本文關(guān)鍵詞： 窩坑陣列 理想地形 多重散射 長波方程 修正緩坡方程 解析解　出處：《廣西民族大學》2016年碩士論文　論文類型：學位論文

【摘要】：本學位論文致力于研究線性水波越過水下變水深軸對稱理想窩坑陣列時散射問題的解析模擬.為了解析解構(gòu)造的可行與方便,我們假定每個窩坑具有軸對稱性,并且為理想窩坑,即以每個窩坑的中心為坐標原點時,相應(yīng)的水深函數(shù)為徑向變量的冪函數(shù):h(r)=βr-α(α0).在此假設(shè)之下,在窩坑內(nèi)的變水深區(qū)域,對線性長波方程可以求出封閉解析解,對修正緩坡方程則可以求出Taylor級數(shù)形式的解析解,而在窩坑外的常數(shù)水深區(qū)域,控制方程退化為Helmholtz方程,容易求出通解.最后對窩坑內(nèi)外求得的通解在所有窩坑邊沿進行耦合,據(jù)此求出通解的系數(shù).與研究單個窩坑散射問題相比,研究窩坑陣列散射問題的難度和復雜性大增,因為所有窩坑各自產(chǎn)生的散射效應(yīng)會相互干涉,它所導致的解析求解方面的麻煩在于,在每個窩坑小范圍內(nèi)求出的自由水面高程的通解都是針對每個窩坑建立的局部坐標系得到的,不同坐標體系下的邊界耦合無法開展,需要利用Graf加法定理將窩坑外圍常數(shù)水深區(qū)域的通解分解為各個局部坐標系下的函數(shù)的疊加.本文有關(guān)線性水波越過水下變水深窩坑陣列的級數(shù)解析解不但推廣了有關(guān)單個窩坑的長波方程解析解和修正緩坡方程解析解,也推廣了水深為分片常數(shù)的圓柱陣列的解析解,即這些解析解均為本文解析解在特殊簡單地形下的特例.基于本文的解析解,我們研究了入射角,窩坑個數(shù),窩坑大小等因素對自由液面相對波高的影響.
[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- 偽 (偽 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.
【學位授予單位】：廣西民族大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：P75;P731.2

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