Abstract Small-amplitude water waves passing through a suspended canopy is studied. The area of suspended canopy is modeled by an array of vertical rigid cylinders with periodic spacing. Assuming that the diameter of cylinders and their spacing are much smaller than the typical incident wavelength, the homogenization theory (method of multiple-scale perturbation) is applied to create coupled micro-scale (cylinder spacing) and macro-scale (wavelength) problems. The micro-scale problem describes turbulent flows within a unit cell of the cylinder array, being driven by the macro-scale pressure gradients. Employing the concept of averaged energy balance over a wave period, the micro-scale flows determine the eddy viscosity, which damps the waves in the macro-scale flows. Eigenfunction expansions method is used to solve the macro-scale problem, in which a complex frequency dispersion relation is solved numerically by a multiple successive approximation technique. The potential decomposition method, which can avoid solving a complex frequency dispersion relation, is also employed to validate the accuracy of the eigenfunction expansions method. Both methods yield accurate solutions. However, the eigenfunction expansions method is relatively straightforward and can unify the solutions for suspended canopy and emergent vegetation. A new set of flume experiments of waves through suspended canopy is conducted and experimental data are used to check present solutions. Very good agreement has been observed. Finally, the effectiveness of suspended canopy, submerged and emergent vegetation on wave attenuation is discussed.

中文翻译：

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通过悬垂的树冠的周期性水波

摘要 研究了小幅水波通过悬空冠层的问题。悬空冠层区域由一系列具有周期性间隔的垂直刚性圆柱体建模。假设圆柱体的直径及其间距远小于典型的入射波长，应用均质化理论（多尺度扰动方法）来创建耦合的微观尺度（圆柱间距）和宏观尺度（波长）问题。微观问题描述了由宏观压力梯度驱动的圆柱阵列单元内的湍流。利用波浪周期内平均能量平衡的概念，微观流动决定了涡粘性，从而抑制了宏观流动中的波浪。特征函数展开方法用于解决宏观尺度问题，其中复杂的频率色散关系通过多重逐次逼近技术进行数值求解。还采用势分解方法来验证特征函数展开方法的准确性，该方法可以避免求解复杂的频率色散关系。这两种方法都能产生准确的解。但是，特征函数展开法相对简单，可以统一悬空冠层和挺水植被的解。进行了一组新的水槽波浪通过悬浮冠层的实验，并使用实验数据来检查现有的解决方案。已经观察到非常好的一致性。最后，讨论了悬垂的树冠、沉水和挺水植被对波浪衰减的有效性。