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

Published online by Cambridge University Press:  26 April 2006

Elisabeth Guazzelli ,
Vincent Rey  and
Max Belzons
Elisabeth Guazzelli
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes, URA 857 du CNRS, ESPCI, 10 rue Vauquelin, 75231 Paris Cedex 05, France
Vincent Rey
Affiliation:
Département de Physique des Systèmes Désordonnés, SETT, URA 1168 du CNRS, Université de Provence, Centre de Saint-Jérôme, Case 161, 13397 Marseille Cedex 13, France
Max Belzons
Affiliation:
Département de Physique des Systèmes Désordonnés, SETT, URA 1168 du CNRS, Université de Provence, Centre de Saint-Jérôme, Case 161, 13397 Marseille Cedex 13, France
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Abstract

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 245 , December 1992 , pp. 301 - 317
Copyright
© 1992 Cambridge University Press

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References

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, 62–74.Google Scholar
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. 1702–1715. ASCE.
Belzons M., Guazzelli, E. & Parodi O. 1988 Gravity wave on a rough bottom: experimental evidence of one-dimensional localization. J. Fluid Mech. 186, 539–558.Google Scholar
Belzons M., Rey, V. & Guazzelli E. 1991 Subharmonic Bragg resonance for surface water waves. Europhys, Lett. 16, 189–194.Google Scholar
Benjamin T. B., Boczar-Karakiewicz, B. & Pritchard W. G. 1987 Reflection of water waves in a channel with corrugated bed. J. Fluid Mech. 185, 249–274.Google Scholar
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
Dalrymple, R. A. & Kirby J. T. 1986 Water waves over ripples. J. Waterway Port Coastal Ocean Engng Div. ASCE 112, 309–319.Google Scholar
Davies A. G. 1982a The reflection of the wave energy by undulations of the seabed. Dyn. Atmos. Oceans 6, 207–232.Google Scholar
Davies A. G. 1982b On the interaction between surface waves and undulations of the seabed. J. Mar. Res. 40, 331–368.Google Scholar
Davies A. G., Guazzelli, E. & Belzons M. 1989 The propagation of long waves over an undulating bed Phys. Fluids A 1, 1331–1340.Google Scholar
Davies, A. G. & Heathershaw A. D. 1984 Surface wave propagation over sinusoidally varying topography. J. Fluid Mech. 144, 419–443.Google Scholar
Devillard P., Dunlop, F. & Souillard B. 1988 Localization of gravity waves on a channel with random bottom. J. Fluid Mech. 186, 521–538.Google Scholar
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, 221–241.Google Scholar
Heathershaw A. D. 1982 Seabed–wave resonance and sand bar growth. Nature 296, 343–345.Google Scholar
Heathershaw, A. D. & Davies A. G. 1985 Resonant wave reflection by transverse bedforms and its relation to beaches and offshore bars. Mar. Geol. 62, 321–338.Google Scholar
Jaggard, D. L. & Jordan A. K. 1984 Inversion theory for almost periodic media. Radio Sci. 19, 1333–1341.Google Scholar
Kirby J. T. 1986 A general wave equation for waves over rippled beds. J. Fluid Mech. 162, 171–186.Google Scholar
Kirby J. T. 1989 Propagation of surface waves over undulating bed Phys. Fluids A 1, 1898–1899.Google Scholar
Kirby, J. T. & Anton J. P. 1990 Bragg reflection of waves by artificial bars. Proc. 22nd Coastal Engng Conf., New York, pp. 757–768. ASCEGoogle Scholar
Kirby, J. T. & Dalrymple R. A. 1983 Propagation of obliquely incident water waves over a trench. J. Fluid Mech. 133, 47–63.Google Scholar
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, 823–833.Google Scholar
Mattioli F. 1991 Resonant reflection of surface waves by non-sinusoidal bottom undulations. Appl. Ocean Res. 13, 49–53.Google Scholar
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, 315–335.Google Scholar
Mei, C. C. & Black J. L. 1969 Scattering of surface waves by rectangular obstacle in waters of finite depth. J. Fluid Mech. 38, 499–511.Google Scholar
Miles J. W. 1967 Surface scattering matrix for a shelf. J. Fluid Mech. 28, 755–767.Google Scholar
Mitra, A. & Greenberg M. D. 1984 Slow interactions of gravity waves and corrugated seabed. Trans. ASME E: J. Appl. Mech. 51, 251–255.Google Scholar
O'Hare, T. J. & Davies A. G. 1990 A laboratory study of sand bar evolution. J. Coastal Res. 6, 531–544.Google Scholar
O'Hare, T. J. & Davies A. G. 1991 A new model for wave propagation over rapidly-varying bottom. Coastal Engng (submitted).Google Scholar
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, 213–232.Google Scholar
Rey V., Belzons, M. & Guazzelli E. 1992 Propagation of surface gravity waves over a rectangular submerged bar. J. Fluid Mech. 235, 453–479.Google Scholar
Rhines P. B. 1970 Wave propagation in a periodic medium with application to the ocean. Rev. Geophys. Space Phys. 8, 303–319.Google Scholar
Short A. D. 1975 Multiple offshore bars and standing waves. J. Geophys. Res. 80, 3838–3840.Google Scholar
Smith, R. & Sprinks T. 1975 Scattering of surface waves by a conical island. J. Fluid Mech. 72, 373–384.Google Scholar
Takano K. 1960 Effets d'un obstacle parallélépipédique sur la propagation de la houle. Houille Blanche 15, 247–267.Google Scholar
Whitham G. B. 1974 Linear and Non Linear Waves. Wiley.