Step Approximation for Water Wave Scattering by Multiple Thin Barriers over Undulated Bottoms

Chia-Cheng Tsai,Jen-Yi Chang,Chang-Thi Tran

doi:10.3390/jmse9060629

Abstract

This paper investigates the scattering of oblique water waves by multiple thin barriers over undulation bottoms using the eigenfunction matching method (EMM). In the solution procedures of the EMM, the bottom topographies are sliced into shelves separated by steps. On each step, surface-piercing or/and bottom-standing barriers can be presented or not. For each shelf, the solution is composed of eigenfunctions with unknown coefficients representing the wave amplitudes. Then applying the conservations of mass and momentum, a system of linear equations is resulted and can be solved by a sparse-matrix solver. If no barriers are presented on the steps, the proposed EMM formulation degenerates to the water wave scattering over undulating bottoms. The effects on the barrier lengths, barrier positions and oblique wave incidences by different undulated bottoms are studied. In addition, the EMM is also applied to solve the Bragg reflections of normal and oblique water waves by periodic barrier over sinusoidal bottoms. The accuracy of the solution is demonstrated by comparing it with the results in the literature.

Highlights

The interaction of surface water waves with an undulation bottom topography is a fundamental interest in understanding wave diffraction along the coastal region
When water waves are generated in deep to a shallow area in natural environments, they experience bathymetric variations, underwater obstacles, nonlinear wave interactions and others
Surface water wave scattering problems by thin impermeable barriers of submerged and bottom-standing configurations are formulated for waves over undulation bottom topography

Summary

Introduction

The interaction of surface water waves with an undulation bottom topography is a fundamental interest in understanding wave diffraction along the coastal region. When water waves are generated in deep to a shallow area in natural environments, they experience bathymetric variations, underwater obstacles, nonlinear wave interactions and others. These are some of the main natural causes that lead to coastal hazards, which seriously affect coastline and human activities. Breakwaters are conventional structures that often rest on the bottom foundation or pierced on the free surface They are specially designed to reduce the directed affectation of water waves from the open sea approach to the nearshore area. They are usually built to satisfy the requirements of maritime economic activities. Wang et al [12] considered the combined effects of multiple barriers and a single step bottom

Methods

Results

Conclusion