Nature-inspired resilience: A macroscopic numerical modelling study of wave interactions with artificial reefs

Porous artificial reefs are increasingly deployed as ecologically enhanced hybrid coastal protection measures, yet predictive frameworks that represent wave energy losses within their internal structure remain limited. This study proposes a novel modular porous artificial reef concept ( Wavesphere ) and develops a calibrated macroscopic numerical framework that represents the reef as an equivalent porous momentum sink within a phase-resolved wave tank. By embedding a pressure-drop formulation into the governing equations and calibrating resistance coefficients against laboratory transmission data, the model captures distributed energy losses without resolving pore-scale flow. Validation against controlled flume experiments across varying water depths (0.25 to 0.375 m) and incident wave heights (0.025 m to 0.112 m) demonstrates strong agreement in the transmission, reflection, and residual energy-loss coefficients. Within the calibrated macroscopic framework, phase-resolved model diagnostics indicate that the equivalent porous region redistributes and attenuates model-resolved wave-induced kinetic energy, with energetic motion concentrated upstream, a persistently low-energy porous region, and limited downstream recovery. Parametric analysis identifies systematic scaling relationships: increasing relative wavelength λ / D s (4.66–10.015) enhances transmission coefficient K t (0.581–0.662) while reducing residual energy-loss coefficient K d (0.642–0.526), whereas increasing wave steepness k A (0.039–0.157) suppresses K t (0.776–0.683) and elevates K d (0.364–0.503). The relative structure height h s / d exhibits a more pronounced effect over the submerged to partially emerged range, with K t decreasing from 0.878 to 0.636 and K d increasing from 0.222 to 0.581 as h s / d increases from 0.8 to 1.2. The consistently low reflection coefficient ( K r < 0.2 ) indicates that reflection plays only a minor role, while the attenuation response is characterised by partial transmission and a comparatively large residual energy-loss component. Additional simulations using JONSWAP-based focused waves indicate that the porous reef suppresses the focused crest amplitude at the nominal focusing location and redistributes spectral energy along the flume. Overall, the proposed Wavesphere concept, together with the calibrated macroscopic framework, provides a practical basis for preliminary design-oriented assessment of porous artificial reefs.