View in EDS

Water-wave diffractions by three-dimensional periodic rectangular blocks: Fourier modal analysis.

Saved in:
Bibliographic Details
Title: Water-wave diffractions by three-dimensional periodic rectangular blocks: Fourier modal analysis.
Authors: Wang, Jiyong, Chung, Fei Fang, Ong, Muk Chen
Source: Physics of Fluids; Jul2024, Vol. 36 Issue 7, p1-11, 11p
Subject Terms: TOEPLITZ matrices, MODAL analysis, WATER waves, FOURIER analysis, WAVE energy
Abstract: Water-wave diffractions caused by three-dimensional (3D) periodic rectangular blocks are analytically modeled with a Fourier modal analysis method using full-linear potential theory. The boundary conditions in the dimension of periodic extent are conjugated into the other two dimensions in terms of Toeplitz matrices. The elements of the Toeplitz matrices are the Fourier harmonics of vertical and horizontal eigenfunctions converted to special-frequency domains. This allows us to reduce the 3D model system to an ordinary two-dimensional counterpart. The boundary matchings finally lead to a general form of block centrosymmetric matrix for the rectangular topography. A fair consistency between the present results and the data from the literature validates such a Fourier modal analysis. Effects of different parameters on multiple-modal diffraction efficiencies of reflected and transmitted wave energy are computed and analyzed. This study is useful for the designers of coastal breakwaters and focusing lens of water waves. [ABSTRACT FROM AUTHOR]
Copyright of Physics of Fluids is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Complementary Index
Description
Abstract:Water-wave diffractions caused by three-dimensional (3D) periodic rectangular blocks are analytically modeled with a Fourier modal analysis method using full-linear potential theory. The boundary conditions in the dimension of periodic extent are conjugated into the other two dimensions in terms of Toeplitz matrices. The elements of the Toeplitz matrices are the Fourier harmonics of vertical and horizontal eigenfunctions converted to special-frequency domains. This allows us to reduce the 3D model system to an ordinary two-dimensional counterpart. The boundary matchings finally lead to a general form of block centrosymmetric matrix for the rectangular topography. A fair consistency between the present results and the data from the literature validates such a Fourier modal analysis. Effects of different parameters on multiple-modal diffraction efficiencies of reflected and transmitted wave energy are computed and analyzed. This study is useful for the designers of coastal breakwaters and focusing lens of water waves. [ABSTRACT FROM AUTHOR]
ISSN:10706631
DOI:10.1063/5.0218962