Hydrodynamic properties of two vertical truncated cylinders in waves

The radiation and diffraction boundary value problem arising from the interaction of linear water waves with two vertical truncated cylinders is investigated by use of the method of separation of variables and the method of matched eigenfunction expansion. Analytical expressions for the radiated and diffracted potentials are obtained as infinite series of orthogonal functions. The unknown coefficients in the obtained expressions are determined by use of the matched eigenfunction expansion method. To verify the obtained expressions, the Green's second identity and the symmetry of the matrices for the added masses and damping coefficients are used. The results show that the analytical expressions presented in this paper are correct. By use of the present analytical solution, the hydrodynamic coefficients and wave forces for some specific cases are calculated and the hydrodynamic effects of the cylinders' radii on the hydrodynamic properties of the cylinders are investigated which will supply some useful information for the design of this kind of system.