Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-03T00:53:20.326Z Has data issue: false hasContentIssue false
  • English
  • Français

Backscattering reduction for resonating obstacle in water-wave channel

Published online by Cambridge University Press:  24 April 2018

Tomasz Bobinski Open the ORCID record for Tomasz Bobinski [Opens in a new window] ,
Agnès Maurel Open the ORCID record for Agnès Maurel [Opens in a new window] ,
Philippe Petitjeans  and
Vincent Pagneux
Tomasz Bobinski*
Affiliation:
Lab. PMMH/ESPCI, 10 rue Vauquelin, 75005 Paris, France Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, 00-665 Warsaw, Poland
Agnès Maurel
Affiliation:
Institut Langevin, UMR 7587, 1 rue Jussieu, 75005 Paris, France
Philippe Petitjeans
Affiliation:
Lab. PMMH/ESPCI, 10 rue Vauquelin, 75005 Paris, France
Vincent Pagneux
Affiliation:
LAUM, UMR 6613, Univ. Maine, Avenue Olivier Messiaen, 72085 Le Mans, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the propagation of water waves in a waveguide with a surface-piercing circular cylinder. A plane wave interacting with the cylinder leads to a Fano resonance resulting in strong scattering with a large reflection coefficient. Using a smoothly varying bathymetry whose shape is optimized, we show both numerically and experimentally that broadband and robust backscattering reduction can be obtained below the first cutoff frequency.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows Waves/Free-surface Flows: Wave scattering
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 845 , 25 June 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

