Wave Forces on a Partially Reflecting Wall by Oblique Bragg Scattering with Porous Breakwaters over Uneven Bottoms

Jen-Yi Chang,Chia-Cheng Tsai

doi:10.3390/jmse10030409

Abstract

In this study, the scattering of oblique water waves by multiple variable porous breakwaters near a partially reflecting wall over uneven bottoms are investigated using the eigenfunction matching method (EMM). In the solution procedure, the variable breakwaters and bottom profiles are sliced into shelves separated steps and the solutions on the shelves are composed of eigenfunctions with unknown coefficients representing the wave amplitudes. Using the conservations of mass and momentum as well as the condition for the partially reflecting sidewall, a system of linear equations is resulted that can be solved by a sparse-matrix solver. The proposed EMM is validated by comparing its results with those in the literature. Then, the EMM is applied for studying oblique Bragg scattering by periodic porous breakwaters near a partially reflecting wall over uneven bottoms. The constructive and destructive Bragg scattering are discussed. Numerical results suggest that the partially reflecting wall should be separated from the last breakwater by half wavelength of the periodic breakwaters to migrate the wave force on the vertical wall.

Highlights

Academic Editor: EvaWhen considering the protection of harbors, wharfs, inlets, and shorelines from wave attacks, porous structures are frequently used as they can further dissipate wave energy.the intensity of the wave energy on the shoreline decreases since only a small part of the wave energy is transmitted to the nearshore
The theory of Sollitt and Cross [1] was widely applied for solving water wave scattering over porous breakwaters by the eigenfunction matching method [6–8] and the mild-slope equation [9–11]
Several cases of water wave scattering by porous structures near a partially reflecting wall are considered

Summary

Introduction

Academic Editor: EvaWhen considering the protection of harbors, wharfs, inlets, and shorelines from wave attacks, porous structures are frequently used as they can further dissipate wave energy.the intensity of the wave energy on the shoreline decreases since only a small part of the wave energy is transmitted to the nearshore. Theoretical study of the energy dissipation inside porous structures was initialized by Sollitt and Cross [1], who evaluated the energy dissipation using the Lorentz’s theory of equivalent work. Et al [2] and Losada, et al [3] applied this theory to compute the reflection and transmission coefficients of water wave scattering by subaerial porous breakwaters. The theory of Sollitt and Cross [1] was widely applied for solving water wave scattering over porous breakwaters by the eigenfunction matching method [6–8] and the mild-slope equation [9–11]. These depth-integrated models are computationally efficient and can be served as preliminary calculations followed by modern three-dimensional numerical models [12–14] and/or experimental studies [15,16]

Methods

Results

Discussion

Conclusion