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Backscattering reduction for resonating obstacle in water-wave channel. (English) Zbl 1404.76035

Summary: 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.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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[1] Alam, M. R., Broadband cloaking in stratified seas, Phys. Rev. Lett., 108, 8, (2012) · doi:10.1103/PhysRevLett.108.084502
[2] Aslanyan, A.; Parnovski, L.; Vassiliev, D., Complex resonances in acoustic waveguides, Q. J. Mech. Appl. Maths, 53, 3, 429-447, (2000) · Zbl 0972.76091 · doi:10.1093/qjmam/53.3.429
[3] Berraquero, C. P.; Maurel, A.; Petitjeans, P.; Pagneux, V., Experimental realization of a water-wave metamaterial shifter, Phys. Rev. E, 88, 5, (2013)
[4] Bonnet-Ben Dhia, A.-S.; Nazarov, S. A.; Taskinen, J., Underwater topography invisible for surface waves at given frequencies, Wave Motion, 57, 129-142, (2015) · Zbl 1524.35454 · doi:10.1016/j.wavemoti.2015.03.008
[5] Chamberlain, P. G.; Porter, D., The modified mild-slope equation, J. Fluid Mech., 291, 393-407, (1995) · Zbl 0843.76006 · doi:10.1017/S0022112095002758
[6] Chen, H.; Yang, J.; Zi, J.; Chan, C. T., Transformation media for linear liquid surface waves, Eur. Phys. Lett., 85, 2, 24004, (2009) · doi:10.1209/0295-5075/85/24004
[7] Cobelli, P.; Maurel, A.; Pagneux, V.; Petitjeans, P., Global measurement of water waves by Fourier transform profilometry, Exp. Fluids, 46, 6, 1037-1047, (2009) · doi:10.1007/s00348-009-0611-z
[8] Cobelli, P.; Pagneux, V.; Maurel, A.; Petitjeans, P., Experimental observation of trapped modes in a water wave channel, Eur. Phys. Lett., 88, 2, 20006, (2009) · Zbl 1225.76008 · doi:10.1209/0295-5075/88/20006
[9] Cobelli, P.; Pagneux, V.; Maurel, A.; Petitjeans, P., Experimental study on water-wave trapped modes, J. Fluid Mech., 666, 445-476, (2011) · Zbl 1225.76008 · doi:10.1017/S0022112010004222
[10] Craster, R. V. & Guenneau, S.2012Acoustic Metamaterials: Negative Refraction, Imaging, Lensing and Cloaking, vol. 166. Springer Science & Business Media.
[11] Dupont, G.; Kimmoun, O.; Molin, B.; Guenneau, S.; Enoch, S., Numerical and experimental study of an invisibility carpet in a water channel, Phys. Rev. E, 91, 2, (2015)
[12] Evans, D. V.; Levitin, M.; Vassiliev, D., Existence theorems for trapped modes, J. Fluid Mech., 261, 21-31, (1994) · Zbl 0804.76075 · doi:10.1017/S0022112094000236
[13] Evans, D. V.; Linton, C. M., Trapped modes in open channels, J. Fluid Mech., 225, 153-175, (1991) · Zbl 0722.76013 · doi:10.1017/S0022112091002008
[14] Evans, D. V.; Linton, C. M.; Ursell, F., Trapped mode frequencies embedded in the continuous spectrum, Q. J. Mech. Appl. Maths, 46, 2, 253-274, (1993) · Zbl 0784.76084 · doi:10.1093/qjmam/46.2.253
[15] Evans, D. V.; Porter, R., Trapped modes about multiple cylinders in a channel, J. Fluid Mech., 339, 331-356, (1997) · Zbl 0909.76010 · doi:10.1017/S0022112097005302
[16] Fano, U., Effects of configuration interaction on intensities and phase shifts, Phys. Rev., 124, 6, 1866-1878, (1961) · Zbl 0116.23405 · doi:10.1103/PhysRev.124.1866
[17] Farhat, M.; Enoch, S.; Guenneau, S.; Movchan, A. B., Broadband cylindrical acoustic cloak for linear surface waves in a fluid, Phys. Rev. Lett., 101, 13, (2008) · doi:10.1103/PhysRevLett.101.134501
[18] Hein, S.; Koch, W.; Nannen, L., Fano resonances in acoustics, J. Fluid Mech., 664, 238-264, (2010) · Zbl 1221.76180 · doi:10.1017/S0022112010003757
[19] Kashiwagi, M., Iida, T. & Miki, M.2015Wave 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.
[20] Limonov, M. F.; Rybin, M. V.; Poddubny, A. N.; Kivshar, Y. S., Fano resonances in photonics, Nature Photon., 11, 543-554, (2017) · doi:10.1038/nphoton.2017.142
[21] Linton, C. M.; Mciver, P., Embedded trapped modes in water waves and acoustics, Wave Motion, 45, 1-2, 16-29, (2007) · Zbl 1231.76046 · doi:10.1016/j.wavemoti.2007.04.009
[22] Luk’Yanchuk, B.; Zheludev, N. I.; Maier, S. A.; Halas, N. J.; Nordlander, P.; Giessen, H.; Chong, C. T., The Fano resonance in plasmonic nanostructures and metamaterials, Nat. Mater., 9, 9, 707-715, (2010) · doi:10.1038/nmat2810
[23] Maurel, A.; Cobelli, P.; Pagneux, V.; Petitjeans, P., Experimental and theoretical inspection of the phase-to-height relation in Fourier transform profilometry, Appl. Opt., 48, 2, 380-392, (2009) · doi:10.1364/AO.48.000380
[24] Newman, J. N., Cloaking a circular cylinder in water waves, Eur. J. Mech. (B/Fluids), 47, 145-150, (2014) · Zbl 1297.76034 · doi:10.1016/j.euromechflu.2013.11.005
[25] Pagneux, V.2013Trapped 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. doi:10.1007/978-3-7091-1619-7_5
[26] Pendry, J. B.; Schurig, D.; Smith, D. R., Controlling electromagnetic fields, Science, 312, 5781, 1780-1782, (2006) · Zbl 1226.78003 · doi:10.1126/science.1125907
[27] Porter, R., Cloaking in water waves, Acoustic Metamaterials and Wave Control, (2018), World Scientific
[28] Porter, R.; Newman, J. N., Cloaking of a vertical cylinder in waves using variable bathymetry, J. Fluid Mech., 750, 124-143, (2014) · doi:10.1017/jfm.2014.254
[29] Przadka, A.; Cabane, B.; Pagneux, V.; Maurel, A.; Petitjeans, P., 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, (2012) · doi:10.1007/s00348-011-1240-x
[30] Zareei, A.; Alam, M. R., Cloaking in shallow-water waves via nonlinear medium transformation, J. Fluid Mech., 778, 273-287, (2015) · Zbl 1382.76037 · doi:10.1017/jfm.2015.350
[31] Zareei, A. & Alam, M. R.2015bCloaking 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. · Zbl 1382.76037
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