A time-domain approach for motion-explicit evaluation of loads on floating structures in fully nonlinear waves

Abstract

This paper presents a novel method for evaluating second-order consistent hydrodynamic loads, which employs nonlinear wave and body kinematics. The pseudo-spectral formulation of nonlinear potential flow wave solvers is exploited, permitting the application of transfer functions on the nonlinear incident wave field. A closed-form expression is accordingly derived for the potential force component, which constitutes a generalisation of the Pinkster approximation to fully nonlinear waves. Moreover, the quadratic force component is reformulated to account for the total nonlinear body motion and velocity rather than their first-order counterparts. Hence, the traditional assumption that first-order body motions are significantly larger than the second-order components, which is violated in the case of moored floating structures, is circumvented. To this end, the radiation potential is treated in the time domain and is distinguished from the incident and scattering wave contributions, which are considered through wavenumber-domain transfer functions. An important advantage of the proposed approach is that it is established on the output of radiation-diffraction analysis in the frequency domain, and therefore is highly practical and efficient. Finally, the derived force model is coupled with a time-domain motion solver, which permits the consideration of the instantaneous body motion and velocity in the force calculation. The solver is employed to investigate the motions of a moored container ship, and the results demonstrate significant improvements over standard second-order radiation-diffraction theory.