Flume experiments on wave attenuation through combined flexible and rigid vegetation

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Vegetation-based wave attenuation provides a sustainable alternative to conventional coastal protection structures; however, the attenuation characteristics of combined flexible and rigid vegetation systems remain insufficiently understood. This study experimentally investigates wave attenuation through combined rigid and flexible vegetation under regular wave conditions. The results show that wave attenuation increases with increasing rigid vegetation proportion and exhibits a nonlinear saturation tendency under relatively deep-water conditions. Compared with flexible vegetation, rigid vegetation provides higher hydrodynamic resistance to wave-induced flow, whereas flexible vegetation undergoes deformation and reconfiguration, resulting in reduced effective resistance. Water depth, incident wave height, and wave period further regulate attenuation by modifying wave-vegetation interactions and the relative contributions of rigid and flexible components. Based on the experimental dataset, a nonlinear contribution model is developed to describe the combined attenuation characteristics of rigid and flexible vegetation. The model agrees well with measured results and reveals nonlinear and asymmetric contributions of the two vegetation components within the tested experimental conditions. These findings improve the understanding of wave attenuation processes in mixed vegetation systems and provide a quantitative basis for evaluating vegetation composition effects on wave attenuation.