Wave resonance reduction over a linear transition bottom with a submerged porous breakwater

Abstract

The wave shoaling phenomenon, driven by changes in seabed morphology, poses a significant threat to coastal regions. Breakwaters are a widely used solution to mitigate these effects. This study introduces a mathematical model to evaluate the effectiveness of submerged porous breakwaters in reducing wave amplitudes over a linear transition bottom—a scenario previously underexplored in the literature. We address two critical issues: wave attenuation and resonance phenomena. Using a modified shallow water equation model for a two-layer system, we analytically derive the wave transmission coefficient and the basin's natural period, essential for understanding resonance. Numerical simulations, based on a finite volume method applied to a staggered grid, are performed to assess the impact of the linear transition bottom and porous breakwaters. Our findings demonstrate that submerged porous breakwaters effectively mitigate shoaling effects by attenuating wave amplitudes and reducing resonance risks, thereby enhancing their role as reliable coastal protection structures.