大数量圆柱绕射问题递推算法的理论基础

利用单根圆柱绕射问题的特征函数展开解，直接构造出浪散射的传输矩阵，进而利用Ｂｅｓｓｅｌ函数和Ｈａｎｋｅｌ函数的平移公式，对水波动力学问题建立了大数量圆柱波浪绕射的递推算法。作为算例，就不同方向、不同波数入射波情况下的双圆柱绕射问题进行了具体计算，并将计算结果与多柱绕射问题截面周线波动源分布法的结果进行了比较，计算比较表明，文中建立的大数量圆柱绕射问题的递推算法是有效的。该算法可以进一步拓广至其他形

Theoretical Basis of the Recursion Formulas for Diffract ion Problems of Circular Piles of Extremely Large Number

By making use of the eigen function expansion for the wave diffraction problem of a single circular cylinder, the wave scattering transfer matrix was directly constructed, which, together with the Graf's addition theorem for Bessel and Hankel functions, was further used to establish a recursion formula for the wave diffraction problems of circular piles of extremely large number. As computational examples, the diffraction of incident waves of different wave angles and wave numbers on twin circular cylinders was investigated, and the computational results were compared with the corresponding results obtained with the wave source distribution method for diffraction problems of multiple cylinder developed by the authors. The comparison shows that the recursion formula is effective for the computations of the wave forces on circular cylinders of extremely large number. This algorithm can be extended to the solution of the wave diffraction problems of bodies with general shape of extremely large number, which will offer a new approach for the determination of the motion characteristics of super large ocean structures in waves.