Comptes Rendus
no. 12
Directional source of water waves by a crystal of surface-piercing cylinders
[Source directive de vagues dans un cristal de cylindres émergeant en surface]
Mathieu Chekroun1  ; Agnès Maurel2  ; Vincent Pagneux1  ; P. Petitjeans3
1 LAUM, Université du Maine, avenue Olivier-Messian, 72085 Le Mans cedex 9, France
2 Institut Langevin, ESPCI, 1, rue Jussieu, 75005 Paris, France
3 PMMH, ESPCI, 10, rue Vauquelin, 75005 Paris, France
Comptes Rendus. Mécanique, Volume 343 (2015) no. 12, pp. 689-699.

On étudie la faisabilité d'une source directive pour les ondes à la surface de l'eau, basée sur les propriétés de la structure de bandes d'un cristal. Cette directivité est caractérisée numériquement pour un réseau périodique de cylindres rigides dans un fluide parfait. Dans l'expérience, la directivité est affaiblie, à cause de l'atténuation. Cependant, en prenant en compte cette atténuation, la propagation des ondes est toujours correctement décrite par l'équation de Helmholtz. Aussi, la robustesse de la directivité est-elle étudiée numériquement plus en détail, vis-à-vis des effets d'atténuation et de désordre.

The feasibility of using the band structure of a crystal to realize directional emission of water waves is investigated numerically and experimentally. The directionality of a source inside a square array of cylinders is obtained numerically for a perfect lattice in a lossless liquid. But in the experiments, the directivity is weakened, due to the effects of losses. Nevertheless, the waves are shown to satisfy the Helmholtz equation when proper attenuation is accounted for. Thus, the robustness of the directionality is studied numerically with respect to the effects of the attenuation and of the disorder.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2015.06.005
Keywords: Metamaterial, Water waves, Periodic crystal
Mot clés : Metamatériau, Cristal périodique
Mathieu Chekroun 1 ; Agnès Maurel 2 ; Vincent Pagneux 1 ; P. Petitjeans 3

1 LAUM, Université du Maine, avenue Olivier-Messian, 72085 Le Mans cedex 9, France
2 Institut Langevin, ESPCI, 1, rue Jussieu, 75005 Paris, France
3 PMMH, ESPCI, 10, rue Vauquelin, 75005 Paris, France 
@article{CRMECA_2015__343_12_689_0,
     author = {Mathieu Chekroun and Agn\`es Maurel and Vincent Pagneux and P. Petitjeans},
     title = {Directional source of water waves by a crystal of surface-piercing cylinders},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {689--699},
     publisher = {Elsevier},
     volume = {343},
     number = {12},
     year = {2015},
     doi = {10.1016/j.crme.2015.06.005},
     language = {en},
}
TY  - JOUR
AU  - Mathieu Chekroun
AU  - Agnès Maurel
AU  - Vincent Pagneux
AU  - P. Petitjeans
TI  - Directional source of water waves by a crystal of surface-piercing cylinders
JO  - Comptes Rendus. Mécanique
PY  - 2015
SP  - 689
EP  - 699
VL  - 343
IS  - 12
PB  - Elsevier
DO  - 10.1016/j.crme.2015.06.005
LA  - en
ID  - CRMECA_2015__343_12_689_0
ER  - 
%0 Journal Article
%A Mathieu Chekroun
%A Agnès Maurel
%A Vincent Pagneux
%A P. Petitjeans
%T Directional source of water waves by a crystal of surface-piercing cylinders
%J Comptes Rendus. Mécanique
%D 2015
%P 689-699
%V 343
%N 12
%I Elsevier
%R 10.1016/j.crme.2015.06.005
%G en
%F CRMECA_2015__343_12_689_0
Mathieu Chekroun; Agnès Maurel; Vincent Pagneux; P. Petitjeans. Directional source of water waves by a crystal of surface-piercing cylinders. Comptes Rendus. Mécanique, Volume 343 (2015) no. 12, pp. 689-699. doi : 10.1016/j.crme.2015.06.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.06.005/

[1] Photonic Band Gap Materials (C.M. Soukoulis, ed.), Kluwer Academic, Dordrecht, The Netherlands, 1996

[2] J.D. Joannopoulos; S.G. Johnson; J.N. Winn; R.D. Meade Photonic Crystals: Molding the Flow of Light, Princeton University Press, Princeton, NJ, USA, 2011

[3] Acoustic Metamaterials and Phononic Crystals (P.A. Deymier, ed.), vol. 173, Springer, 2013

[4] I. Bulu; H. Cayagan; E. Ozbay Highly directive radiation from sources embedded inside photonic crystals, Appl. Phys. Lett., Volume 83 (2003) no. 16, pp. 3263-3265

