| Refraction and di?raction e?ects of ocean surface waves have important researchvalue in design of the ports, docks, navigation channels, breakwater, forecast of thetsunami and evaluation of the seakeeping capability of platforms and ships in the sea,etc. For di?culty and complexity of the physical problems, numerical simulations aregenerally adopted. However, the numerical solutions or the numerical models must beverified by experimental data or analytic solutions. Compared with experimental data,the advantages of the low cost , the high accuracy and the ease to find laws make analyticsolutions to be the most popular. While the existing results are usually restricted tosimple equations or topographies. For example, the topographies are mostly assumed tobe idealized, which means the water depth function over the variable region is a powerfunction of the independent variable, i.e., the vertex of the shoal is located on the stillwater level. As under this assumption, the governing equation can be transformed intoclassical Euler or Bessel equation, in which the closed-form analytic solutions are easilyobtained.The innovation of this thesis is generalizing the idealized topographies into un-idealized. The so-called un-idealized means that the water depth function over thevariable region is no longer a power function of the independent variable. It is thisgeneralization that increase the di?culty for us to guarantee the convergency of theanalytic solution.In this text, firstly, we investigate the re?ection e?ects of linear long waves prop-agating over a one-dimensional rectangular obstacle with scour trenches. Secondly, wegive the di?raction e?ects of linear long waves scattering by a shoal, a circular cylinderisland mounted on an un-idealized shoal and an un-idealized truncated shoal, respec-tively. Finally, we study the re?ection e?ects of linear waves encompassing the wholewave range propagating over a one-dimensional un-idealized trench. |
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