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Gravity waves on a rough bottom: experimental evidence of one-dimensional localization

Published online by Cambridge University Press:  21 April 2006

Max Belzons ,
Elisabeth Guazzelli  and
Olivier Parodi
Max Belzons
Affiliation:
Département de Physique des Systèmes Désordonnés, UA 857 du CNRS, Université de Provence, Centre de Saint-Jérome, F-13397 Marseille CEDEX 13, France
Elisabeth Guazzelli
Affiliation:
Département de Physique des Systèmes Désordonnés, UA 857 du CNRS, Université de Provence, Centre de Saint-Jérome, F-13397 Marseille CEDEX 13, France
Olivier Parodi
Affiliation:
Département de Physique des Systèmes Désordonnés, UA 857 du CNRS, Université de Provence, Centre de Saint-Jérome, F-13397 Marseille CEDEX 13, France
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Abstract

We present experimental evidence of the localization of linear gravity waves on a rough (i.e. random) bottom in a one-dimensional channel. The localization phenomenon is observed through very precise measurements in a wave tank. Viscous dissipation and rough-bed finite-size effects are examined. The experimental estimation of the localization lengths are compared with the theoretical predictions of Devillard, Dunlop & Souillard (1988). Finally, the resonant modes due to the disorder are directly observed for the first time.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 186 , January 1988 , pp. 539 - 558
Copyright
© 1988 Cambridge University Press

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References

Akkermans, E. & Maynard, R. 1984 Chains of random impedance. J. Phys. Paris 45, 1549–1557.Google Scholar
Azbel, M. Ya. 1983 Resonance tunneling and localization spectroscopy. Solid State Commun. 45, 527–530.Google Scholar
Baluni, V. & Willemsen, J. 1985 Transmission of acoustic waves in a random layered medium. Phys. Rev. A 31, 3358–3363.Google Scholar
Belzons, M., Devillard, P., Dunlop, F., Guazzelli, E., Parodi, O. & Souillard, B. 1987 Localization of gravity waves on a rough bottom: theory and experiment. Europhys. Lett. (to appear).Google Scholar
Borland, R. 1963 The nature of the electronic states in disordered one-dimensional systems. Proc. R. Soc. Lond. A 274, 529–545.Google Scholar
Bouchaud, E. & Daoud, M. 1986 Reflection of light by a random layered system. J. Phys. Paris 47, 1467–1475.Google Scholar
Cohen, S. M. & Matcha, J. 1985 Localization of third sound by a disordered substrate. Phys. Rev. Lett. 54, 2242–2245.Google Scholar
Condat, C. A. & Kirkpatrick, T. R. 1986 Localization and resonant transmission of third-sound waves on a random substrate. Phys. Rev. B33, 3102–3114.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 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 on the seabed. J. Mar. Res. 40, 331–368.Google Scholar
Davies, A. G. & Heathershaw, A. D. 1983 Surface wave propagation over sinusoidally varying topography: theory and observation. Inst. Oceanogr. Sci. Rep. 159.
Davies, A. G. & Heathershaw, A. D. 1984 Surface-wave propagation over sinusoidally varying topography. J. Fluid Mech. 144, 419–443.Google Scholar
Delyon, F., Lévy, Y.-E. & Souillard, B. 1985 Approach ‘a la Borland’ to multi-dimensional localization. Phys. Rev. Lett. 55, 618–621.Google Scholar
Dépollier, C., Kergomard, X. & Laloe, F. 1986 Localisation d'Anderson des ondes dans les réseaux acoustiques unidimensionnels aléatoires. Ann. Phys. 11, 457–492.Google Scholar
Devillard, P., Dunlop, F. & Souillard, B. 1988 Localization of gravity waves on a channel with a random bottom. J. Fluid Mech. 186, 521–538.Google Scholar
Escande, D. & Souillard, B. 1984 Localization of waves in a fluctating plasma. Phys. Rev. Lett. 52, 1296–1299.Google Scholar
Flesia, C., Johnston, R. & Kunz, H. 1987 Strong localization of classical waves: a numerical study. Europhys. Lett. 3, 497–502.Google Scholar
Guazzelli, E. 1986 Deux études experimentales 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.
Guazzelli, E., Guyon, E. & Souillard, B. 1983 On the localization of shallow water waves by a random bottom. J. Phys. Paris 44, L837–841.Google Scholar
Heathershaw, A. D. 1982 Seabed-wave resonance and sand bar growth. Nature 296, 343–345.Google Scholar
Hebrard, P. & Toulouse, G. 1983 Etude du mouvement de la houle. Rapport final 2148. DERMES ONERA-CERT-Toulouse.
Hodges, C. H. 1982 Confinement of vibration by structural irregularity. J. Sound Vib. 82, 411–424.Google Scholar
Hodges, C. H. & Woodhouse, J. 1983 Vibration isolation from irregularity in a nearly periodic structure: theory and measurements. J. Acoust. Soc. Am. 74, 894–905.Google Scholar
Ishii, K. 1973 Localization of eigenstate and transport phenomena in the one-dimensional disordered system. Prog. Theor. Phys. Suppl. 53, 77–138.Google Scholar
Kittel, C. 1983 Physique de l'Etat Solide, 5ème éd. Dunod Université.
Kirby, J. T. 1986 A general wave equation for waves over rippled beds. J. Fluid Mech. 162, 171–186.Google Scholar
Kirkpatrick, T. R. 1985 Localization of acoustic waves. Phys. Rev. B31, 5746–5755.Google Scholar
Lee, P. A. & Ramakrishnan, T. V. 1985 Disordered electronic systems. Rev. Mod. Phys. 57, 287–335.Google Scholar
Mcgoldrick, L. F. 1968 Long waves over a wavy bottom. University of Chicago, Department of Geophysical Sciences, ONR Ocean Science and Technology Group, Tech. Rep. 1, 67 pp.
Mei, C. C. 1983 The Applied Dynamics of Ocean Surface Waves. Wiley Interscience.
Mei, C. C. 1985 Resonant reflection of surface water waves by periodic sandbars. J. Fluid Mech. 152, 315–335.Google Scholar
Miles, J. W. 1967 Surface-wave scattering matrix for a shelf. J. Fluid Mech. 28, 755–767.Google Scholar
Mitra, A. & Greenberg, M. D. 1984 Slow interaction of gravity waves and a corrugated seabed. Trans. ASME E: J. Appl. Mech. 51, 251–255.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
Rhines, P. B. & Bretherton, F. P. 1973 Topographic Rossby waves in a rough-bottomed ocean. J. Fluid Mech. 61, 583–607.Google Scholar
Souillard, B. 1987 Waves and electrons in inhomogeneous media. In Chance and Matter, Proc. Les Houches (ed. J. Souletie, J. Vannimenus & R. Stora). North-Holland.
Thouless, D. J. 1974 Electrons in disordered systems and the theory of localization. Phys. Rep. 13, 93–142.Google Scholar
Thouless, D. J. 1982 Lower dimensionality and localization. Physica 109, 110B, 1523–1530.Google Scholar
Whitham, G. B. 1974 Linear and Non Linear Waves. Wiley.