[5] H. Caglayan; I. Bulu; E. Ozbay Off-axis directional beaming via photonic crystal surface modes, Appl. Phys. Lett., Volume 92 (2008) no. 9, p. 092114

[6] C. Qiu; Z. Liu Acoustic directional radiation and enhancement caused by band edge states of two dimensional phononic crystals, Appl. Phys. Lett., Volume 89 (2006), p. 063106

[7] M. Ke; Z. Liu; P. Pang; C. Qiu; D. Zhao; S. Peng; J. Shi; W. Wen Experimental demonstration of directional acoustic radiation based on two dimensional photonic crystal band edge states, Appl. Phys. Lett., Volume 90 (2007), p. 083509

[8] W. Liu; X. Su Collimation and enhancement of elastic transverse waves in two-dimensional solid phononic crystals, Phys. Lett. A, Volume 374 (2010), p. 2968

[9] B. Morvan; A. Tinel; J.O. Vasseur; R. Sainidou; P. Rembert; A.C. Hladky-Hennion; N. Swinteck; P.A. Deymier Ultra-directional source of longitudinal acoustic waves based on a two-dimensional solid/solid phononic crystal, J. Appl. Phys., Volume 116 (2014) no. 21, p. 214901

[10] M. Torres; J.P. Adrados; F.M. de Espinosa; D. Garcia-Pablos; J. Fayos Parametric Bragg resonances in waves on a shallow fluid over a periodically drilled bottom, Phys. Rev. E, Volume 63 (2000) no. 1, p. 011204

[11] Y. Shen; K. Chen; Y. Chen; X. Liu; J. Zi Self-collimation in liquid surface waves propagating over a bottom with periodically drilled holes, Phys. Rev. E, Volume 71 (2005) no. 3, p. 036301

[12] R.P. Feynman; R.B. Leighton; M. Sands The Feynman Lectures on Physics, vol. I, Addison–Wesley, Reading, MA, USA, 1963 (Chaps. 51–54)

[13] J. Mei; C. Qiu; J. Shi; Z. Liu Enhanced and directional water wave emission by embedded sources, Wave Motion, Volume 47 (2010) no. 3, pp. 131-138

[14] P. Cobelli; A. Przadka; P. Petitjeans; G. Lagubeau; V. Pagneux; A. Maurel Different regimes for water wave turbulence, Phys. Rev. Lett., Volume 107 (2011) no. 21, p. 214503

[15] A. Przadka; S. Feat; P. Petitjeans; V. Pagneux; A. Maurel; M. Fink Time reversal of water waves, Phys. Rev. Lett., Volume 109 (2012) no. 6, p. 064501

[16] C.P. Berraquero; A. Maurel; P. Petitjeans; V. Pagneux Experimental realization of a water-wave metamaterial shifter, Phys. Rev. E, Volume 88 (2013) no. 5, p. 051002

[17] D.M. Henderson; J.W. Miles Surface-wave damping in a circular cylinder with a fixed contact line, J. Fluid Mech., Volume 275 (1994), pp. 285-299

[18] L. Jiang; M. Perlin; W.W. Schultz Contact-line dynamics and damping for oscillating free surface flows, Phys. Fluids, Volume 16 (2004) no. 3, pp. 748-758

[19] P. Cobelli; V. Pagneux; A. Maurel; P. Petitjeans Experimental study on water-wave trapped modes, J. Fluid Mech., Volume 666 (2011), pp. 445-476

[20] C.M. Linton; P.A. Martin Multiple scattering by random configurations of circular cylinders: second-order corrections for the effective wavenumber, J. Acoust. Soc. Amer., Volume 117 (2005) no. 6, pp. 3413-3423

[21] P.J. Cobelli; A. Maurel; V. Pagneux; P. Petitjeans Global measurement of water waves by Fourier Transform Profilometry, Exp. Fluids, Volume 46 (2009), pp. 1037-1047

[22] A. Maurel; P.J. Cobelli; V. Pagneux; P. Petitjeans Experimental and theoretical inspection of the phase-to-height relation in Fourier transform profilometry, Appl. Opt., Volume 48 (2009) no. 2, pp. 380-392

[23] A. Przadka; B. Cabane; V. Pagneux; A. Maurel; P. Petitjeans Fourier transform profilometry for water waves: how to achieve clean water attenuation with diffusive reflection at the water surface?, Exp. Fluids, Volume 52 (2012) no. 2, pp. 519-527

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Theoretical and practical limits of superdirective antenna arrays

Abdullah Haskou; Ala Sharaiha; Sylvain Collardey

C. R. Phys (2017)

Shear-layer acoustic radiation in an excited subsonic jet: experimental study

Vincent Fleury; Christophe Bailly; Daniel Juvé

C. R. Méca (2005)

Metamaterials for optical and radio communications

Boubacar Kante; Abdelwaheb Ourir; Shah Nawaz Burokur; ...

C. R. Phys (2008)