Trapping and near-trapping by arrays of cylinders in waves
type: Item
instance of: scholarly article
title: Trapping and near-trapping by arrays of cylinders in waves
zbMATH Open document ID: 0954.76007
DOI: 10.1023/A:1004358725444
author: V. Pereyra
published in: Journal of Engineering Mathematics
publication date: 2001-02-08T00:00:00Z
review text: The authors present recent developments and some new results concerning the trapping and near-trapping of water waves by arrays of cylinders. First, they discuss forces on a circular array of four identical cylinders. This is followed by Rayleigh-Bloch waves along linear arrays of cylinders, with applications of these waves to near-trapping of waves by large but finite linear periodic arrays of vertical cylinders as described by \textit{H. D. Maniar} and \textit{J. N. Newman} [J. Fluid Mech. 339, 309-330 (1997; Zbl 0888.76010)]. The authors also describe the method of \textit{M. Callan}, \textit{C. M. Linton} and \textit{D. V. Evans} [J. Fluid Mech. 229, 51-64 (1991; Zbl 0850.76075)] for predicting trapped modes near a circular cylinder in a channel. Further, the theory of Callan et al. is extended to multiple cylinders centered on the center-plane of a channel, and then the corresponding Neumann and Dirichlet trapped modes are obtained. It is shown that, in the case of the finite linear array, the near-trapping frequencies of waves are related to the Rayleigh-Bloch trapped wave frequencies for the infinite array. This is an interesting paper which will be useful for calculating wave forces on fixed or moving offshore structures in oceans.
Mathematics Subject Classification ID: 76B15
zbMATH DE Number: 1360006
zbMATH Keywords: Neumann trapped modes
zbMATH Keywords: trapping
zbMATH Keywords: near-trapping
zbMATH Keywords: circular array of four cylinders
zbMATH Keywords: Rayleigh-Bloch waves
zbMATH Keywords: linear arrays of cylinders
zbMATH Keywords: multiple cylinders
zbMATH Keywords: Dirichlet trapped modes
zbMATH Keywords: finite linear array of cylinders
zbMATH Keywords: near-trapping frequencies
reviewed by: Lokenath Debnath
MaRDI profile type: Publication
full work available at URL: a:1004358725444
OpenAlex ID: W1562574511
description: scientific article; zbMATH DE number 1360006