ABSTRACT:

A Boundary Element Model is used in this, paper to calculate solitary, wave motion in front of a vertical "wall. Its fundamental formulation is based on Cauchy"S integral theorem, similar to that of Vinje and Brevig (1981)., The mathematical and numerical formulation of the model is described. A method of dealing with the reflected waves is proposed. "The comparison between numerical and experimental results shows good agreement.

INTRODUCTION

Vertical walls are widely used in coastal and port engineering., Wave forces are the main active load on the structures. In coastal areas, due to the large value of ratio between wave height and water depth, waves are nonlinear. Using linear, wave theory to calculate waves in front of a vertical wall often leads to under estimated values. It is needed to use nonlinear wave theory. Linear or weakly nonlinear irrotational surface waves evolving slowly "can be considered as time-harmonic which enables the time dependency. to be separated from the wave equation. A simple relationship between the surface displacement and the velocity potential can be established. For strongly nonlinear waves, such as solitary waves, there is no such simple relationship as the waves are no longer time-periodic. More sophisticated techniques are therefore required. Among these techniques the one based on Boundary Element Method (BEM) can be considered as one of the most efficient methods. The problem of determining solitary waves in front of a vertical wall usually arises in the study of the coastal effects of tsunamis. Tsunamis are long water waves of small steepness generated by impulsive geophysical events on the "ocean floor or at the coastline. Solitary waves are believed to model some important aspects of tsunamis well Tsunamis frequently, happen and lead to huge loses of property and life.

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