Wave diffraction modifies attenuation in semi-infinite submerged vegetation

Abstract

Coastal vegetation is increasingly recognized for enhancing coastal resilience against climate change. Studies show that alternating vegetated and unvegetated patches can effectively dissipate wave energy, while emphasizing the need to better characterize wave diffraction in such configurations. In this study, we develop a semi-analytical framework that combines vegetation-induced wave attenuation with diffraction for regions partially covered by submerged vegetation and evaluate it using experiments. The model extends classical semi-infinite breakwater diffraction theory by incorporating Dalrymple-type dissipation due to an array of vegetation elements and an empirical lateral scaling that accounts for the porous nature of the vegetation. Under assumptions of spatially uniform vegetation within the vegetated region, laterally uniform incident waves, and linear wave dynamics, the local velocity potential is expressed as the incident potential multiplied by a modified diffraction coefficient. Twenty-one experiments were conducted in a shallow wave basin under varying wave heights, periods, and water depths for semi-infinite and periodically arranged vegetation patches. Comparisons between analytical predictions and over 15,000 wave-height measurements show that the model captures the dominant attenuation–diffraction patterns under the tested conditions, with a typical normalized RMSE of approximately 13%. The analysis clarifies how to estimate the wave decay coefficient in laterally non-uniform wave fields and demonstrates that, for the geometries tested, Dalrymple's formulation remains applicable when the wave decay coefficient is based on locally attenuated waves. This coupled diffraction–attenuation framework provides a practical tool for analyzing hydrodynamics in partially vegetated regions and for guiding the arrangement of vegetated patches in nature-based coastal-protection systems.