Wave scattering by an array of metamaterial cylinders

Abstract

Abstract

Scattering of surface waves by a vertical truncated structured cylinder

“…The model of Marangos & Porter [4] applies to close spacing between the plates where tensor elements are expressed explicitly in terms of the distances from the surface to the top of the array of plates and to the base of the fluid. This model arises from homogenization which exploits the contrast in the lengthscales in the problem and is adopted from Porter [6] and Zheng et al [7]. In these two problems, the plate arrays extend throughout the fluid depth allowing the exact depth dependence of the fluid to be factorized from the solution without depth averaging and is therefore not restricted to long wavelengths.…”

“…Whilst Porter's [6] work concentrated on refraction across planar interfaces, Zheng et al [7] considered the effect on waves of plate arrays confined within a circular cylinder. The small gaps between the plates provide an environment for resonance and slow wave propagation across the cylinder giving it the ability to concentrate wave energy which can either be harnessed/dissipated via a local damping mechanism or redirected to create a water wave lensing device.…”

“…In this paper, we consider the effect that truncating the vertical extent of cylinder considered by Zheng et al [7] has on the scattering of incident waves. Specifically, we have assumed the cylinder extends upwards from the base of the fluid to a constant level below the surface.…”

“…The structural uniformity in the depth exploited by Zheng et al [7] is absent here and this introduces additional mathematical challenges not previously encountered. It is the description of this novel and bespoke solution process for the full depth-dependent model on which the emphasis of this work is placed.…”

Extending limits for wave power absorption by axisymmetric devices

“…Indeed, Garnaud & Mei (2009) have previously shown that a compact array of floating buoys extracting power in heave and distributed over a circular region of the surface can absorb more than the equivalent size of a rigid cylinder. Zheng, Porter & Greaves (2020) have demonstrated how a structured porous cylinder can be capable of exceeding the equivalent rigid-body absorption limits. Very recently, Michele et al.…”