A semi-analytical solution for water wave scattering by partially immersed perforated and solid barriers with a quadratic pressure discharge condition

Abstract

Partially immersed perforated and/or solid barriers in the ocean are often considered as important components of many marine applications, and they have received significant attentions by ocean engineering research community with potential flow methods. In this study, water wave interaction with a system that consists of a vertical perforated front barrier and a vertical impermeable rear barrier, as a representative unit, is investigated based on the linear potential flow theory. A semi-analytical solution for this problem is derived using an eigenfunction expansion method and an iterative resolution method. To model the flow passing through the perforated barrier, a quadratic pressure discharge condition of practical validity is applied. The reflection coefficient predicted by the present analytical model agrees well with the published theoretical result. The validated model is used to perform a parametric study to examine the effects of the width, submergence depth, porosity, incident wave steepness and wave frequency on the hydrodynamic characteristics of the perforated system. It is found that larger incident wave steepness can result in smaller transmission coefficient and dimensionless horizontal wave force acting on the impermeable rear barrier and larger dimensionless horizontal wave force acting on the perforated front barrier due to the nonlinear nature of the quadratic pressure discharge condition. By examination over a broad range of circumstances, we find that the partially immersed perforated system is more effective when the ratio of the width to the incident wavelength B/L is located between 0.2+0.5n and 0.35+0.5n (n=1,2,…). The present study can be utilized for a range of marine applications in wave preventing and wave energy absorption or conversion.