Radiation and diffraction of water waves by a submerged sphere in finite depth

Abstract

The problems of radiation (both heave and sway) and diffraction of water waves by a submerged sphere in finite depth are formulated using the multiple method. In each case this leads to an infinite system of linear equations which are easily solved numerically. Simple expressions are derived for the hydrodynamic characteristics of such a body. A far-field approximation for the scattering problem is also presented. Results showing the effect of varying the depth on both the hydrodynamic characteristics and the diffraction forces are given and it is shown how the method can be used to predict free-surface elevations in the vicinity of the sphere.