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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
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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
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Copyright
© 2016 Cambridge University Press 

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