Numerical Simulation of the Field Velocities and Local Disturbances of a Long Gravity Wave Passing above an Immersed Vertical Barrier

Guerziz Allaoua,Laouar Abdelhamid

doi:10.1155/2008/135982

Abstract

This work is interested in the study of the passage of a long gravity wave above an immersed vertical barrier. The latter is placed at a right angle in the middle of the occupied fluid domain which is limited vertically by both a free surface and an impermeable horizontal bottom. We want to determine the field velocity and the local disturbances in the vicinity of the barrier. For this, we use the generalized theory of shallow water and complex variables method. For illustration, we consider a solitary wave as an emitted long wave.

Highlights

The problem ofthe passage of gravity waves above an immersed obstacle was studied by several authors cf. 1–5
This work is interested in the study of the passage of a long gravity wave above an immersed vertical barrier
The latter is placed at a right angle in the middle of the occupied fluid domain which is limited vertically by both a free surface and an impermeable horizontal bottom

Summary

Introduction

The problem ofthe passage of gravity waves above an immersed obstacle was studied by several authors cf. 1–5. Dean’s work 2 is classified in the theory of the short waves; it concerns the determination of the coefficients of reflection and transmission of the waves passing a completely immersed obstacle e.g., a barrier. In 6 , the study of a passage of a long wave over vertical barrier, Germain’s shallow water theory associated with the complex variable method has been used to determine the flow. We would like to know with accuracy the kinematic of the flow at the vicinity of the obstacle while the passage of the long gravity wave above the thin immersed vertical barrier. The last section presents an application and a numerical simulation

Description of the phenomenon

System of equations

Technique of resolution

A6 a b

Application

Numerical simulation