随着资源的开发进一步向深海海域推进，以各类圆柱结构为水下支撑结构的海洋结构物得到更加广泛的应用。波浪与圆柱群阵列的水动力相互作用是海洋工程结构设计的核心问题之一。对于像浅海海域的钻井平台，跨海大桥等结构物，作为支撑结构的圆柱群阵列坐于海底垂直穿出海面，一般模型化为坐底圆柱群阵列。对于像浮式钻井平台，海上漂浮机场等结构物，圆柱群阵列漂浮在海面上，各个圆柱单元之间是固定的，一般称为“柱间无相对运动”的截断圆柱阵列。而对于各个圆柱之间没有刚性连接或者刚性连接很弱的波浪能发电单元等结构物，在波浪作用下会产生相对位移，这一类圆柱群阵列称为“柱间有相对运动”的截断圆柱阵列。

目前来看，虽然基于势流理论的线性波浪理论正趋于成熟和完善，但是已有的研究对圆柱群阵列水动力特性的理解还不完整。对于坐底圆柱群阵列，许多学者对坐底圆柱阵列水动力幅值曲线所反映的捕获波模态以及其附近的一系列次级峰谷进行了大量研究。而对于水动力幅值曲线上反映的有规律的波动特性没有研究。对于截断圆柱阵列，目前的研究多集中于“柱间无相对运动”的截断圆柱阵列；而对波浪入射作用下的“柱间有相对运动”的截断圆柱阵列的水动力特性问题研究还相对较少。本文主要关注于对坐底圆柱阵列水动力波动特性的深入理解和对波浪入射作用下“柱间有相对运动”的截断圆柱阵列的水动力特性的研究。

对于有限长的单排坐底圆柱阵列，研究了水动力幅值随无量纲波数变化曲线的波动特性。经过大量的研究及规律总结，将坐底圆柱阵列水动力幅值曲线分为典型的三个区域。由捕获波模态引起的高耸的尖峰称为Region I；Region I左侧的一系列次级波峰和波谷称为Region II。除了Region I和Region II两个区域之外的区域被称为Region III。目前对Region I和Region II区域的研究和认识较为深入，而对Region III区域中波浪力幅值曲线的波动规律和物理意义认识较少。研究发现，在Region III区域，波浪力幅值曲线具有非常有规律的波动现象。该曲线相邻极大或极小值点的横坐标间距Δ在Region III中是定值，不随无量纲波浪频率改变。Δ只与阵列中圆柱总数N，标识圆柱位置的圆柱编号k，波浪入射角β有关。我们基于水波绕射理论和波的相长/相消理论这两种方法证明，上述看似复杂无章的波动现象实际上可以由非常简洁的公式来预测，并揭示了波动现象的物理机理。第k柱波动间距Δ的数值主要由第k柱上游和下游距离其最远的圆柱阵列端部的两个圆柱的贡献决定。这种波动现象是由于第k柱上下游柱子绕射波的相长和相消干涉交替出现所致，它与非齐次方程的解有关。相反Region I和Region II与齐次方程的特征值问题有关。

对于波浪入射作用下“柱间有相对运动”的截断圆柱阵列，重点研究了不同参数组合下的水动力特性。首先，基于相互作用理论，编写了波浪入射作用下“柱间有相对运动”的截断圆柱阵列绕-辐射计算程序，将波浪绕射激振力、绕辐射力、辐射运动振幅、波浪爬升以及水动力系数等物理量与已有文献进行了对比，验证了本文的正确性。其次，研究了柱间非传播模态对“柱间有相对运动”的截断圆柱阵列水动力特性的影响。研究发现，柱间距、水深-吃水比对柱间非传播模态都有影响。随着柱间距的增大，柱间非传播模态的影响越小；随着水深-吃水比的减小，柱间非传播模态的影响增大。然后，初步研究了“柱间有相对运动”的截断圆柱阵列波浪激振力和辐射问题的振幅的高耸的尖峰。研究发现，截断圆柱阵在波浪作用下的绕射水动力幅值曲线具有和坐底圆柱阵列的绕射水动力幅值曲线一样的波动特性，绕射水动力幅值曲线和辐射运动的振幅存在明显的类似于坐底圆柱阵列捕获波模态的高耸尖峰。最后，研究了水深-吃水比和阵列排布对波浪入射作用下“柱间有相对运动”的截断圆柱阵列波浪爬升的影响。截断圆柱阵列波浪爬升随着吃水的增加而增大，随着圆柱阵列行数的增加而增大。另外，波浪场中某一点的波浪爬升高程随无量纲波数的变化曲线存在与坐底圆柱阵列水动力幅值曲线类似的波动特性。波浪高程的计算点越靠近阵列前面几个圆柱，波动就越密集，反之亦然。

As the development of resources moves into deeper waters, marine structures supported by various types of cylinder arrays under waters are more widely used in ocean industry. Hydrodynamic interaction between waves and arrays consisting of large number of cylinders is one of the key problems in the design of ocean engineering structures. For structures like drilling platforms in shallow waters, and the concept of bridges across the sea, cylinder arrays used as a support structure sit at the bottom of the sea and pierce the water surface, which are generally modeled as arrays of bottom-mounted cylinders. For structures like floating drilling platforms and floating airports, where the supporting arrays consisting of cylinders float on the sea and the elements are fixed between each other, these types of arrays are generally called truncated cylinder arrays of “cylinders without relative motions”. And for structures like wave energy devices with weak or no rigid connection between elements, relative motions will occur between the elements under the action of incident waves. These types of arrays are generally modeled as truncated cylinder arrays of “cylinders with relative motions”.

