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

Guillaume Dupont (1, 2) , Sébastien Guenneau (3) , Olivier Kimmoun (1) , Bernard Molin (1) , Stefan Enoch (4, 2)

1 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre
2 FRESNEL - Institut FRESNEL
3 EPSILON - EPSILON
4 CLARTE - CLARTE

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.

Domaines: Mécanique des fluides [physics.class-ph]

Guillaume Dupont, Sébastien Guenneau, Olivier Kimmoun, Bernard Molin, Stefan Enoch. Cloaking a vertical cylinder via homogenization in the mild-slope equation. Journal of Fluid Mechanics, 2016, 796, pp.R1-R12. ⟨10.1017/jfm.2016.249⟩. ⟨hal-01318053⟩