【作者】 叶春生；

【导师】 史庆增；

【作者基本信息】 天津大学 ， 港口、海岸及近海工程， 2004， 博士

【摘要】 本文研究的主要内容是海洋内波的特性与内波荷载,后者主要针对连续分层的情况进行分析和计算。 首先,推导了内波控制方程。对于二维情形,从 Euler 方程组出发,将其线性化,得到简谐情况下的内波垂向结构方程,结合表面“刚盖”条件与水底条件,构成了求解内波的本征值问题;对于三维情况,仍从 Euler 方程组出发,推导了内波控制方程及其色散关系。针对密度分布的三层模式,计算了垂向速度模态与内波的色散关系;连续分层的情况,则给出了半板造波的垂向模态分布与空间传播形态。 其次,详细分析了密度连续分层时的垂向结构问题。利用微分动力系统的知识,定性地分析了垂向结构方程解的特性。若简谐频率与浮力频率的交点位于水深范围之内,则交点确定的区域存在内波,而区域外不存在内波,且解是单调的;若理论上的两个交点位于水深范围之外,则全水深存在内波;若简谐频率高于浮力频率最大值,则没有内波存在且刚盖条件不再适用。 数值求解内波垂向结构方程,利用两次 Sturm 变换,将其转化为Sturm-Liouville 标准型,获得了齐次边界条件。其解系构成完备的加权(权函数为1)内积空间,即Hilbert空间,从而内波现象可以展成该解系的广义Fourier级数;采用差分方法,将 Sturm-Liouville 方程转化为矩阵特征值问题,每一个特征值对应一个内波波数,该特征值对应的解则是内波的某一模态。当圆频率连续变化时,就确定了内波不同模态时的色散关系;由 Sturm 反变换和连续性方程,计算了垂直和水平速度幅值的纵向分布,继而给出二维内波流场和水质点的运动轨迹图像;此外,将 Sturm 变换的结果与直接求解内波垂向结构方程的结果进行了比较,直接求解的结果不满足正交性,且不完备;利用已有的实验数据和数值结果,进一步探讨了边界条件问题,并给出了更为简明的内波控制方程。 在二维内波流场求解的基础上,采用小尺度物体受力的 Morison 公式进行了圆柱形杆件的空间受力分析;针对半日潮频(0.08cph)和高频(3~5cph)内波成分,详细计算了三种浅水情况下的内波荷载,给出了荷载的分布以及总荷载的数值,并与表面波和海流情况的荷载进行了对比。由于内波谱的存在,文中给出了不同周期时的内波荷载数值结果。 最后,对内波荷载实验进行了量纲分析及实验装置设计,为模型实验打下了良好的基础。更多还原

【Abstract】 The thesis is dedicated to the study of internal wave’s characters and its load onlong and slim cylinder. And numerical calculation is performed when density isstratified continuously. First, governing equation of internal wave is deduced. As to 2-dimension problem,based on Euler’s equation and using its linear form, vertical structure equation isobtained. With rigid surface and water bottom conditions adopted, eigenvalueproblem of internal wave is reached. As to 3-dimension case, governing equation anddispersion relation of internal wave are deduced from Euler’s equation, too. Later,calculation of vertical velocity and dispersion relation for three-ply type areperformed, as is done for the case when density is stratified continuously. For thelatter, it gives internal wave’s propagation form in space. Second, the problem of vertical structure is thoroughly discussed when density isstratified continuously. With the knowledge of differential system, characters ofsolution to vertical structure equation are analyzed. Theoretically, circle frequency hastwo intersections with the curve of Blunt frequency. If the two points are betweenwater surface and bottom, internal wave will exist among the area between the points,while there is no internal wave out of the area, with its solution monotone; if the twopoints are out of water depth, internal wave will exist all the depth; if frequency isbigger than the maximum of Blunt frequency, there will not exist internal wave, andit’s nonsense of rigid surface condition. In numerical calculation, with twice-Sturm transform adopted, standardSturm-Liouville equation and homogenous boundary conditions are obtained. Thesolutions compose self-contained inner product space (weight function is constant 1),i.e., they are basic series of Hilbert space; hence any internal waves could beexpanded into generalized Fourier series. With difference method, Sturm-Liouvilleequation is transformed to matrix eigenvalue problem. Each eigenvalue is related to ahorizontal wave number, and relevant solution is a certain mode of internal wave. Ascircle frequency varies continuously, internal wave’s dispersion relation for differentmode is got. With reverse Sturm transform and equation of continuum, verticaldistribution of vertical and horizontal velocity’s range are calculated, with2-dimension fluid field and track of water point being given. Moreover, the results ofthe method of twice-Sturm transform and those of direct solution of internal wave’svertical structure equation are compared. It points out that the direct solutions aren’tself-contained or orthogonal. Later, further discussion of boundary conditions iscarried out with the results of numerical method and experiments, and then moresimple form of internal wave’s governing equation is given. On the basis of the solution to 2-dimension internal wave’s field, Morisonformula is used in analyzing and calculating the force of long and slim cylinder. Threedifferent water depths are chosen to calculate for half-day tide frequency (0.08cph)and high-frequency (3~5cph). It gives load distribution along the cylinder and total ii<WP=5>force imposed on the cylinder by internal wave, and then compares them to those ofocean current and surface wave respectively. Also, internal wave’s loads for differentcycles are given since the spectrum characteristic of internal wave. At last, dimension analysis and experiment equipments are studied initially,which gives a well base for modeltest.更多还原