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首页> 外文会议>IUTAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity Jul 16-20, 2000 Manchester, United Kingdom >THE FINITE DOCK PROBLEM
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THE FINITE DOCK PROBLEM

机译：有限的码头问题

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摘要

Problems concerning the interaction of water waves with a rigid plate of finite width and infinite length lying in the free surface have a long history. Such problems are interesting for many reasons. First the simple geometry allows considerable mathematical progress to be made and thus dock problems can be used as model problems against which to test new techniques or numerical results. Secondly they can be used as the first approximation in a perturbation analysis of wave interactions with shallow-draft ships. Most work on finite dock problems has concentrated on the infinite depth case, but numerical calculations of the reflection and transmission coefficients for the scattering problem in finite depth were presented in . Only normal incidence was considered, though the matched eigen-function technique that was employed easily generalizes to the oblique incidence case. The purpose of this paper is to show that this problem can in fact be solved in an elegant manner, one which has the advantage over Mei and Black's solution procedure in that it takes into account the fact that the semi-infinite dock problem possesses an explicit solution. Another advantage of the method described below over Mei and Black's approach is that it accurately models the known singularity in the derivative of the potential at the plate edge.
机译：关于水波与自由表面上有限宽度和无限长度的刚性板相互作用的问题已有很长的历史。由于许多原因，这些问题很有趣。首先，简单的几何结构允许进行相当大的数学进展，因此可以将对接问题用作模型问题，以测试新技术或数值结果。其次，它们可以用作波浪与浅吃水船相互作用的扰动分析中的一阶近似。关于有限坞问题的大多数工作都集中在无限深度的情况下，但是在有限深度中给出了散射问题的反射和透射系数的数值计算。仅考虑正常发病率，尽管采用的匹配特征函数技术很容易推广到倾斜发病率情况。本文的目的是证明该问题实际上可以用一种优雅的方式解决，它比Mei和Black的求解过程具有优势，因为它考虑到了半无限对接问题具有显式的事实。解。相对于Mei和Black的方法，下面描述的方法的另一个优点是，它可以精确地模拟板边缘电势导数中的已知奇点。

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