Analytical solution to wave diffraction by a hemisphere in infinite water depth using the multipole expansion method

Abstract

Linear water wave diffraction by a hemisphere in infinite water depth is investigated using the multipole expansion method in this paper. In the spherical coordinate system, the diffraction potential is expressed in the form of multipole wave potentials and the wave-free potential, as derived by Hulme (1982) for radiation potentials. The issues associated with the high-order multipole expansion are solved in this paper. The new method can calculate the multipole wave potentials at arbitrary orders and thus successfully calculate the diffraction potentials on the body surface and free surface around a hemisphere. The wave exciting forces acting on hemispheres are calculated using the near-field and far-field methods, which utilizes the radiation potential computed by Hulme's (1982) method to verify the accuracy of the analytical solution in this paper. Compared with the far-field method, the analytical solution in this paper converges more quickly as the truncation term N increases, especially when the wavenumber Ka is large. In this paper, the theory of applying the multipole expansion method to solve hydrodynamic problems with a hemisphere on the free surface is completed, which makes the multipole expansion method no longer limited to low-order expansion calculations and can be applied to more fields.