Hybrid time-domain model for ship motions in nonlinear extreme waves using HOS method

HOS (High-Order Spectral) method incorporated with a 3-D time-domain ship motion model based on the weakly nonlinear assumption has been proposed and applied to compute motions of a ship advancing with constant speed in various nonlinear waves. In the proposed approach, HOS method is employed to simulate arbitrary incident wave systems described in earth-based coordinate, including regular, irregular waves and focused waves and resolve nonlinear wave-wave interactions up to an arbitrary order. Its fast convergence and high efficiency allow modelization of long-time nonlinear propagation of predetermined input wave spectra and simulation of realistic sea states and extreme events while keeping reasonable computational efforts. Nonlinear F-K (Froude-krylov) forces and restoring forces are calculated and evaluated over the instantaneous wetted surface to capture the strong nonlinear features of incident wave field simulated by HOS method. The equations of time-domain ship motions in nonlinear waves are established. This hybrid model benefits from the efficiency of HOS method to solve nonlinear free surface boundary conditions for incident wave, in the same breath, the timedomain model employed here is computationally simple and of great practical significance. To illustrate the feasibility and accuracy of this method, comparisons to experiment data have been conducted in the case of regular head waves and gain satisfactory agreement. Furthermore, the nonlinearities of focused waves as well as irregular waves and the subsequent nonlinear effects to ship motions are investigated. It is shown that the nonlinearity of the incident waves plays a significant role for the extreme wave occurrence and results in a larger F-K force and a remarkable larger heave motion.