Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-23T12:20:13.381Z Has data issue: false hasContentIssue false
  • English
  • Français

Graded resonator arrays for spatial frequency separation and amplification of water waves

Published online by Cambridge University Press:  12 September 2018

Luke G. Bennetts Open the ORCID record for Luke G. Bennetts [Opens in a new window] ,
Malte A. Peter  and
Richard V. Craster
Luke G. Bennetts*
Affiliation:
School of Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, Australia
Malte A. Peter
Affiliation:
Institute of Mathematics, University of Augsburg, 86135 Augsburg, Germany Augsburg Centre for Innovative Technologies, University of Augsburg, 86135 Augsburg, Germany
Richard V. Craster
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A structure capable of substantially amplifying water waves over a broad range of frequencies at selected locations is proposed. The structure consists of a small number of C-shaped cylinders in a line array, with the cylinder properties graded along the array. Using linear potential-flow theory, it is shown that the energy carried by a plane incident wave is amplified within specified cylinders for wavelengths comparable to the array length and for a range of incident directions. Transfer-matrix analysis is used to attribute the large amplifications to excitation of local Rayleigh–Bloch waves and gradual slowing down of their group velocity along the array.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave scattering Waves/Free-surface Flows: Waves/Free-surface Flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 854 , 10 November 2018 , R4
Check for updates
Copyright
© 2018 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

Arnold, J. M. & Felsen, L. B. 1983 Rays and local modes in a wedge-shaped ocean. J. Acoust. Soc. Am. 73, 1105–1119.Google Scholar
Bennetts, L. G., Peter, M. A. & Montiel, F. 2017 Localisation of Rayleigh–Bloch waves and damping of resonant loads on arrays of vertical cylinders. J. Fluid Mech. 813, 508–527.Google Scholar
Bennetts, L. G. & Squire, V. A. 2009 Wave scattering by multiple rows of circular ice floes. J. Fluid Mech. 639, 213–238.Google Scholar
Brûlé, S., Javelaud, E. H., Enoch, S. & Guenneau, S. 2014 Experiments on seismic metamaterials: molding surface waves. Phys. Rev. Lett. 112, 133901.Google Scholar
Cebrecos, A., Picó, R., Sánchez-Morcillo, V. J., Staliunas, K., Romero-García, V. & Garcia-Raffi, L. M. 2014 Enhancement of sound by soft reflections in exponentially chirped crystals. AIP Adv. 4, 124402.Google Scholar
Dupont, G., Remy, F., Kimmoun, O., Molin, B., Guenneau, S. & Enoch, S. 2017 Type of dike using C-shaped vertical cylinders. Phys. Rev. B 96 (18), 180302.Google Scholar
Evans, D. V. & Porter, R. 1999 Trapping and near-trapping by arrays of cylinders in waves. J. Engng Maths 35, 149–179.Google Scholar
Falnes, J. 1980 Radiation impedance matrix and optimum power absorption for interacting oscillators in surface waves. Appl. Ocean Res. 2 (2), 75–80.Google Scholar
Faltinsen, O. M. 1990 Wave loads on offshore structures. Annu. Rev. Fluid Mech. 22, 35–56.Google Scholar
Göteman, M. 2017 Wave energy parks with point-absorbers of different dimensions. J. Fluids Struct. 74, 142–157.Google Scholar
Hu, X., Chan, C. T., Ho, K. M. & Zi, J. 2011 Negative effective gravity in water waves by periodic resonator arrays. Phys. Rev. Lett. 106 (17), 1–4.Google Scholar
Hu, X., Yang, J., Zi, J., Chan, C. T. & Ho, K. M. 2013 Experimental observation of negative effective gravity in water waves. Sci. Rep. 3, 10–13.Google Scholar
Jimenez, N., Romero-Garcia, V., Cebrecos, A., Pico, R., Sanchez-Morcillo, V. J. & Garcia-Raffi, L. M. 2016 Broadband quasi perfect absorption using chirped multi-layer porous materials. AIP Adv. 6, 121605.Google Scholar
Kagemoto, H. & Yue, D. K. P. 1986 Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method. J. Fluid Mech. 166, 189–209.Google Scholar
Liu, Z., Zhang, X., Mao, Y., Zhu, Y. Y., Yang, Z., Chan, C. T. & Sheng, P. 2000 Locally resonant sonic materials. Science 289 (5485), 1734–1736.Google Scholar
Martinelli, L., Ruol, P. & Zanuttigh, B. 2008 Wave basin experiments on floating breakwaters with different layouts. Appl. Ocean Res. 30 (3), 199–207.Google Scholar
Mavrakos, S. A. & McIver, P. 1997 Comparison of methods for computing hydrodynamic characteristics of arrays of wave power devices. Appl. Ocean Res. 19 (97), 283–291.Google Scholar
Montiel, F., Chung, H., Karimi, M. & Kessissoglou, N. 2017 An analytical and numerical investigation of acoustic attenuation by a finite sonic crystal. Wave Motion 70, 135–151.Google Scholar
Narimanov, E. E. & Kildishev, A. V. 2009 Optical black hole: broadband omnidirectional light absorber. Appl. Phys. Lett. 95 (4), 2007–2010.Google Scholar
Pendry, J. B. 2000 Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969.Google Scholar
Pendry, J. B., Schurig, D. & Smith, D. R. 2006 Controlling electromagnetic fields. Science 312 (5781), 1780–1782.Google Scholar
Peter, M. A. & Meylan, M. H. 2004 Infinite depth interaction theory for arbitrary floating bodies applied to wave forcing of ice floes. J. Fluid Mech. 500, 145–167.Google Scholar
Prez-Collazo, C., Greaves, D. & Iglesias, G. 2015 A review of combined wave and offshore wind energy. Renew. Sustain. Energ. Rev. 42, 141–153.Google Scholar
Romero-García, V., Picó, R., Cebrecos, A., Sánchez-Morcillo, V. J. & Staliunas, K. 2013 Enhancement of sound in chirped sonic crystals. Appl. Phys. Lett. 102 (9), 091906.Google Scholar
Schurig, D., Mock, J. J., Justice, B. J., Cummer, S. A., Pendry, J. B., Starr, A. F. & Smith, D. R. 2006 Metamaterial electromagnetic cloak at microwave frequencies. Science 314 (5801), 977–980.Google Scholar
Scruggs, J. & Jacob, P. 2009 Harvesting ocean wave energy. Science 323, 1176–1178.Google Scholar
Thompson, I., Linton, C. M. & Porter, R. 2008 A new approximation method for scattering by long finite arrays. Q. J. Mech. Appl. Maths 61 (3), 333–352.Google Scholar
Tsakmakidis, K. L., Boardman, A. D. & Hess, O. 2007 Trapped rainbow storage of light in metamaterials. Nature 450, 397–401.Google Scholar
Wegener, M. 2013 Metamaterials beyond optics. Science 342 (6161), 939–940.Google Scholar