Wave-induced forces on submerged permeable fence-like structures: prototype-scale experiments and empirical model

Permeable, fence-like coastal structures are increasingly deployed in coastal engineering applications for wave attenuation and shoreline stabilization. Despite their growing relevance, a quantitative understanding of wave-induced forces on quasi-two-dimensional permeable structures remains limited, particularly regarding the role of structural permeability on hydrodynamic loading. This study presents results from prototype-scale wave flume experiments in which fully submerged permeable ( p = 0 − 0.25 ) willow fences were exposed to oscillatory flow across three water depths, covering shallow to transitional water ( 0.03 < d / L m < 0.24 ). Drag and inertia coefficients were determined using a weighted least squares (WLS) approach within the Morison equation framework. The results demonstrate a strongly drag-dominated hydrodynamic response across all tested configurations ( C D = 3.1 − 24.9 ), with inertia contributions becoming negligible for permeable structures. The drag coefficient C D is shown to depend on both the Reynolds number R e and the permeability p . Based on regression analysis, a novel empirical model is proposed that expresses the drag coefficient as a function of these two parameters. By incorporating high-permeability data from the literature, the scope of the model is extended to permeabilities up to p = 0.8 . The proposed model reproduces the calculated drag coefficients (derived from WLS) with a mean deviation of − 0.43 and a standard deviation of 1.98 , demonstrating robust predictive capability within the investigated range. The findings offer a practical engineering tool for the rapid estimation of wave-induced forces on fully submerged, quasi-two-dimensional coastal structures such as groynes and willow or bamboo fences, directly supporting their hydrodynamic design in coastal protection schemes