Wave Attenuation by Vegetation

TLDR

The study models small‑amplitude waves over submerged vegetation by applying continuity and linearized momentum equations above and within the vegetation, treating vegetation effects as a drag force, and validating the analytical solution against 60 test runs with artificial kelp. The analytical solution predicts exponential wave‑height decay, with wave‑number and decay‑coefficient expressions reducing to linear‑wave theory for weak damping, and shows that calibrated drag coefficients vary widely due to kelp motion and viscous effects, while the model also indicates subaerial vegetation could dissipate wave energy more effectively.

Abstract

The vertically two‐dimensional problem of small‐amplitude waves propagating over submerged vegetation is formulated using the continuity and linearized momentum equations for the regions above and within the vegetation. The effects of the vegetation on the flow field are assumed to be expressible in terms of the drag force acting on the vegetation. An analytical solution is obtained for the monochromatic wave whose height decays exponentially. The expressions for the wave number and the exponential decay coefficient derived for arbitrary damping are shown to reduce to those based on linear wave theory and the conservation equation of energy if the damping is small. The analytical solution is compared with 60 test runs conducted using deeply submerged artificial kelp. The calibrated drag coefficients for these runs are found to vary in a wide range and appear to be affected by the kelp motion and viscous effects that are neglected in the analysis. The analytical solution is also shown to be applicable to subaerial vegetation, which is predicted to be much more effective in dissipating wave energy.