Influence of second-order wave force and focusing position on dynamic responses of tension leg platform under a freak wave

As a semicompliant and semirigid column group structure, both second-order sum-frequency and diff-frequency wave forces and focusing positions are important for tension leg platforms (TLPs) under freak waves. The double-wave train superposition model is widely used to generate freak waves; however, multiple trials are inevitable for freak wave generation owing to the uncertainty in parameter selection, which may decrease the simulation efficiency. In this study, the effects of the energy ratio of the focused wave train, number of constituent waves, and parameters of the JONSWAP wave spectrum on the generation probability of freak waves are studied, and the generation probability of the freak wave is fitted by a Gamma cumulative probability density function. The advantage of the fitted formula is that the generation probability of a freak wave is quantified, and an appropriate number of constituent waves can be determined for a given energy ratio of the focused wave to increase the simulation efficiency. Furthermore, the dynamic responses of a TLP in a freak wave considering the influences of second-order wave forces and focusing positions are simulated and discussed. Two main findings are that the second-order diff-frequency wave force may cause large-amplitude low-frequency motion in the surge direction and set-down motion in the heave direction, which are 3.71 and 4.08 times the first-order surge and heave responses, respectively, whereas the second-order sum-frequency wave force may cause high-frequency oscillation in the pitch direction, the amplitude of which is 3.9 times the amplitude of the first-order pitch response. The response of the TLP is significantly increased under the freak wave, especially when the second-order wave force is considered. The apparent focusing position of the maximum response changes with the spectral peak period owing to the nonrepeatability of the freak wave and phase difference of the columns. The maximum predicted errors of surge, heave, and pitch motion reached 42.0%, 41.1%, and 98.9%, respectively, when the freak wave acts on the front column, center of the platform, and back column, which may significantly underestimate the dynamic response. Therefore, the effects of the focusing position should be considered when calculating the response of a TLP under a freak wave.