Second-Order Hydrodynamic Interactions in an Array of Vertical Cylinders in Bichromatic Waves
Second-Order Hydrodynamic Interactions in an Array of Vertical Cylinders in Bichromatic Waves
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DOI：
10.1006/jfls.1995.1004
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发表时间：
1995
影响因子：
3.6
通讯作者：
W. Moubayed;A. N. Williams
中科院分区：
文献类型：
--
作者：
W. Moubayed;A. N. Williams
摘要本文给出了双色波作用于任意横截面的底置、穿透表面的垂直圆柱体阵列上的水动力的完整二阶解。利用恒定的结构横截面，线性化的潜力的垂直依赖性表示在本征函数展开。然后可以利用二维绿色函数方法来求解一阶问题。绿色的第二个身份是用来表示由于二阶势的自由表面和结构的积分，涉及一阶量和相关的线性化辐射的潜力，通过振荡的每个结构，依次在一阶波的分量的和和差频率。相当多的注意力集中在发展一种有效的数值技术来计算出现在二阶力公式的振荡自由面积分。在近场的积分进行数值计算，而在远场的积分进行分析，利用潜在的组件的渐近行为。数值计算结果表明，在两个和差频率上的二阶流体动力载荷的气缸上的相互作用的影响的重要性，为一个阵列的四个圆柱。
Abstract A complete second-order solution is presented for the hydrodynamic forces on an array of bottom-mounted, surface-piercing, vertical cylinders of arbitrary cross-section in bichromatic waves. Exploiting the constant structural cross-sections, the vertical dependency of the linearized potentials is expressed in terms of eigenfunction expansions. A two-dimensional Green's function approach may then be utilized to solve the first-order problem. Green's second identity is applied to express the second-order forces due to the second-order potential in terms of free-surface and structural integrals involving firs-order quantities and associated linearized radiation potentials obtained by oscillating each of the structures in turn at the sum and difference frequencies of the component first-order waves. Considerable attention is focussed on developing an efficient numerical technique to compute the oscillatory free-surface integral appearing in the second-order force formulation. In the near field the integration is carried out numerically, while in the far-field the integration is carried out analytically utilizing the asymptotic behavior of the potential components. Numerical results are presented for an array of four circular cylinders which illustrate the importance of interaction effects at both the sum and difference frequencies on the second-order hydrodynamic loads on the cylinders.