Based on the second-order Stokes wave theory and introducing a wave spectrum transformation method, the wave spectrum of nonlinear waves can be obtained from the wave spectrum of linear waves. Then, the nonlinear wave elevation time history can be described as the function of the wave spectrum of nonlinear waves and linear wave elevation responses obtained from frequency domain. The nonlinear air gap of a semi-submersible unit, including the effect of nonlinear wave elevations and nonlinear wave excitation forces, is investigated in time domain. Comparisons between the linear and nonlinear air gap are made to investigate the nonlinear effect. The numerical results indicate that the nonlinearity has a significant effect on the air gap.


Floating platform is widely used in the field of offshore oil and gas exploration. For floating submersible platform, the air gap problem is relatively complicated owing to the coupling effect of its own motions and waves. Not only the radiation, diffraction and second-order nonlinear motions, but also the nonlinear wave itself, should be considered in the air gap analysis (DNVGL-OTG-13, 2019).

Due to the complicated nature of the air gap, model test is the most used methodology in the past, which is expensive to cost (Kriebel and Wallendorf, 2001; Alexandre, 2006). With the development of computers and the linear method based on the first-order potential theory can offer more accurate of platform motion (Pessoa and Moe, 2017). However, the wave elevation of any position may be underestimated (Stansberg and Baarholm, 2005). For nonlinear problems, focuses are on the non-linear diffraction, nonlinear platform motions and nonlinear waves (Lu and Zhao, 2020; Sweetman and Winterstein, 2002; Lin and Treakle, 2000; Huo and Zhang, 2015). Less attention has been given to the combination of all these nonlinear effects. Some researchers adopted CFD method (Wu and Danmeier, 2014; Liang and Yang, 2010), which can capture the characteristics of flow field and wave elevation nearby the column accurately. Nevertheless, it is difficult to simulate the six degree of freedom motion and complicated mooring system of the platform. Moreover, it is time-consuming.

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