Summary

In this article, we study the existence of solutions for the problem of interaction of linear water waves with an array of three-dimensional fixed structures in a density-stratified multi-layer fluid, where in each layer the density is assumed to be constant. Considering time-harmonic small-amplitude motion, we present recursive formulae for the coefficients of the eigenfunctions of the spectral problem associated with the water-wave problem in the absence of obstacles and for the corresponding dispersion relation. We derive a variational and operator formulation for the problem with obstacles and introduce a sufficient condition for the existence of propagating waves trapped in the vicinity of the array of obstacles. We present several (arrays of) structures supporting trapped waves and discuss the possibility of approximating the continuously stratified fluid by a multi-layer model.

中文翻译：

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多层流体中的截留模式

概括

在本文中，我们研究了密度分层的多层流体中线性水波与三维固定结构阵列相互作用的问题的解决方案的存在，其中每一层的密度均假定为常数。考虑到时谐小振幅运动，我们给出了在没有障碍物的情况下与水波问题有关的频谱问题的本征函数系数的递推公式，以及相应的色散关系。我们导出了具有障碍物问题的变分和算子公式，并为存在于障碍物阵列附近的传播波的存在引入了充分条件。