Simulation of diffraction of ocean waves by a submerged sphere in finite depth

Abstract

Based on the linear diffraction theory, an investigation is made on the interaction of water waves with a completely submerged sphere in water of finite depth in this paper. 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 the infinite set of infinite matrix equations. The truncation property of the matrices and the convergence of the multipole series coefficients are investigated for various wavelengths and depths. The systematic numerical simulation, based on our analytical solution, is carried out and the fields of the hydrodynamic diffraction pressure and fluid velocity around the sphere, the three-dimensional free surface elevation, and total exciting forces acting on the sphere are graphically presented for a wide range of the body submergences, ocean depths and wavelengths.