Second-order sum- and difference-frequency bichromatic wave forces on three-dimensional bodies in a channel

In Huang and Teng (2020), the effects of the channel walls on the second-order hydrodynamic characteristics of three-dimensional bodies in monochromatic incident waves were investigated. To ensure the high accuracy and efficiency of the calculation, robust numerical algorithms have been developed to treat the troublesome integrals over the free surface, body surface and up- and down-wave vertical surfaces involved in the second-order analysis. In the present study, Huang and Teng (2020)'s work is extended to the cases of bichromatic incident waves, and some improvements in the numerical algorithms are made. The expressions of the locked potentials including both the propagating and evanescent modes are derived. Since the up- and down-wave vertical surfaces are allowed to be placed close to the body, the calculation of the free surface integral can be performed in a small region, and an analytical method is developed to directly evaluate the up- and down-wave vertical surface integrals. After solving the boundary integral equation, the sum- and difference-frequency radiation and diffraction potentials are obtained explicitly. Numerical results for the quadratic transfer functions of the second-order free surface elevation, pressure and force are given for a series of geometries in channels.