An extended analytic solution of combined refraction and diffraction of long waves propagating over circular island
type: Item
instance of: scholarly article
title: An extended analytic solution of combined refraction and diffraction of long waves propagating over circular island
zbMATH Open document ID: 1308.35083
DOI: 10.1155/2012/742705
author: Y. S. Kuo
author: Tai-Wen Hsu
author: C. C. Tsai
author: Yu-Hsuan Huang
published in: Journal of Applied Mathematics
publication date: 2013-06-03T00:00:00Z
review text: Summary: An analytic solution of long waves scattering by a cylindrical island mounted on a permeable circular shoal was obtained by solving the linear long wave equation (LWE). The solution is in terms of the Bessel function expressed by complex variables. The present solution is suitable for arbitrary bottom configurations described by a power function with two independent parameters. For the case of the paraboloidal shoal, there exists a singular point \((\alpha = 2)\) which can be removed using Frobenius series, where \(\alpha\) is a real constant. The present solution is reduced to \textit{X. Yu} and \textit{B. Zhang}'s [Ocean Engineering 30, No. 10, 1253--1267 (2003; \url{doi:10.1016/S0029-8018(02)00104-X})] solution for impermeable circular shoal. The numerical results show some special features of the combined effect of wave refraction and diffraction caused by a porous circular island. The effect of key parameters of the island dimension, the shoal slope, and permeability on wave scattering was discussed based on the analytic solution.
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35P25
zbMATH DE Number: 6169968
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/742705
OpenAlex ID: W2005303327
Wikidata QID: Q58907269
cites work: Extensions of the mild-slope equation
cites work: New solutions for the propagation of long water waves over variable depth
cites work: Scattering of long waves around a circular island mounted on a conical shoal
DBLP publication ID: journals/jam/KuoHTH12
description: scientific article; zbMATH DE number 6169968