波浪在半球上绕射的解析解

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摘要

基于线性势流理论，推导了无限水深中波浪在半球上绕射问题的解析解.给出了球坐标系下无限水深入射波速度势的表达式；利用多极子展开法，以包含未知系数和连带勒让德函数的无限序列的形式给出了流场中绕射速度势的表达式；通过物面边界条件建立了方程组，进而求解了未知系数.计算了作用在半球上总的波浪激励力，并通过与利用Haskind关系得到的结果以及他人的数值结果进行比较，验证了文中结果的正确性.

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Abstract：

Based on the linear potential theory, an analytical solution is presented to study the diffraction problem of a hemisphere on the surface of water with infinite depth. The incident wave potential in the spherical coordinate system was proposed and the method of multipole expansion was employed to obtain the diffraction wave potential in the form of infinite series of the associated Legendre functions with the unknown coefficients which could be determined by solving a set of linear equations from the body boundary condition. The wave exciting force acting on the hemisphere was calculated and the results were compared with those from the Haskind relationship and some numerical results from the published literature.

收稿日期: 2012-10-16 出版日期: 2013-10-30

ZTFLH:

U 661.22

基金资助:

国家自然科学基金资助项目（51079082,40676053），劳氏教育基金会UCL-SJTU-HEU深水工程及水动力学联合研究中心资助项目

引用本文:

周华伟1，张洪生1，2 . 波浪在半球上绕射的解析解[J]. 上海交通大学学报（自然版）, .
ZHOU Huawei1,ZHANG Hongsheng1，2. Analytical Solution to Wave Diffraction by a Hemisphere. J. Shanghai Jiaotong Univ.(Sci.) , 2013, 47(10): 1597-1600.

链接本文:

http://www.qk.sjtu.edu.cn/jsjtunc/CN/ 或 http://www.qk.sjtu.edu.cn/jsjtunc/CN/Y2013/V47/I10/1597

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