Characters Of Internal Wave And Its Load

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 iiforce 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.