Wave transmission and reflection by multi-row submerged restored oyster reefs: laboratory experiments and empirical predictive formulas

Restored oyster reefs are increasingly considered nature-based coastal protection measures because they can reduce wave energy while providing ecological benefits. However, hydrodynamic design guidance for multi-row reef layouts, particularly under highly porous reef materials, remains limited. This study investigates the interaction of regular and irregular waves with multi-row submerged reefs for three configurations: impermeable (IM), porous (PO), and porous with an internal impermeable vertical screen (SC). A large experimental dataset was obtained for varying wave conditions, reef spacing, and reef row number. The analysis focuses on wave transmission coefficient Kt, wave reflection coefficient Kr, dissipation Kd2, and breaking. The results show that impermeable reefs attenuate incident waves primarily through relatively strong reflection together with breaking-induced dissipation, whereas porous and screened porous multi-row reefs attenuate waves through a combination of breaking, internal dissipation, and reflection. A modified empirical breaking boundary is proposed for PO and SC configurations within the tested range. Separate empirical expressions for Kt and Kr are derived for the three permeability conditions. Within the tested parameter ranges, the screened porous configuration yielded the lowest transmission levels. Within the tested parameter ranges, the results provide practical guidance for the hydraulic design of multi-row reefs and demonstrate that permeability should be considered explicitly.