Theoretical Models for Wave Energy Dissipation Caused by Vegetation

Abstract

The paper presents theoretical and numerical analyses of random wave attenuation attributable to vegetation. Existing models based on Rayleigh distribution of wave heights are critically examined followed by the development of two new models for random waves over vegetation. The first model is derived on the basis of Hasselmann and Collins’ treatment of energy dissipation of random waves attributable to the bottom friction. The second model is derived on the basis of Longuet-Higgins’ probability density function for the joint distribution of wave heights and wave periods, which recovers to the model that uses the Rayleigh distribution of wave heights if the spectrum becomes narrow banded. Such a model allows for quantifying the effects of the spectral width on the model performances. Comparisons of the modeled and measured root-mean-square wave heights over vegetation show good agreement. Moreover, the Joint distribution-based model provides insight into the spectral distribution of the energy dissipation, which is different from other dissipation models that follow exactly the wave energy spectrum.