Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T13:21:20.198Z Has data issue: false hasContentIssue false
  • English
  • Français

Cloaking a vertical cylinder via homogenization in the mild-slope equation

Published online by Cambridge University Press:  06 May 2016

G. Dupont ,
S. Guenneau ,
O. Kimmoun ,
B. Molin  and
S. Enoch
G. Dupont*
Affiliation:
Aix-Marseille Université, CNRS, Centrale Marseille, Institut Fresnel UMR 7249, 13013 Marseille, France
S. Guenneau
Affiliation:
Aix-Marseille Université, CNRS, Centrale Marseille, Institut Fresnel UMR 7249, 13013 Marseille, France
O. Kimmoun
Affiliation:
Aix-Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13013 Marseille, France
B. Molin
Affiliation:
Aix-Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13013 Marseille, France
S. Enoch
Affiliation:
Aix-Marseille Université, CNRS, Centrale Marseille, Institut Fresnel UMR 7249, 13013 Marseille, France
*
†Email address for correspondence: guillaume.dupont@fresnel.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

We describe a method to construct devices which allows a vertical rigid cylinder to be cloaked for any far-field observer in the case of linear water waves. An adaptation of parameters given by a geometric transform performed in the mild-slope equation is achieved via homogenization. The final device, which respects the physical constraints of the problem, is obtained with a conformal mapping. The result of this algorithm is a structure surrounding the vertical cylinder, composed of an annular region with varying bathymetry and with rigid vertical objects piercing the free surface. An approximate cloaking is achieved, which implies a reduction of the mean drift force acting on the cylinder.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave scattering
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 796 , 10 June 2016 , R1
Check for updates
Copyright
© 2016 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, 084502.Google Scholar
Berkhoff, J. C. W. 1972 Computation of combined refraction–diffraction. Coast. Engng Proc. 1 (13).Google Scholar
Berraquero, C. P., Maurel, A., Petitjeans, P. & Pagneux, V. 2013 Experimental realization of a water-wave metamaterial shifter. Phys. Rev. E 88, 051002.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, 023010.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, 134501.Google Scholar
Farhat, M., Guenneau, S., Enoch, S. & Movchan, A. B. 2009 Cloaking bending waves propagating in thin elastic plates. Phys. Rev. B 79, 033102.Google Scholar
Guenneau, S., Zolla, F. & Nicolet, A. 2007 Homogenization of 3D finite photonic crystals with heterogeneous permittivity and permeability. Waves in Random and Complex Media 17 (4), 653–697.Google Scholar
Kadic, M., Buckmann, T., Schittny, R. & Wegener, M. 2013 Metamaterials beyond electromagnetism. Rep. Prog. Phys. 76 (12), 126501.CrossRefGoogle ScholarPubMed
Kohn, R. V., Shen, H., Vogelius, M. S. & Weinstein, M. I. 2008 Cloaking via change of variables in electric impedance tomography. Inverse Problems 24 (1), 015016.Google Scholar
Leonhardt, U. 2006 Optical conformal mapping. Science 312 (5781), 1777–1780.Google Scholar
MacCamy, R. C. & Fuchs, R. A.1954 Wave forces on piles: a diffraction theory. Tech. Rep. DTIC document.Google Scholar
McIver, M. 2014 The scattering properties of a system of structures in water waves. Q. J. Mech. Appl. Maths 67 (4), 631–639.CrossRefGoogle Scholar
Milton, G. W., Briane, M. & Willis, J. R. 2006 On cloaking for elasticity and physical equations with a transformation invariant form. New J. Phys. 8 (10), 248.Google Scholar
Newman, J. N. 2014 Cloaking a circular cylinder in water waves. Eur. J. Mech. (B/Fluids) 47, 145–150; Enok Palm Memorial Volume.Google Scholar
Norris, A. N. 2008 Acoustic cloaking theory. Proc. R. Soc. Lond. A 464, 2411–2434.Google Scholar
Papanicolau, G., Bensoussan, A. & Lions, J.-L. 1978 Asymptotic Analysis for Periodic Structures. Elsevier.Google Scholar
Pendry, J. B., Schurig, D. & Smith, D. R. 2006 Controlling electromagnetic fields. Science 312 (5781), 1780–1782.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
Smith, R. & Sprinks, T. 1975 Scattering of surface waves by a conical island. J. Fluid Mech. 72 (2), 373–384.CrossRefGoogle Scholar
Zareei, A. & Alam, M.-R. 2015 Cloaking in shallow-water waves via nonlinear medium transformation. J. Fluid Mech. 778, 273–287.Google Scholar