Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2025-01-03T23:25:00.033Z Has data issue: false hasContentIssue false
  • English
  • Français

Resonant reflection of surface water waves by periodic sandbars

Published online by Cambridge University Press:  20 April 2006

Chiang C. Mei
Chiang C. Mei
Affiliation:
Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
Get access Rights & Permissions [Opens in a new window]

Abstract

One of the possible mechanisms of forming offshore sandbars parallel to a coast is the wave-induced mass transport in the boundary layer near the sea bottom. For this mechanism to be effective, sufficient reflection must be present so that the waves are partially standing. The main part of this paper is to explain a theory that strong reflection can be induced by the sandbars themselves, once the so-called Bragg resonance condition is met. For constant mean depth and simple harmonic waves this resonance has been studied by Davies (1982), whose theory, is however, limited to weak reflection and fails at resonance. Comparison of the strong reflection theory with Heathershaw's (1982) experiments is made. Furthermore, if the incident waves are slightly detuned or slowly modulated in time, the scattering process is found to depend critically on whether the modulational frequency lies above or below a threshold frequency. The effects of mean beach slope are also studied. In addition, it is found for periodically modulated wave groups that nonlinear effects can radiate long waves over the bars far beyond the reach of the short waves themselves. Finally it is argued that the breakpoint bar of ordinary size formed by plunging breakers can provide enough reflection to initiate the first few bars, thereby setting the stage for resonant reflection for more bars.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 152 , March 1985 , pp. 315 - 335
Copyright
© 1985 Cambridge University Press

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

Carter, T. G., Liu, P. L-F. & Mei, C. C. 1973 Mass transport by waves and offshore sand bedforms. J. Waterways, Harbours, Coastal Engng Div. ASCE 99, 165–184.Google Scholar
Craik, A. D. D. & Adam, J. A. 1978 Evolution in space and time of resonant wave triads. Proc. R. Soc. Lond. A 363, 243–255.Google Scholar
Davies, A. G. 1982 The reflection of wave energy by undulations on the seabed. Dyn. Atmos. Oceans 6, 207–232.Google Scholar
Dolan, T. J. 1983 Wave mechanics for the formation of multiple longshore bars with emphasis on the Chesapeake Bay. M.S. thesis, Civil Engineering, University of Delaware.
Evans, O. F. 1940 The low and ball of the eastern shore of Lake Michigan. J. Geol. 48, 476–511.Google Scholar
Heathershaw, A. D. 1982 Seabed-wave resonance and sandbar growth. Nature 296, 343–345.Google Scholar
Herbich, J. B., Murphy, H. D. & Van Weele, B. 1965 Scour of flat sand beaches due to wave action in front of sea walls. Coastal Engineering: Santa Barbara Specialty Conf., ASCE, pp. 705–726.
Johns, B. 1970 On the mass transport induced by oscillatory flow in a turbulent boundary layer. J. Fluid Mech. 43, 177–185.Google Scholar
Keulegan, G. H. 1948 An experimental study of submarine sandbars. Beach Erosion Board Tech. Rep. 3, U.S. Army Corps Engrs. Reprinted in Schwarz, M. L. (ed.) 1972 Spits and Bars. Dowden, Hutchinson & Ross.Google Scholar
Kindle, E. M. 1936 Notes on shallow water sand structures. J. Geol. 44, 861–869.Google Scholar
Lau, J. & Travis, B. 1973 Slowly varying Stokes waves and submarine longshore bars. J. Geophys. Res. 78, 4489–4498.Google Scholar
Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. A 345, 535–581.Google Scholar
Longuet-Higgins, M. S. 1958 The mechanics of the boundary layer near the bottom in a progressive wave. In Proc. 6th Conf. Coastal Engineering, pp. 184–193.
Mcgoldrick, L. F. 1968 Long waves over wavy bottoms. Office Nav. Res. Ocean Sci. Tech. Group Tech. Rep. 1.Google Scholar
Mei, C. C. 1983 Applied Dynamics of Ocean Surface Waves. Wiley-Interscience.
Mei, C. C. & Benmoussa, C. 1984 Long waves induced by short-wave groups over an uneven bottom. J. Fluid Mech. 139, 219–235.Google Scholar
Mitra, A. & Greenberg, M. D. 1984 Slow interaction of gravity waves and a corrugated seabed. Trans. ASME E: J. Appl. Mech. 51, 251–255Google Scholar
Nielsen, P. 1979 Some basic concepts of wave sediment transport. Tech. Univ. Denmark, Inst. Hydrodyn. Hydraul. Engng Ser. Paper 20.
Pinsker, Z. G. 1978 Dynamical Scattering of X-rays in Crystals. Springer.
Rhines, P. B. & Bretherton, F. P. 1973 Topographic Rossby waves in a rough-bottomed ocean. J. Fluid Mech. 61, 583–607.Google Scholar
Saylor, J. H. & Hands, E. B. 1970 Properties of longshore bars in the Great Lakes. In Proc. 12th Conf. Coastal Engineering, vol. 2, pp. 839–853.
Sheppard, F. P. 1950 Longshore bars and longshore troughs. Beach Erosion Board Tech. Memo. 15, Us Army Corps Engrs. Reprinted in Schwarz, M. L. (ed.) 1972 Spits and Bars. Dowden, Hutchinson & Ross.
Short, A. D. 1975 Multiple offshore bars along the Alaskan Arctic Coast. J. Geol. 83, 209–211.Google Scholar
Tagaki, S. 1969 A dynamic theory of diffraction for a deformed crystal. J. Phys. Soc. Japan 27, 1239–1253.Google Scholar
Zenkovich, V. P. 1967 Processes of Coastal Development, pp. 219–236. Interscience.