Effect of flexible coastal vegetation on waves in water of intermediate depth

This paper presents a new theoretical framework, based on the homogenization theory, for studying small-amplitude periodic water waves through emergent flexible vegetation in water of intermediate depth. The vegetation is modeled by an array of flexible cantilever-type cylinders with uniform properties. It is assumed that the cylinders oscillate with small amplitude in the stream-wise direction at the frequency of incoming water wave, and that each cylinder moves without the direct interaction with its neighbors. Using the homogenization theory, the wave-flexible-vegetation problem is separated into micro- and macro-scale problems, respectively. The fluid flows consist of contributions from the interactions between incident waves and an array of rigid cylinders and the vibrations of cylinders, which are superimposed and coupled within the framework of small-amplitude wave theory. The micro-scale problem is solved numerically by a finite-element method, while the macro-scale problem is solved using a second-order finite difference method. It is found that the present model can successfully reproduce the results of rigid stationary forest, when the Young's modulus E > 1 GPa. The model also shows good agreements with laboratory data for flexible cylinders. Moreover, the detailed fluid flows in the vicinity of a flexible cylinder, and a synthetic analysis of the effects of cylinder material properties on wave attenuation are also presented.