A comparative study of wave scattering by a submerged porous breakwater in wall-bounded and unbounded domains

Wave scattering over porous structures plays an important role in the design of coastal and offshore protective structures. The present study investigates the scattering of water waves over a finite porous region with three primary objectives: (a) to compare the hydrodynamic behaviour under two scenarios: bounded by a rigid wall and unbounded; (b) to examine the influence of turbulence by comparing two resistance coefficient models, one incorporating the turbulent term and one neglecting it; and (c) to analyse the hydrodynamic coefficients for varying physical parameters under each scenario and model. The resistance coefficient is formulated by incorporating laminar, inertial, and turbulent terms, and the eigenfunction expansion method is employed to find the hydrodynamic coefficients. The numerical results reveal that incorporating turbulence gives significantly greater energy dissipation and reduced net wave load, particularly in the low frequency range and for structures with lower porosity. This study presents a mathematical approach to wave scattering over porous structures, offering a basis for future nonlinear models. Beyond its mathematical contribution, the present analysis also provides guidance into the practical performance of porous structures in different coastal engineering configurations. In particular, the findings offer practical guidance for two common design contexts: minimising wave induced loading on breakwaters attached to quays or seawalls, and maximising the attenuation and coastal protection afforded by free standing offshore breakwaters constructed from coarse, highly permeable material.