packwood, A. R. & Peregrine, D. H. 1980 The propagation of solitary waves and bores over a porous bed. Coastal Engng 3, 221–242.CrossRefGoogle Scholar
Peregrine, D. H. & Williams, S. M. 2001 Swash overtopping a truncated beach. J. Fluid Mech. 440, 391–399.CrossRefGoogle Scholar
Pritchard, D. & Hogg, A. J. 2005 On the transport of suspended sediment by a swash event on a plane beach. Coastal Engng 52, 1–23.CrossRefGoogle Scholar
Sallenger, A. 1979 Beach-cusp formation. Mar. Geol. 29, 23–37.CrossRefGoogle Scholar
Shen, M. C. & Meyer, R. E. 1963 Climb of a bore on a beach. Part 2. Non-uniform beach slope. J. Fluid Mech. 16, 108–112.CrossRefGoogle Scholar
Werner, B. T. & Fink, T. M. 1993 Beach cusps as self-organized patterns. Science 260, 968–971.CrossRefGoogle ScholarPubMed