【摘要】：海洋有著豐富的資源,開發(fā)利用海洋資源有助于緩解社會(huì)發(fā)展與陸上資源短缺的矛盾。海洋中的島礁為人們利用海洋中的自然資源提供了便利。弄清島礁周圍的水動(dòng)力環(huán)境也是合理利用海島資源必不可缺的。 以三維Laplace方程作為控制方程,由格林第二定理導(dǎo)出邊界積分方程,采用時(shí)域高階邊界元方法研究了波浪在島礁地形的繞射問題。其中,格林函數(shù)選用Rankine源和它關(guān)于水平海底的像,去除了局部地形以外的水平海底邊界,積分區(qū)域?yàn)榫植康匦魏陀邢迏^(qū)域的靜水面。數(shù)值過程中,運(yùn)用高階邊界元方法離散此方程。采用預(yù)修正快速傅里葉變換的方法,不顯示生成由積分方程得到的線性方程組,算法的存儲(chǔ)量由顯示生成的O(N2)降為O(N),計(jì)算量由直接求解顯示線性方程組所需的O(N3)降為O(N In N), N為未知量個(gè)數(shù)。根據(jù)線性邊界條件,采用四階龍格庫塔法實(shí)現(xiàn)時(shí)間的步進(jìn),得到各時(shí)刻下的不同位置處的波面高度。 首先,研究了時(shí)域內(nèi)波浪對(duì)置于圓錐形、拋物形地形上圓柱島的全繞射。計(jì)算了兩種地形上的圓柱島與靜水面交線處的波高,最大波高出現(xiàn)在圓柱島的迎浪側(cè),最小值在出現(xiàn)在背浪側(cè)。入射波浪周期越短,圓柱島相鄰位置處的波面高度差異越來越明顯；圓柱島的淹沒深度越深,圓柱島與水面交線及整個(gè)自由水面上的波高均減小,其中最小值變化較小,最大值變化較大；圓柱島下方局部地形坡度越陡,交線位置處的最大波高越小。 然后,研究了時(shí)域內(nèi)波浪對(duì)圓柱形、圓臺(tái)形以及拋物形三種暗礁地形的全繞射。數(shù)值結(jié)果表明：隨著入射波浪周期的增加,水面上最大波高出現(xiàn)的位置逐漸向礁石軸線靠攏,數(shù)值逐漸減�。浑S著礁石高度的減小,即暗礁頂面距離靜水面的距離ha的增加,自由水面波高的最大值逐漸減小,最大值出現(xiàn)的位置逐漸遠(yuǎn)離暗礁的軸線位置；當(dāng)礁石底半徑、水深及入射波浪為周期、礁石高度相同的情況下,圓柱形礁石上的波高最大,拋物形礁石上的波高最小,圓臺(tái)形礁石的結(jié)果位于兩者之間；在保持頂面半徑不變的情況下,隨著圓臺(tái)形暗礁地形變陡,自由水面的最大波高減小,出現(xiàn)的位置向著圓臺(tái)的中軸線處靠攏。
[Abstract]:There are abundant resources in the ocean, and the exploitation and utilization of marine resources is helpful to alleviate the contradiction between social development and the shortage of land resources. The islands and reefs in the sea facilitate the use of the natural resources in the sea. Understanding the hydrodynamic environment around islands and reefs is also essential for rational utilization of island resources. Taking the three-dimensional Laplace equation as the governing equation, the boundary integral equation is derived from Green's second theorem, and the problem of wave diffraction on the island and reef terrain is studied by using the time-domain higher-order boundary element method. The Green's function selects the Rankine source and its image of the horizontal seabed to remove the horizontal seabed boundary except the local terrain, and the integral region is the local terrain and the static water surface of the finite region. In the numerical process, the high order boundary element method is used to discretize the equation. Using the method of pre-modified fast Fourier transform, the system of linear equations derived from integral equations is not shown. The storage capacity of the algorithm is reduced from O (N2) generated by display to O (N), computation from O (N3) required for direct solution of linear equations to O (N In N), N as the number of unknowns. According to the linear boundary condition, the fourth order Runge-Kutta method is used to realize the step of time, and the wave surface height at different positions at each moment is obtained. First, the total diffraction of a cylindrical island on a conical and parabolic terrain is studied in time domain. The wave height at the intersection line between the cylindrical island and the hydrostatic surface on two kinds of topography is calculated. The maximum wave height appears on the front side of the cylindrical island and the minimum at the back side. The shorter the incident wave period, the more obvious the difference of the wave surface height at the adjacent position of the cylindrical island, the deeper the submerged depth of the cylindrical island, the lower the wave height of the intersecting line between the cylindrical island and the water surface and the whole free water surface, in which the minimum change is small. The steeper the slope is, the smaller the maximum wave height is at the intersection position. Then, the total diffraction of waves in time domain to the cylindrical, platform and parabolic reef topography is studied. The numerical results show that with the increase of the incident wave period, the position of the maximum wave height on the surface of the water gradually draws closer to the reef axis and decreases gradually, and with the decrease of the reef height, that is, the distance ha from the top of the reef to the static water surface increases. The maximum value of free water surface wave height decreases gradually, and the position of the maximum appears gradually away from the axis of the reef. When the bottom radius of the reef, the depth of water and the incident wave are periodic, the wave height on the cylindrical reef is the largest when the height of the reef is the same. The wave height on the parabolic reef is the smallest, and the results of the circular reef lie between the two. While the radius of the top surface is constant, the maximum wave height of the free water decreases as the topography of the reef becomes steeper. The position that appears is close to the central axis of the platform.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：P731.22

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