Interaction Of Water Waves With A Submerged Sphere In The Ocean Of Finite Depth: Numerical Simulation And Graphical Visualization

Abstract

The interaction of water waves with a completely submerged spherical structure in water of finite depth is considered in this paper based on the first order diffraction theory. The method of multipole expansions is used to obtain the fluid velocity potential in the form of double series of the associated Legendre polynomials with the coefficients being solutions 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 pressure and fluid velocity around the structure, the three-dimensional free surface elevation, total pressure at the structure surface. diffraction pressure at the ocean bed, and total exciting forces acting on the structure are investigated for a wide range of the structure submergences. ocean depths and wavelengths. The results are presented in the comprehensive graphical form. Some important , both from the theoretical and practical viewpoints, features of the wave-structure interaction are found. Where possible, the results are compared with known works and excellent agreement is observed.