Alam, M. R. 2012 Broadband cloaking in stratified seas. Phys. Rev. Lett. 108 (8), 084502.Google Scholar
Aslanyan, A., Parnovski, L. & Vassiliev, D. 2000 Complex resonances in acoustic waveguides. Q. J. Mech. Appl. Maths 53 (3), 429–447.Google Scholar
Berraquero, C. P., Maurel, A., Petitjeans, P. & Pagneux, V. 2013 Experimental realization of a water-wave metamaterial shifter. Phys. Rev. E 88 (5), 051002.Google Scholar
Bonnet-Ben Dhia, A.-S., Nazarov, S. A. & Taskinen, J. 2015 Underwater topography invisible for surface waves at given frequencies. Wave Motion 57, 129–142.Google Scholar
Chamberlain, P. G. & Porter, D. 1995 The modified mild-slope equation. J. Fluid Mech. 291, 393–407.Google Scholar
Chen, H., Yang, J., Zi, J. & Chan, C. T. 2009 Transformation media for linear liquid surface waves. Eur. Phys. Lett. 85 (2), 24004.Google Scholar
Cobelli, P., Maurel, A., Pagneux, V. & Petitjeans, P. 2009a Global measurement of water waves by Fourier transform profilometry. Exp. Fluids 46 (6), 1037–1047.Google Scholar
Cobelli, P., Pagneux, V., Maurel, A. & Petitjeans, P. 2009b Experimental observation of trapped modes in a water wave channel. Eur. Phys. Lett. 88 (2), 20006.Google Scholar
Cobelli, P., Pagneux, V., Maurel, A. & Petitjeans, P. 2011 Experimental study on water-wave trapped modes. J. Fluid Mech. 666, 445–476.Google Scholar
Craster, R. V. & Guenneau, S. 2012 Acoustic Metamaterials: Negative Refraction, Imaging, Lensing and Cloaking, vol. 166. Springer Science & Business Media.Google Scholar
Dupont, G., Kimmoun, O., Molin, B., Guenneau, S. & Enoch, S. 2015 Numerical and experimental study of an invisibility carpet in a water channel. Phys. Rev. E 91 (2), 023010.Google Scholar
Evans, D. V., Levitin, M. & Vassiliev, D. 1994 Existence theorems for trapped modes. J. Fluid Mech. 261, 21–31.Google Scholar
Evans, D. V. & Linton, C. M. 1991 Trapped modes in open channels. J. Fluid Mech. 225, 153–175.Google Scholar
Evans, D. V., Linton, C. M. & Ursell, F. 1993 Trapped mode frequencies embedded in the continuous spectrum. Q. J. Mech. Appl. Maths 46 (2), 253–274.Google Scholar
Evans, D. V. & Porter, R. 1997 Trapped modes about multiple cylinders in a channel. J. Fluid Mech. 339, 331–356.CrossRefGoogle Scholar
Fano, U. 1961 Effects of configuration interaction on intensities and phase shifts. Phys. Rev. 124 (6), 1866–1878.Google Scholar
Farhat, M., Enoch, S., Guenneau, S. & Movchan, A. B. 2008 Broadband cylindrical acoustic cloak for linear surface waves in a fluid. Phys. Rev. Lett. 101 (13), 134501.Google Scholar
Hein, S., Koch, W. & Nannen, L. 2010 Fano resonances in acoustics. J. Fluid Mech. 664, 238–264.CrossRefGoogle Scholar
Kashiwagi, M., Iida, T. & Miki, M. 2015 Wave drift force on floating bodies of cloaking configuration and associated wave patterns. In 30th International Workshop on Water Waves and Floating Bodies, Bristol, http://www.iwwwfb.org/Abstracts/iwwwfb30/iwwwfb30_26.pdf.Google Scholar
Limonov, M. F., Rybin, M. V., Poddubny, A. N. & Kivshar, Y. S. 2017 Fano resonances in photonics. Nature Photon. 11, 543–554.Google Scholar
Linton, C. M. & McIver, P. 2007 Embedded trapped modes in water waves and acoustics. Wave Motion 45 (1–2), 16–29.CrossRefGoogle Scholar
Luk’yanchuk, B., Zheludev, N. I., Maier, S. A., Halas, N. J., Nordlander, P., Giessen, H. & Chong, C. T. 2010 The Fano resonance in plasmonic nanostructures and metamaterials. Nat. Mater. 9 (9), 707–715.Google Scholar
Maurel, A., Cobelli, P., Pagneux, V. & Petitjeans, P. 2009 Experimental and theoretical inspection of the phase-to-height relation in Fourier transform profilometry. Appl. Opt. 48 (2), 380–392.Google Scholar
Newman, J. N. 2014 Cloaking a circular cylinder in water waves. Eur. J. Mech. (B/Fluids) 47, 145–150.CrossRefGoogle Scholar
Pagneux, V. 2013 Trapped modes and edge resonances in acoustics and elasticity. In Dynamic Localization Phenomena in Elasticity, Acoustics and Electromagnetism (ed. Craster, R. V. & Kaplunov, J.), pp. 181–223. Springer Vienna.CrossRefGoogle Scholar
Pendry, J. B., Schurig, D. & Smith, D. R. 2006 Controlling electromagnetic fields. Science 312 (5781), 1780–1782.CrossRefGoogle ScholarPubMed
Porter, R. 2018 Cloaking in water waves. Acoustic Metamaterials and Wave Control. World Scientific.Google Scholar
Porter, R. & Newman, J. N. 2014 Cloaking of a vertical cylinder in waves using variable bathymetry. J. Fluid Mech. 750, 124–143.Google Scholar
Przadka, A., Cabane, B., Pagneux, V., Maurel, A. & Petitjeans, P. 2012 Fourier transform profilometry for water waves: how to achieve clean water attenuation with diffusive reflection at the water surface? Exp. Fluids 52 (2), 519–527.Google Scholar
Zareei, A. & Alam, M. R. 2015a Cloaking in shallow-water waves via nonlinear medium transformation. J. Fluid Mech. 778, 273–287.Google Scholar
Zareei, A. & Alam, M. R. 2015b Cloaking water waves via an elastic buoyant carpet. In Bulletin of the American Physical Society, vol. 60, http://meetings.aps.org/link/BAPS.2015.DFD.R31.2.Google Scholar