The second-order interaction of monochromatic waves with three-dimensional bodies in a channel. (1st December 2020) - Huang, J.; Teng, B.
Abstract: A numerical model is developed to investigate the effect of the channel walls on the second-order hydrodynamic characteristics of three-dimensional bodies with arbitrary geometries in a wave channel based on the higher order boundary element method in the frequency domain. The second-order double-frequency radiation and diffraction potentials are obtained explicitly. In contrast to the second-order wave-body interaction problem in the open sea, the main difficulty stems from the boundary integral equation with the supplementary contribution of the up-wave and down-wave vertical surfaces of the channel in the second-order diffraction analysis. By exploiting the free-surface channel Green function and the known first-order scattering potential in eigenfunction expansion, the rapidly convergent integrals over the up-wave and down-wave vertical surfaces in the near fields can be evaluated analytically. Numerical results for the wave interaction with a bottom-mounted vertical circular cylinder, a fixed truncated vertical circular cylinder and a freely floating four-column structure are presented, and show that in comparison with the results in the open-sea condition, the second-order hydrodynamic properties of a body in a channel are affected more seriously than the linear ones due to the side-wall reflections. Highlights: A frequency-domain second-order method for the problems of wave-body interaction in channels is developed with application of the free surface channel Green function. The integrals on the outer free surface and up-wave and down-wave vertical surfaces are derived analytically. It is proved that the integral on the up-wave and down-wave vertical surfaces can be canceled with the integral at the outer boundary of the free surface. The effect of the channel side walls on the second-order forces is examined. It shows that second-order hydrodynamic properties of a body in a channel are affected seriously due to the side-wall reflections.