Analytical study of wave diffraction and radiation by a submerged sphere in infinite water depth

Abstract

The wave diffraction and radiation of a submerged sphere in deep water are studied using the multipole method within the frame of linear wave theory. By expressing the velocity potential in spherical harmonics and formulating the problems into truncating and solving M sets of linear equation systems, simple analytical expressions are derived for the hydrodynamic characteristics. A novel analytical expression for the multipoles coefficient is derived to accelerate the numerical implementation. A similar procedure of Wu et al. (1994) and Rahman (2001) is used to condense the expression for the total wave potentials at the sphere surface in the diffraction problem. Results obtained by present model precisely coincide with other numerical schemes, and converge very rapidly with the increase of the truncation parameter that generally the number of series terms N=4 and M=0,1 are sufficient to an accuracy of 3 decimals. A further analysis shows that for large submergences, the surge and the heave exciting forces approach equal. In the mean time, there exists an exact relationship a11−0.5=(a00−0.5)/2 between the surge and the heave added mass, and b11=b00/2 between the surge and the heave damping, where j=0 and j=1 correspond to the heave and surge motion, respectively. Extensive numerical results involving convergence of the multipole method, exciting forces and hydrodynamic coefficients for various parameters are also presented.