Skip to main content Accessibility help

Higher-order Bragg reflection of gravity surface waves by periodic beds

  • Elisabeth Guazzelli (a1), Vincent Rey (a2) and Max Belzons (a2)


Experiments are described which demonstrate higher-order Bragg resonant interactions between linear gravity waves and doubly sinusoidal beds. These higher-order effects, which include harmonic and subharmonic Bragg reflections, have been observed by making very precise measurements in a wave tank. Subharmonic reflection was found to be very large, even for small bottom undulation amplitudes. The experimental data are compared with the predictions of a numerical model based on the full potential theory of linear waves.



Hide All
Abramowitz, M. & Stegun A. 1965 Handbook of Mathematical Functions. Dover.
Baillard J. A., DeVries, J. & Kirby J. T. 1992 Considerations in using Bragg reflection for storm erosion protection. J. Waterway, Port, Coastal Ocean Engng 118, 6274.
Bailard J. A., DeVries J., Kirby, J. T. & Guza R. T. 1990 Bragg reflection breakwater: a new shore protection method? Proc. 22nd Coastal Engng Conf., New York, pp. 17021715. ASCE.
Belzons M., Guazzelli, E. & Parodi O. 1988 Gravity wave on a rough bottom: experimental evidence of one-dimensional localization. J. Fluid Mech. 186, 539558.
Belzons M., Rey, V. & Guazzelli E. 1991 Subharmonic Bragg resonance for surface water waves. Europhys, Lett. 16, 189194.
Benjamin T. B., Boczar-Karakiewicz, B. & Pritchard W. G. 1987 Reflection of water waves in a channel with corrugated bed. J. Fluid Mech. 185, 249274.
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, 165184.
Dalrymple, R. A. & Kirby J. T. 1986 Water waves over ripples. J. Waterway Port Coastal Ocean Engng Div. ASCE 112, 309319.
Davies A. G. 1982a The reflection of the wave energy by undulations of the seabed. Dyn. Atmos. Oceans 6, 207232.
Davies A. G. 1982b On the interaction between surface waves and undulations of the seabed. J. Mar. Res. 40, 331368.
Davies A. G., Guazzelli, E. & Belzons M. 1989 The propagation of long waves over an undulating bed Phys. Fluids A 1, 13311340.
Davies, A. G. & Heathershaw A. D. 1984 Surface wave propagation over sinusoidally varying topography. J. Fluid Mech. 144, 419443.
Devillard P., Dunlop, F. & Souillard B. 1988 Localization of gravity waves on a channel with random bottom. J. Fluid Mech. 186, 521538.
Guazzelli E. 1986 Deux études expérimentales du désordre en hydrodynamique physique: désordre spatial de structures convectives; effet du désordre sur la propagation d'ondes de gravité. Thèse d'Etat, Université de Provence, Marseille.
Hara, T. & Mei C. C. 1987 Bragg scattering of surface waves by periodic bars: theory and experiment. J. Fluid Mech. 178, 221241.
Heathershaw A. D. 1982 Seabed–wave resonance and sand bar growth. Nature 296, 343345.
Heathershaw, A. D. & Davies A. G. 1985 Resonant wave reflection by transverse bedforms and its relation to beaches and offshore bars. Mar. Geol. 62, 321338.
Jaggard, D. L. & Jordan A. K. 1984 Inversion theory for almost periodic media. Radio Sci. 19, 13331341.
Kirby J. T. 1986 A general wave equation for waves over rippled beds. J. Fluid Mech. 162, 171186.
Kirby J. T. 1989 Propagation of surface waves over undulating bed Phys. Fluids A 1, 18981899.
Kirby, J. T. & Anton J. P. 1990 Bragg reflection of waves by artificial bars. Proc. 22nd Coastal Engng Conf., New York, pp. 757768. ASCE
Kirby, J. T. & Dalrymple R. A. 1983 Propagation of obliquely incident water waves over a trench. J. Fluid Mech. 133, 4763.
Kittel C. 1976 Introduction to Solid State Physics, 5th Edn. Wiley.
Mattioli F. 1990 Resonant reflection of a series of submerged breakwaters. II Nuovo Cimento 13, 823833.
Mattioli F. 1991 Resonant reflection of surface waves by non-sinusoidal bottom undulations. Appl. Ocean Res. 13, 4953.
Mei C. C. 1983 The Applied Dynamics of Ocean Surface Waves, John Wiley.
Mei C. C. 1985 Resonant reflection of surface waves by periodic sandbars. J. Fluid Mech. 152, 315335.
Mei, C. C. & Black J. L. 1969 Scattering of surface waves by rectangular obstacle in waters of finite depth. J. Fluid Mech. 38, 499511.
Miles J. W. 1967 Surface scattering matrix for a shelf. J. Fluid Mech. 28, 755767.
Mitra, A. & Greenberg M. D. 1984 Slow interactions of gravity waves and corrugated seabed. Trans. ASME E: J. Appl. Mech. 51, 251255.
O'Hare, T. J. & Davies A. G. 1990 A laboratory study of sand bar evolution. J. Coastal Res. 6, 531544.
O'Hare, T. J. & Davies A. G. 1991 A new model for wave propagation over rapidly-varying bottom. Coastal Engng (submitted).
Rey V. 1991 Propagation d'ondes de gravité au dessus de fonds solides ou constitués de sédiments: application à l'étude d'interactions dynamiques ondes-sédiments. Thèse de l'Université de Provence, Marseille.
Rey V. 1992 Propagation and local behaviour of normal incident gravity waves over varying topography. Eur. J. Mech. B: Fluids 11, 213232.
Rey V., Belzons, M. & Guazzelli E. 1992 Propagation of surface gravity waves over a rectangular submerged bar. J. Fluid Mech. 235, 453479.
Rhines P. B. 1970 Wave propagation in a periodic medium with application to the ocean. Rev. Geophys. Space Phys. 8, 303319.
Short A. D. 1975 Multiple offshore bars and standing waves. J. Geophys. Res. 80, 38383840.
Smith, R. & Sprinks T. 1975 Scattering of surface waves by a conical island. J. Fluid Mech. 72, 373384.
Takano K. 1960 Effets d'un obstacle parallélépipédique sur la propagation de la houle. Houille Blanche 15, 247267.
Whitham G. B. 1974 Linear and Non Linear Waves. Wiley.
MathJax is a JavaScript display engine for mathematics. For more information see

Higher-order Bragg reflection of gravity surface waves by periodic beds

  • Elisabeth Guazzelli (a1), Vincent Rey (a2) and Max Belzons (a2)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed