A theoretical model for solving wave scattering by multiple submerged horizontal plates and membranes

Abstract

This paper presents a theoretical model for water wave scattering by arrays of submerged horizontal plates and membranes. Based on linear potential flow theory and the Fourier transform, the model overcomes limitations of eigenfunction matching by accommodating arbitrary plate arrangements. The potential jump across the plate is represented using Chebyshev polynomial expansions that inherently capture edge singularities, ensuring rapid convergence. A key theoretical finding proves that swapping the positions of two staggered porous flexible plates leaves the wave transmission coefficient unchanged across all frequencies. For coaxial dual plates, the reflection coefficient exhibits bimodal peaks. Staggered or side-by-side configurations shift these peaks lower and enhance short-wave attenuation. Larger plate spacing amplifies force oscillations on the seaward plate due to wave interference. The model is extended to analyse wave scattering by metastructures with square, circular, trapezoidal, and inverted trapezoidal profiles. The inverted trapezoidal design enhances low-frequency reflection through its extended shallow plates, while its deeper elements reduce short-wave interaction, enabling optimised performance for coastal protection applications.