New analytical solutions of oblique wave scattering by submerged horizontal perforated plates using quadratic pressure drop condition

Abstract

This study develops new analytical solutions for oblique wave scattering by horizontal perforated plates submerged below the water free surface using a quadratic pressure drop boundary condition. Both kinds of submerged plates are considered: a) A horizontal perforated plate as an offshore breakwater; b) A horizontal perforated plate attached to a vertical wall as a wave absorber. The velocity potential decomposition method combined with an efficient iterative algorithm is adopted to obtain the analytical solutions, and the hydrodynamic parameters of engineering interest for the reflection, transmission and energy-loss coefficients as well as the vertical wave force are considered. A new simple formula for predicting the discharge coefficient in the quadratic pressure drop condition, which is critical to make the analytical solutions to be practically applicable, is developed by fitting the analytical results and an amount of experimental data in literature. The present analytical solutions are in good agreement with previous analytical solution for special case and the numerical results of an independently developed multi-domain boundary element method solution. The reflection and transmission coefficients calculated by the present analytical solutions are also in good agreement with experimental data when adopting a well-predicted discharge coefficient. The present analytical solutions are valuable for fast assessing the hydrodynamic performance of horizontal perforated plates in the initial stage of engineering design. The present analytical model can also be readily extended to the multi-layer horizontal perforated plates and similar structures.