水波越过变水深轴对称理想窝坑阵列的解析模拟

发布时间：2018-01-20 06:47

本文关键词： 窝坑阵列理想地形多重散射长波方程修正缓坡方程解析解　出处：《广西民族大学》2016年硕士论文　论文类型：学位论文

【摘要】：本学位论文致力于研究线性水波越过水下变水深轴对称理想窝坑阵列时散射问题的解析模拟.为了解析解构造的可行与方便,我们假定每个窝坑具有轴对称性,并且为理想窝坑,即以每个窝坑的中心为坐标原点时,相应的水深函数为径向变量的幂函数:h(r)=βr-α(α0).在此假设之下,在窝坑内的变水深区域,对线性长波方程可以求出封闭解析解,对修正缓坡方程则可以求出Taylor级数形式的解析解,而在窝坑外的常数水深区域,控制方程退化为Helmholtz方程,容易求出通解.最后对窝坑内外求得的通解在所有窝坑边沿进行耦合,据此求出通解的系数.与研究单个窝坑散射问题相比,研究窝坑阵列散射问题的难度和复杂性大增,因为所有窝坑各自产生的散射效应会相互干涉,它所导致的解析求解方面的麻烦在于,在每个窝坑小范围内求出的自由水面高程的通解都是针对每个窝坑建立的局部坐标系得到的,不同坐标体系下的边界耦合无法开展,需要利用Graf加法定理将窝坑外围常数水深区域的通解分解为各个局部坐标系下的函数的叠加.本文有关线性水波越过水下变水深窝坑阵列的级数解析解不但推广了有关单个窝坑的长波方程解析解和修正缓坡方程解析解,也推广了水深为分片常数的圆柱阵列的解析解,即这些解析解均为本文解析解在特殊简单地形下的特例.基于本文的解析解,我们研究了入射角,窝坑个数,窝坑大小等因素对自由液面相对波高的影响.
[Abstract]:This dissertation is devoted to the analytical simulation of the scattering problem of linear water waves over the underwater axisymmetric ideal pit array. For the feasibility and convenience of constructing the analytical solution, we assume that each pit is axisymmetric. And it is an ideal pit, that is, when the center of each pit is taken as the origin of the coordinate, the corresponding water depth function is the power function of radial variable: Hu rn = 尾 r- 伪 (伪 0). Under this assumption. In the region of varying water depth in the pit, the closed analytical solution can be obtained for the linear long-wave equation, the analytical solution for the modified gentle slope equation can be obtained in the form of Taylor series, and the constant water depth region outside the pit can be obtained. The governing equation is degenerated into Helmholtz equation, which is easy to obtain the general solution. Finally, the general solution obtained inside and outside the pit is coupled at the edge of all pits. Compared with the study of single pit scattering, it is more difficult and more complex to study the scattering problem of pit array, because the scattering effect of all pits will interfere with each other. The problem with the analytical solution is that the general solution of the free water surface height obtained in the small range of each pit is obtained from the local coordinate system established for each pit. The boundary coupling under different coordinate systems cannot be carried out. It is necessary to decompose the general solution of the constant water depth region around the pit into the superposition of the functions in each local coordinate system by using the Graf addition theorem. In this paper, the series analytic solution of linear water wave over the array of variable depth pits under water is discussed. However, the analytical solutions of the long wave equation and the modified gentle slope equation for a single pit are generalized. We also generalize the analytical solutions of cylindrical arrays whose water depth is piecewise constant, that is, these analytical solutions are special cases of the analytical solutions in this paper under the special simple terrain. Based on the analytical solutions in this paper, we study the incidence angle and the number of pits. The influence of pit size and other factors on the relative wave height of free liquid surface.
【学位授予单位】：广西民族大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：P75;P731.2

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