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Analytical Simulations for Long Waves Scattering by an Un-idealized Submerged Breakwater and by a Cylinder with a Scour Trench

Author: LiuRui
Tutor: LiuHuanWen
School: Guangxi University for Nationalities
Course: Computational Mathematics
Keywords: Breakwater Island with scour pit Long wave equation Analyticalsolution Taylor series Reflection coefficient Maximum wave amplification
CLC: O241.6
Type: Master's thesis
Year: 2011
Downloads: 14
Quote: 1
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Abstract


During the propagation of ocean surface waves from the deep ocean to coastal region,wave scattering (reflection, refraction and diffraction) will occur because the water depthbecomes shallower and shallower, which leads to wave runup with great energy. These waveenergies on one hand can benefits human being, for example they produce electricity throughwave power station, on the other hand, they may brings great damage to the coastline andcoastal constructions such as port and platform. It is significant in theory and applicationto study the propagation of ocean waves.Ocean surface waves can be classified into three kinds: long waves, intermediate wavesand short waves. This thesis focus on long waves governed by the long-wave equation. Gen-erally, three main methods are used in the simulation of wave scattering, they are analyticalmodelling, numerical modelling and experimental modelling. In this thesis, we focus on theanalytical modelling.Submerged breakwaters can be used to reflect ocean waves an to protect coastline andcoastal constructions. The first goal of this thesis is to conduct analytical study for wavepropagation over a submerged breakwater with un-idealized shapes. By solving the long-wave equation, an analytical solution of the reflection coeflcient in the Taylor series formis presented. Because of the generality of the shape of the breakwater in this study, theanalytical solution obtained in this study finds almost all well-known analytical solutions tobe its special cases, which include the wave reflection from a rectangular obstacle by Mei,an infinite step by Lamb, an infinite step behind a linear slope by Dean, an infinite stepbehind a parabolic slope by Kajiura, an trench of general trapezoidal shape by Liu andLin and a breakwater of general trapezoidal shape by Lin and Liu. The present analyticalsolution, however, covers a much wider range of problems. On the other hand, also becauseof the un-idealization of the shape of the breakwater in this study, it is more di?cult toobtain an analytical solution since the singularities to the governing equation become morecomplicated, therefore the solution technique need to be more skillful, see details in section2.2.In the second part of this thesis, wave scattering by a cylindrical island with a scour pitis studied based on the long-wave equation. Using the technique of variable separation, thetwo dimensional partial di?erential equation can be simplified into an ordinary differential equation and a solution in the form of Taylor series is found. This solution includes Mac-Camy and Fuchs’classical analytical solution for wave scattering by a cylindrical island asa special case. Based on the computational results of our analytical solution, the influenceof the scour pit’s width and depth on the wave amplification is investigated.

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > Linear algebra method of calculating
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