Abstract: The accurate numerical prediction of large-amplitude nonlinear ship motions is quite important for the safe navigation of ships under rough sea conditions. A weakly nonlinear ship motion model is proposed to analyze the vertical ship motion in the wave. In the numerical model, the radiation force and the diffraction force are estimated by using the impulse response function, and the ship slamming force is introduced according to the momentum impact theory. The incident wave forces (Froude-Krylov forces (F-K)) and hydrostatic forces on the instantaneous wetted ship surface are calculated for ship under the incident wave profile. One of the unique features is that the fully nonlinear stream function wave theory is introduced to estimate the incident wave kinematics, dynamic pressure and the F-K fluid loads, where the detailed numerical results are presented and discussed. The proposed numerical model is used to estimate the vertical nonlinear ship motions of a S175 container ship sailing in regular waves. It is found that the vertical FK forces and the heave motions based on the stream function wave theory are slightly larger than those of the linear wave theory especially when the incident wave steepness is relatively large. Another feature is that the momentum impact theory is used to estimate the section slamming forces. The results show that at a relatively high speed, the slamming force greatly impact the ship vertical motion, and the inclusion of the slamming force contributes evidently to the reduction of the motion amplitude.

Key words: stream function wave theory, weakly nonlinear ship motion model, Froude-Krylov(F-K) force, ship slamming force, nonlinear vertical motion

摘要： 为了保证船舶在高海况下的安全航行,对大振幅非线性船舶运动进行精确的数值预报是非常重要的。为了分析波浪中船舶的垂向运动,提出了一种弱非线性船舶运动模型。在数值模型中,利用脉冲响应函数估计辐射力和绕射力,并根据动量冲击理论引入船舶砰击力,在入射波面下计算瞬时浸湿船舶表面上的入射波浪力（Froude-Krylov力,简称：F-K力）和静水压力。该文算法模型的一个特色是引入了全非线性的流函数波动理论来估计入射波的运动学、动压力和F-K力流体载荷,给出详细的数值结果并进行了讨论。利用该数值模型对S175集装箱船在规则波中的垂向非线性运动进行了计算。结果表明：基于流函数波浪理论的垂向F-K力和垂荡运动略大于线性波理论,特别是当入射波的陡度较大时。此外,文中采用动量冲击理论来估算截面砰击力,数值结果表明：在相对较高的航速下,砰击力对船舶垂向运动影响较为显著,相对不考虑的情况可进一步减小运动幅值。

关键词: 流函数波浪理论, 弱非线性船舶运动模型, Froude-Krylov（F-K）力, 船舶砰击力, 非线性垂向运动