The interaction of water waves with submerged spheres and circular cylinders

The evaluation of hydrodynamic coefficients and loads on submerged or floating bodies has a lot of significance in designing these structures. Some special type of geometries such as circular cylinders, elliptic cylinders and spherical structures (hemisphere, sphere, spheroid) can be considered to derive analytical solutions to the wave diffraction and radiation problem. The work presented here is mainly the result of water wave interaction with submerged spheres. We also present some analysis and discussion regarding the hydrodynamic interaction with circular cylinders.; In the first part of this study, analytical expressions for various hydrodynamic coefficients and loads due to the effects of diffraction and radiation are derived separately. The case of the combined effect of diffraction and radiation is also been considered in a similar way. The solution to the boundary value problem is obtained by considering two separate problems, namely the diffraction and the radiation problem. The exciting force components are derived by solving the diffraction problem: the added-mass and damping coefficients are evaluated by solving the radiation problem. Theory of multipole expansions has been used to expressed the velocity potentials in terms of an infinite series of associated Legendre polynomials with unknown coefficients. The orthogonality of those polynomials has been exploited to simplify the expressions. The responses due to surge, heave and pitch, induced by wave excitation, are determined from the equation of motion. Since the infinite series appearing in various expressions have excellent truncation properties, these series are evaluated by considering only a finite number of terms. Gaussian quadrature has been used to evaluate the integrals. Numerical estimates for the analytical expressions for the hydrodynamic coefficients and loads are presented for various depth to radius ratios.; In the second part of the study, an analysis is presented for the second-order diffraction problem for a large vertical cylinder. Expressions are derived for first-order and second-order potentials. The second-order loads are divided into three components: waterline force, dynamic force and quadratic force. The first-order potentials contribute to the waterline and dynamic forces whereas the second-order potentials contribute to the quadratic force. Our emphasis is on obtaining the second-order potential: we also discuss the quadratic force. Numerical results for various analytical expressions are presented in tabular and graphical forms, for different wave parameters.