Wave diffraction by a long array of cylinders

Abstract

Water wave diffraction by an array of bottom-mounted circular cylinders is analysed under the assumptions of linear theory. The cylinders are identical, and equally spaced along the array. When the number of cylinders is large, but finite, near-resonant modes occur between adjacent cylinders at critical wavenumbers, and cause unusually large loads on each element of the array. These modes are associated with the existence of homogeneous solutions for the diffraction by an array which extends to infinity in both directions. This phenomenon is related to the existence of trapped waves in a channel. A second trapped wave is established, corresponding to Dirichlet boundary conditions on the channel walls, as well as a sequence of higher wavenumbers where ‘nearly trapped’ modes exist.

Diffraction of cnoidal waves by vertical cylinders in shallow water

“…This effect, described above, occurs in the results of both equations and in both the two-and three-cylinder cases. These results are in agreement with the study of Maniar and Newman [43], who found that near-resonant modes can occur between adjacent cylinders at critical wavelengths, resulting in relatively larger wave loads. 0D.…”

Trapped waves in thin elastic plates

“…These conditions imply, using image arguments, the existence of trapped waves for an infinite periodic array of circular holes in an infinite thin elastic plate. In this context, the practical importance of trapped waves is that large resonances can be expected to occur for large finite linear periodic arrays of circular holes, in accordance with [24] work showing the relationship between trapped waves in acoustic waveguides and acoustic scattering by large periodic arrays.…”

Motion-resonant modes of large articulated damped oscillators in waves

“…wave energy conversion. Indeed, many studies have been carried out to investigate the occurrence of resonant amplifications resulting from wave-structure interactions in acoustics (see for example Farhat et al, 2010), optics (see for example Ruan and Fan, 2010) and hydrodynamics (Budal, 1977;Falnes, 1980;Thomas and Evans, 1981;Heathershaw, 1982;Mei et al, 1988Mei et al, , 1994Maniar and Newman, 1997;Sammarco et al, 1997a,b;Porter and Evans, 1999;Hu and Chan, 2005;Adamo and Mei, 2005;Sammarco and Renzi, 2008;Renzi and Sammarco, 2010;Stefanakis et al, 2011;Hu et al, 2011;Dias, 2012, 2013a,b;Renzi et al, 2014a,b). In the latter discipline, a significant effort was directed towards understanding the mechanisms of resonant amplification of water waves impinging on fixed structures, such as periodic bathymetric formations or surface scatterers.…”

“…Interaction of water waves with fixed structures is a living matter also in offshore ocean engineering. In this field, a significant advancement of knowledge has been achieved with the discovery of the Rayleigh-Bloch surface waves trapped along arrays of cylinders (Maniar and Newman, 1997;Porter and Evans, 1999). Concerning the interaction of water waves with moving bodies, the theory of interacting point oscillators in water waves is indeed a subject with honourable history (Budal, 1977;Falnes, 1980;Thomas and Evans, 1981).…”