Nonlinear Diffraction by Eigenfunction Expansions

A nonlinear diffraction theory correct to second-order is presented which is based on an eigenfunction expansion of the Green's function for fixed axisymmetric bodies subjected to two-dimensional sinusoidal waves. The boundary value problem for the second-order scattered velocity potential is linearly decomposed into two separate boundary value problems, each having only one inhomogeneous boundary condition. Numerical results indicate that the second-order contributions to the total hydrodynamic pressure force from the inhomogeneous free surface boundary condition are much less than the second-order contributions from the inhomogeneous boundary condition on the axisymmetric body. Second-order contributions are also found to be greater in intermediate water depth conditions than for deep water wave conditions. Theoretical numerical results are also compared with experimental values measured on a fixed vertical circular cylinder.