Abstract The purpose of this paper is to study the diffraction of second order Stokes waves by four cylinders in a uniform current and mainly focus on the near-trapping phenomenon. A time domain second-order theory is employed to establish the mathematical Smodel by splitting the total potential into the disturbed velocity potential caused by current, the first- or linear and second-order potentials, which satisfy their own boundary conditions. Each potential is calculated through the finite element method (FEM). Numerical results for four bottom-mounted cylinders in a uniform current are provided to show the resonant behaviour of waves and hydrodynamic forces including linear and second order at near-trapped frequencies, and the current effect on the wave and force are also analysed and discussed. Some results for a single- and four-cylinder cases are compared with previous studies.

中文翻译：

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均匀电流中多圆柱体二阶波谐振的有限元分析

摘要 本文的目的是研究均匀流中四个圆柱体对二阶斯托克斯波的衍射，主要关注近俘获现象。采用时域二阶理论建立数学S模型，将总电位分解为电流引起的扰动速度电位，满足各自边界条件的一阶或线性和二阶电位。每个电位都通过有限元方法 (FEM) 计算。提供了四个底部安装的圆柱体在均匀流中的数值结果，以显示波浪和水动力的共振行为，包括近陷波频率下的线性和二阶，并且还分析和讨论了电流对波浪和力的影响。