An Analytical Solution for the Interaction of Waves with Arrays of Circular Cylinders

Zhao Mi,Wang Piguang,Zhang Chao,Long Pengzhen,Du Xiuli,Mathiyalagan Kalidass

doi:10.1155/2021/5710894

Abstract

This paper presents an analytical method to investigate the multiple scattering problem within arrays of vertical bottom-mounted circular cylinders subjected to linear incident waves. Based on the Laplace equation and boundary conditions on the seabed and surface, a formulation of a two-dimensional multiple scattering problem is first obtained by using the variable separation method. Furthermore, the analytical solution of the wave forces on multiple circular cylinders is derived, which consists of the incident wave force due to the linear incident wave and the scattered wave forces considering multiple scattering waves. The presented analytical solution is validated by comparing its results with a numerical method, and the result shows that the analytical solution is in good agreement with the numerical one. Finally, the multiple scattering analysis is conducted on arrays of cylinders with different incident wave numbers, distances between cylinders, and quantities.

Highlights

Many sea-crossing bridges and offshore structures have been built worldwide in recent years
Pile group foundations play an important role in these offshore structures, and ocean wave is one of the major loadings that threaten the safety of offshore structures. erefore, it is necessary to determine the wave forces on offshore structures when designing and constructing those structures
An analytical solution for the linear wave diffraction by a bottom-fixed vertical circular cylinder in finite water depth was proposed by MacCamy and Fuchs [1]. is paper is to extend the analytical solution for a single circular cylinder to circular cylinder arrays

Summary

Introduction

Many sea-crossing bridges and offshore structures have been built worldwide in recent years. Linear diffraction theory is often used to analyze the interaction of ocean waves with cylinders based on the potential theory. Based on this theory, an analytical solution for the linear wave diffraction by a bottom-fixed vertical circular cylinder in finite water depth was proposed by MacCamy and Fuchs [1]. Bhatta et al presented an analytical approach to predict the wave forces due to scattering and radiation on a floating circular cylinder in the water of finite depth [5]. Liu et al presented analytical solutions to estimate the diffraction wave forces on a uniform vertical cylinder and a truncated cylinder whose cross sections are arbitrarily smooth [7, 8]. Zhai et al investigated the diffraction of waves from a system that is made up of a cylinder and an arc-shaped wall and proposed an analytical solution using the eigenfunction expansion approach [9]

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Conclusion