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.

本文提出了一种基于均质化理论的新的理论框架，用于研究中等深度水中通过新兴柔性植被的小幅度周期性水波。植被由一系列具有统一属性的柔性悬臂式圆柱体建模。假设圆柱体以流入水波的频率在水流方向上以小幅度振荡，并且每个圆柱体在与其相邻圆柱体没有直接相互作用的情况下移动。使用同质化理论上，波浪柔性植被问题分别分为微观和宏观尺度问题。流体流动由入射波与刚性圆柱阵列之间的相互作用以及圆柱振动的贡献组成，它们在小振幅波理论的框架内叠加和耦合。微观问题采用有限元法数值求解，宏观问题采用二阶有限差分法求解。发现当杨氏模量E > 1 GPa。该模型还显示出与柔性气缸实验室数据的良好一致性。此外，还详细介绍了柔性圆柱体附近的流体流动，并对圆柱体材料特性对波衰减的影响进行了综合分析。