Green-gray connections: Coupled equations of wave attenuation and structural response for engineering design of hybrid infrastructure

A quantitative method is proposed for predicting the engineering performance of a hybrid green-gray system comprised of a mangrove forest seaward of a conventional engineered structure to mitigate wave action. The method coupled existing empirical equations to (1) predict the wave height attenuation of random waves transmitted through the mangrove forest and (2) use the resulting significant wave height as input to existing equations to estimate wave overtopping on a vertical wall or rubble-mound revetment or wave force on a vertical wall. The predicted wave height attenuation was parameterized by a drag coefficient obtained from an empirical relation developed from previous laboratory results. The method was validated with data from two large-scale wave flume studies of wave overtopping and wave force, which used similar model mangroves at 1:2 and 1:1 scale, respectively. The method conservatively predicted the overtopping of a vertical wall or rubble-mound revetment within a factor of 1.7 for discharge rates greater than 1 × 10⁻³ m³/s/m and a factor of 3.5 for discharge rates greater than 1 × 10⁻⁴ m³/s/m. The predictions of wave forces were also conservative and were within a factor of 1.3 compared to the measurements. The overprediction of the wave force increased slightly with mangrove forest density, indicating a possible interaction between the waves and the green and gray features that reduced the wave forces more than expected from the wave attenuation alone. The apparent interaction was small, and the results of the proposed method were reasonable compared to the observations. The present results show promise for a design approach which assumes independent performance of the components to motivate a calculation coupling empirical equations to estimate the performance of hybrid green-gray systems for coastal defenses. Future study is necessary to parameterize wave attenuation by natural mangrove forests and to account for nonlinear processes such as wave breaking and wave-induced setup.