For the current point of view, although the linear theory of waves based on the potential flow theory is tending maturity and perfection, the understandings of hydrodynamic characteristics of arrays consisting of cylinders are still incomplete. For arrays of bottom-mounted cylinders, many scholars have done a lot of researches on the narrow towering peaks corresponding to trapped modes and a sequence of secondary peaks and intermediate troughs associated with trapped modes of the hydrodynamic magnitude-wavenumber curve for a long array of bottom-mounted cylinders. However, there are no researches on the regular fluctuation characteristics reflected on the hydrodynamic magnitude-wavenumber curve. For arrays of truncated cylinders, the current researches mainly focus on truncated cylinder arrays of “cylinders without relative motions”. But for that of “cylinders with relative motions” under the action of incident waves, studies for the hydrodynamic characteristics are rare. This paper mainly focuses on the in-depth understanding of the fluctuation phenomenon of wave load for bottom-mounted cylinder arrays and hydrodynamic characteristics of truncated cylinder arrays of “cylinders with relative motions” under the action of incident waves.

The present paper studies the fluctuation characteristics of wave load against the non-dimensional wavenumber for a long but finite bottom-mounted array. With a lot of researches, the curve of magnitude of wave load acting on a certain cylinder in a long but finite array in the presence of incident waves can be divided into three regions in this study. Several spikes corresponding to the trapped modes are collectively termed Region I, a sequence of secondary peaks and intermediate troughs near Region I are termed Region II, and the regions other than Regions I and II are grouped into Region III. At present, although physical insights for in-depth understanding of the common phenomena in Regions I and II have been presented in many references, little is known about the fluctuation phenomenon of the magnitude of wave loads and its physical significance in Region III. In the present study, we found that the fluctuations in Region III are actually regular, and their characteristics can be predicted using simple analytical formulae. We found that in Region III, the horizontal distance D between two adjacent local maximum/minimum points is constant and does not change with non-dimensional wavenumbers. D is termed the minimum fluctuation spacing, which is related only to the total number of cylinders N, identification number k indicating the position of a cylinder, and wave incidence angle ꞵ. Based on the interaction theory and constructive/destructive interference, respectively, we demonstrate that the fluctuation characteristics can be predicted using simple analytical formulae and reveal the intrinsic mechanism of the fluctuation phenomenon. When the diffraction waves emitted from the cylinders at the ends of array and the cylinder concerned interfere constructively/destructively, peaks/troughs are formed. The fluctuation phenomenon in Region III is related to solutions of inhomogeneous equations. By contrast, spikes and secondary peaks are associated with solutions of the eigenvalue problem.

For truncated cylinder arrays of “cylinders with relative motions” under the action of incident waves, this paper mainly studies the hydrodynamic characteristics under different parameter combinations. Firstly, based on using the interaction theory, the calculation program for the diffraction-radiation theory of truncated cylinder arrays of “cylinders with relative motions” under the action of incident waves is developed and the correctness of this paper is verified by comparing the wave diffraction excitation force, radiation force, radiation motion amplitude, wave height and hydrodynamic coefficient with the existing literatures. Secondly, the effects of non-propagating modes (evanescent modes) between cylinders on hydrodynamic characteristics of truncated cylinder arrays of “cylinders with relative motions” are studied. It is found that the cylinder spacing, the depth-draft ratio and the total number of cylinders in the array have influence on the non-propagation modes between cylinders. With the increase of the cylinder spacing, the effects of the non-propagating modes between the cylinders become smaller. But as the depth-draft ratio decreases, the effects of non-propagating modes between cylinders will increase. Then, several towering narrow peaks of the magnitude of wave loads for diffraction problem and motion amplitudes for radiation problem are studied preliminarily. It is found that the magnitude of diffraction wave loads of truncated cylinder array under the action of incident waves has the same fluctuation characteristics as that of the bottom-mounted arrays, the magnitude of diffraction wave loads and the motion amplitudes of its radiation both have obvious towering peaks related to trapped modes of the bottom-mounted arrays. Finally, the effects of the depth-draft ratio and the array arrangement on the wave height for truncated cylinder arrays of “cylinders with relative motions” under the action of incident waves are studied. It is found that the wave height increases with the draft and the number of rows of the array. In addition, there exists some fluctuation characteristics in curve of wave height at a point in wave field against non-dimensional wavenumber, which is similar to magnitude of wave load acting on a certain cylinder in a long but finite bottom-mounted array. The fluctuation will be much denser if the calculation point of wave height is closer to the first several cylinders in the array, and vice versa.