Porosity Effects on the Dispersion Relation of Water Waves through Dense Array of Vertical Cylinders

Joffrey Jamain,Vincent Rey,Julien Touboul,Kostas Belibassakis

doi:10.3390/jmse8120960

Abstract

There is growing interest for water-wave flows through arrangements of cylinders with application to the performance of porous marine structures and environmental flows in coastal vegetation. For specific few cases experimental data are available in the literature concerning the modification of the dispersion equation for waves through a dense array of vertical cylinders. This paper presents a numerical study of the porosity effects on the dispersion relation of water waves through such configurations. To this aim, the sloshing problem in a tank full of vertical cylinders intersecting the free surface is studied using the finite element method, and the influence of the porosity on the wave number is quantified. On the basis of numerical results, a new modification of a dispersion relation for porous medium is suggested based on a wide range of collected data. Moreover, the domain of validity of this new dispersion relation is examined considering the number of cylinders and the extrapolation to the infinite medium.

Highlights

For many years, the scientific community dedicated significant efforts to the understanding and modeling of the wave–structure interaction; see, e.g., Mei [1] and Molin [2]
After the validation of for rectangular tank with vertical walls against the 61 the finite element method (FEM) solver theoretical value of k for213 a tank without cylinders, the present method was tested against the experimental value for a dense array of cylinders presented in Molin et al [26]; see Figure 9
After the validation of the FEM solver for rectangular tank with vertical walls against the theoretical value of k for a tank without cylinders, the present method was tested against the experimental value for a dense array of cylinders presented in Molin et al [26]; see Figure 9

Summary

Introduction

The scientific community dedicated significant efforts to the understanding and modeling of the wave–structure interaction; see, e.g., Mei [1] and Molin [2]. Many experimental works (e.g., Goda [3]), mathematical models and numerical methods (e.g., John [4], Yang and Ertekin [5]) are developed to understand the reference problem of water waves interacting with a single, bottom mounted or floating, surface piercing, vertical cylinder; see Young [6], Sabunku and Calisal [7]. With the development of complex ocean structures, such as very large floating structures (Wang and Tay [9]), arrays of devices for the outtake of marine renewable energies (Falnes [10], Balitsky et al [11]), and for porous coastal and harbor defenses (Arnaud [12]), the problem has been expanded to more complex geometrical configurations, where dense arrangements of vertical cylinders are involved. There is growing interest concerning similar problems in environmental flows in vegetation, such as the propagation of water waves in mangrove forests (e.g., Massel [13], Mei et al [14])

Objectives

Results

Conclusion