Trapping and near-trapping by arrays of cylinders in waves
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.
scientific article; zbMATH DE number 1360006