Multiple-scales analysis of wave evolution in the presence of rigid vegetation

The study of free-surface flows over vegetative structures presents a challenging setting for theoretical, computational and experimental analysis. In this work, we develop a multiple-scales asymptotic framework for the evolution of free-surface waves over rigid vegetation and a slowly varying substrate. The analysis quantifies the balance between the competing effects of vegetation and shoaling, and provides a prediction of the amplitude as the wave approaches a coastline. Our analysis unifies and extends existing theories that study these effects individually. The asymptotic predictions are shown to provide good agreement with full numerical simulations (varying depth) and published experimental results (constant depth).