Analytic solution for wave diffraction of a submerged hollow sphere with an opening hole

An investigation is carried out on the interaction of surface waves with a submerged sphere having an opening hole in finite-depth water in this article. Based on the linear wave theory, the method of multipole expansions is used to obtain the fluid velocity potential in the form of double series of the associated Legendre functions with the unknown coefficients of an infinite set. In terms of the body surface boundary condition and the matching condition between the inner and outer flows at the hole, the complex matrix equations for the coefficients of the series are established. The infinite sets of matrix equations are solved by truncating the series at a finite number. The hydrodynamic pressure on the structure surface and the exciting forces acting on the structure are graphically presented. The dynamic pressure on the wave front surface of the sphere varies slightly with angle of opening hole increasing, while that on the wave back surface does obviously. When the angles of opening hole are increasing, the absolute values of the complex exciting forces tend to fall as a whole.