A second-order consistent force model for non-slender structures in fully nonlinear waves

In this paper, we derive a force model for non-slender structures in fully nonlinear waves. The model utilizes nonlinear incident wave kinematics and evaluates the wave loads at a post-processing stage using linear and quadratic operators from radiation-diffraction analysis. The method is based on spatial Fourier decomposition of the incident wave field, which allows construction of an approximate scattering potential that satisfies the wall condition on the body for all wave components. The associated potential force is then evaluated using the linear force transfer function in the wavenumber space. In a second-order wave field, this is found equivalent to the Pinkster approximation. Full consistency with second-order diffraction theory is recovered by the inclusion of the force from an additional correction potential that satisfies the free surface boundary condition. The hydrodynamic loads are complemented by the quadratic pressure and waterline integral terms, which are evaluated through quadratic transfer functions in the wavenumber domain. The model formulation is valid for multi-directional waves with a restriction of the formal accuracy to second order. However, through the use of the approximate scattering potential, it incorporates loads from all free and bound components of the incident wave field at any order. The method and its implementation are verified for two configurations in unidirectional waves, a monopile and a fixed containership. When a second-order wave field is used, exact agreement is found with second-order diffraction theory.