Towards a unified drag coefficient formula for quantifying wave energy reduction by salt marshes

Coastal regions are susceptible to increasing flood risks amid climate change. Coastal wetlands play an important role in mitigating coastal hazards. Vegetation exerts a drag force to the flow and dampens storm surges and wind waves. The prediction of wave attenuation by vegetation typically relies on a pre-determined drag coefficient C-D. Existing C-D formulas are subject to vegetation biomechanical properties, especially the flexibility. Accounting for vegetation flexibility through the effective plant height (EPH), we propose and validate a species-independent relationship between C-D and the Reynolds number Re based on three independent datasets that cover a wide range of hydrodynamic conditions and vegetation traits. The proposed C-D-Re relationship, used together with EPH, allows for predicting wave attenuation in salt marshes with high accuracy. Furthermore, a total of 308,000 numerical experiments with diverse wave conditions are conducted using the proposed C-D-Re relationship and EPH to quantify the wave attenuation capacity of two typical salt mash species: Elymus athericus (highly flexible) and Spartina alterniflora (relatively rigid). It is found that wave attenuation is controlled by wave height to water depth ratio and EPH to water depth ratio. When swaying in large waves in shallow to intermediate water depth, a 50-m-long Elymus athericus field may lose up to 30% capacity for wave attenuation. As wave height increases, highly flexible vegetation causes reduced wave attenuation, whereas relatively rigid vegetation induces increased wave attenuation. The leaf contribution to wave attenuation is highly dependent on the leaf rigidity. It is recommended that leaf properties, especially its Young's modulus be collected in future field experiments.