Abstract The interaction between cnoidal waves and a concentric cylindrical structure with an arc-shaped outer wall has been investigated theoretically using eigenfunction expansion approach. The arc-shaped outer cylinder is permeable and thin, protecting the porous dual-cylinder structure. Three cylinders are surface-piercing and rigidly installed on the flat bottom of an ocean. Analytical solutions were obtained based on the first approximation to cnoidal waves. A series of linear equations pertaining to unknown coefficients were solved using matching boundary conditions. Hydrodynamic forces on the cylinders and the diffracted wave faces around the cylinders were evaluated, and the effects of water depth, annular spacing, angle of incidence and structure configuration including the porosity parameter of the cylinders and the opening angle are illustrated via numerical results. The numerical results obtained for limiting cases agreed well with published results for a solid cylinder. The results indicated that the wave forces on the inner structure did not change significantly when the opening angle was greater than 2 π ∕ 3 . The hydrodynamic loads on the inner cylinder of the concentric cylindrical structure were significantly lower than the wave force on a single cylinder. Moreover, the value of wave force on the inner cylinder of a concentric dual-cylinder structure with an arc-shaped outer wall was similar to that on the inner cylinder of a concentric two-cylinder system.

中文翻译：

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cnoidal波与弧形外筒同心圆柱结构之间的水动力相互作用

摘要 利用本征函数展开法，从理论上研究了圆锥波与圆弧外壁同心圆柱结构之间的相互作用。弧形外筒透水薄，保护多孔双筒结构。三个圆柱体可穿透水面并牢固地安装在平坦的海洋底部。解析解是基于对 cnoidal 波的一次近似获得的。使用匹配边界条件求解了一系列与未知系数有关的线性方程。对圆柱体和圆柱体周围的衍射波面的水动力进行了评估，并评估了水深、环形间距、通过数值结果说明了入射角和结构配置，包括圆柱体的孔隙率参数和开度角。极限情况下获得的数值结果与实心圆柱体的公布结果非常吻合。结果表明，当张角大于 2 π ∕ 3 时，作用在内部结构上的波浪力变化不大。同心圆柱结构内圆柱体上的水动力载荷显着低于单个圆柱体上的波浪力。此外，弧形外壁的同心双筒结构的内筒上的波浪力值与同心双筒系统的内筒上的波浪力值相似。极限情况下获得的数值结果与实心圆柱体的公布结果非常吻合。结果表明，当张角大于 2 π ∕ 3 时，作用在内部结构上的波浪力变化不大。同心圆柱结构内圆柱体上的水动力载荷显着低于单个圆柱体上的波浪力。此外，弧形外壁的同心双筒结构的内筒上的波浪力值与同心双筒系统的内筒上的波浪力值相似。极限情况下获得的数值结果与实心圆柱体的公布结果非常吻合。结果表明，当张角大于 2 π ∕ 3 时，作用在内部结构上的波浪力变化不大。同心圆柱结构内圆柱体上的水动力载荷显着低于单个圆柱体上的波浪力。此外，弧形外壁的同心双筒结构的内筒上的波浪力值与同心双筒系统的内筒上的波浪力值相似。同心圆柱结构内圆柱体上的水动力载荷显着低于单个圆柱体上的波浪力。此外，弧形外壁的同心双筒结构的内筒上的波浪力值与同心双筒系统的内筒上的波浪力值相似。同心圆柱结构内圆柱体上的水动力载荷显着低于单个圆柱体上的波浪力。此外，弧形外壁的同心双筒结构的内筒上的波浪力值与同心双筒系统的内筒上的波浪力值相似。