Abstract

The Dirichlet-Neumann operator for the linear water-wave problem describing oblique waves over a submerged horizontal cylinder of small (but otherwise, fairly arbitrary) cross-section in a layer of finite depth is constructed in the form of convergent series in powers of the small parameter characterizing the “thinness” of the cylinder. The terms of these series are expressed through the solution of the exterior Neumann problem for the Laplace equation describing the flow of unbounded fluid past the cylinder. As an application, discrete eigenvalues of this operator which are frequancies of trapped modes of the problem are obtained.

中文翻译：

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薄圆柱体上斜水波的Dirichlet–Neumann算子及其应用

摘要

线性水波问题的Dirichlet-Neumann算子以幂级数的收敛级数形式构造，该斜波描述了在有限深度的层中具有较小（但相当相当任意）横截面的淹没水平圆柱体上的斜波。表征圆柱体“厚度”的小参数。这些序列的项通过外部拉曼方程的诺伊曼问题的解来表示，该拉普拉斯方程描述了无约束流体通过圆柱体的流动。作为应用，获得了该算子的离散特征值，该离散特征值是问题的被困模式的频率。