波浪在岛礁地形上绕射的研究
发布时间：2018-08-07 12:12
【摘要】：海洋有着丰富的资源,开发利用海洋资源有助于缓解社会发展与陆上资源短缺的矛盾。海洋中的岛礁为人们利用海洋中的自然资源提供了便利。弄清岛礁周围的水动力环境也是合理利用海岛资源必不可缺的。 以三维Laplace方程作为控制方程,由格林第二定理导出边界积分方程,采用时域高阶边界元方法研究了波浪在岛礁地形的绕射问题。其中,格林函数选用Rankine源和它关于水平海底的像,去除了局部地形以外的水平海底边界,积分区域为局部地形和有限区域的静水面。数值过程中,运用高阶边界元方法离散此方程。采用预修正快速傅里叶变换的方法,不显示生成由积分方程得到的线性方程组,算法的存储量由显示生成的O(N2)降为O(N),计算量由直接求解显示线性方程组所需的O(N3)降为O(N In N), N为未知量个数。根据线性边界条件,采用四阶龙格库塔法实现时间的步进,得到各时刻下的不同位置处的波面高度。 首先,研究了时域内波浪对置于圆锥形、抛物形地形上圆柱岛的全绕射。计算了两种地形上的圆柱岛与静水面交线处的波高,最大波高出现在圆柱岛的迎浪侧,最小值在出现在背浪侧。入射波浪周期越短,圆柱岛相邻位置处的波面高度差异越来越明显；圆柱岛的淹没深度越深,圆柱岛与水面交线及整个自由水面上的波高均减小,其中最小值变化较小,最大值变化较大；圆柱岛下方局部地形坡度越陡,交线位置处的最大波高越小。 然后,研究了时域内波浪对圆柱形、圆台形以及抛物形三种暗礁地形的全绕射。数值结果表明：随着入射波浪周期的增加,水面上最大波高出现的位置逐渐向礁石轴线靠拢,数值逐渐减小；随着礁石高度的减小,即暗礁顶面距离静水面的距离ha的增加,自由水面波高的最大值逐渐减小,最大值出现的位置逐渐远离暗礁的轴线位置；当礁石底半径、水深及入射波浪为周期、礁石高度相同的情况下,圆柱形礁石上的波高最大,抛物形礁石上的波高最小,圆台形礁石的结果位于两者之间；在保持顶面半径不变的情况下,随着圆台形暗礁地形变陡,自由水面的最大波高减小,出现的位置向着圆台的中轴线处靠拢。
[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.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：P731.22
本文编号：2169990
[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.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：P731.22
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