The scattering of water waves by an array of circular cylinders in a channel

Abstract

The full linear problem of the scattering of water waves by an array of N bottom-mounted vertical circular cylinders situated in a channel of constant depth and width is solved using the method of multipoles. A simple formula is derived for the velocity potential in the vicinity of a cylinder, and in particular on the cylinder surfaces, which allows hydrodynamic quantities such as forces to be easily evaluated. The simplicity of the solution makes the evaluation of quantities of interest straightforward and extensive results are given. An approximate solution for the forces on the cylinders, based on the assumption that the wavelength of the incident wave is long compared with the cylinder radii, is also given, and this is compared with results from the 'exact' linear solution.

Wave-power extraction by a compact array of buoys

“…When both the buoy dimension and the spacing are not small compared to the wavelength, direct numerical methods are available but require greater computational effort. For simple geometries such as vertical circular cylinders, formally exact theories have been reported by Linton & Evans (1990) ;Manihar & Newman (1997); Linton & Mclver (1996);Chamberlain (2007); Linton & Evans (1992); Linton & Mclver (1996) for an infinite or semi-infinite line of fixed vertical cylinders with finite radius. These methods still call for significant numerical work.…”

Resonances in Wave Diffraction/Radiation for Arrays of Elastically Connected Cylinders

“…Alternative expressions of the channel multipoles, where the singularity at (0, y H ) is expanded about another point (0, y N ), jOp, can be obtained from equations (A.10)}(A.15) of Linton & McIver (1996) for l"0 and applying a similar procedure for l"1, 2, 2 ,R, we obtain…”

“…where A H L_J and B H L>_J are the unknown coe$cients to be determined, and H L_J and H L>_J are the channel multipoles [see McIver & Bennett (1993), Linton & McIver (1996)]. The factor Z L_J is de"ned as…”

Type of dike using C-shaped vertical cylinders

“…Regarding the control of water wave trajectories, periodic structures present some interesting properties. The study of such structures in solid-state physics and optics has emerged in the area of photonic crystals [2], and has been translated in water wave physics [11][12][13][14][15][16][17].…”