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Backscattering reduction for resonating obstacle in water-wave channel

  • Tomasz Bobinski (a1) (a2), Agnès Maurel (a3), Philippe Petitjeans (a1) and Vincent Pagneux (a4)


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.


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Alam, M. R. 2012 Broadband cloaking in stratified seas. Phys. Rev. Lett. 108 (8), 084502.
Aslanyan, A., Parnovski, L. & Vassiliev, D. 2000 Complex resonances in acoustic waveguides. Q. J. Mech. Appl. Maths 53 (3), 429447.
Berraquero, C. P., Maurel, A., Petitjeans, P. & Pagneux, V. 2013 Experimental realization of a water-wave metamaterial shifter. Phys. Rev. E 88 (5), 051002.
Bonnet-Ben Dhia, A.-S., Nazarov, S. A. & Taskinen, J. 2015 Underwater topography invisible for surface waves at given frequencies. Wave Motion 57, 129142.
Chamberlain, P. G. & Porter, D. 1995 The modified mild-slope equation. J. Fluid Mech. 291, 393407.
Chen, H., Yang, J., Zi, J. & Chan, C. T. 2009 Transformation media for linear liquid surface waves. Eur. Phys. Lett. 85 (2), 24004.
Cobelli, P., Maurel, A., Pagneux, V. & Petitjeans, P. 2009a Global measurement of water waves by Fourier transform profilometry. Exp. Fluids 46 (6), 10371047.
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.
Cobelli, P., Pagneux, V., Maurel, A. & Petitjeans, P. 2011 Experimental study on water-wave trapped modes. J. Fluid Mech. 666, 445476.
Craster, R. V. & Guenneau, S. 2012 Acoustic Metamaterials: Negative Refraction, Imaging, Lensing and Cloaking, vol. 166. Springer Science & Business Media.
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.
Evans, D. V., Levitin, M. & Vassiliev, D. 1994 Existence theorems for trapped modes. J. Fluid Mech. 261, 2131.
Evans, D. V. & Linton, C. M. 1991 Trapped modes in open channels. J. Fluid Mech. 225, 153175.
Evans, D. V., Linton, C. M. & Ursell, F. 1993 Trapped mode frequencies embedded in the continuous spectrum. Q. J. Mech. Appl. Maths 46 (2), 253274.
Evans, D. V. & Porter, R. 1997 Trapped modes about multiple cylinders in a channel. J. Fluid Mech. 339, 331356.
Fano, U. 1961 Effects of configuration interaction on intensities and phase shifts. Phys. Rev. 124 (6), 18661878.
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.
Hein, S., Koch, W. & Nannen, L. 2010 Fano resonances in acoustics. J. Fluid Mech. 664, 238264.
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,
Limonov, M. F., Rybin, M. V., Poddubny, A. N. & Kivshar, Y. S. 2017 Fano resonances in photonics. Nature Photon. 11, 543554.
Linton, C. M. & McIver, P. 2007 Embedded trapped modes in water waves and acoustics. Wave Motion 45 (1–2), 1629.
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), 707715.
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), 380392.
Newman, J. N. 2014 Cloaking a circular cylinder in water waves. Eur. J. Mech. (B/Fluids) 47, 145150.
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. 181223. Springer Vienna.
Pendry, J. B., Schurig, D. & Smith, D. R. 2006 Controlling electromagnetic fields. Science 312 (5781), 17801782.
Porter, R. 2018 Cloaking in water waves. Acoustic Metamaterials and Wave Control. World Scientific.
Porter, R. & Newman, J. N. 2014 Cloaking of a vertical cylinder in waves using variable bathymetry. J. Fluid Mech. 750, 124143.
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), 519527.
Zareei, A. & Alam, M. R. 2015a Cloaking in shallow-water waves via nonlinear medium transformation. J. Fluid Mech. 778, 273287.
Zareei, A. & Alam, M. R. 2015b Cloaking water waves via an elastic buoyant carpet. In Bulletin of the American Physical Society, vol. 60,
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Backscattering reduction for resonating obstacle in water-wave channel

  • Tomasz Bobinski (a1) (a2), Agnès Maurel (a3), Philippe Petitjeans (a1) and Vincent Pagneux (a4)


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