Freak Waves Within the Third Order Model

After the New Year Wave was recorded in January 1995, considerable works have been devoted to explore the definition, physical nature and occurrence probability of freak waves. Within the frame of classical wave theories, the linear and 2^nd-order random wave models have been chosen most often in the numerical simulations to study the occurrence of freak waves. This paper employs the 3^rd-order random wave theory in simulation to investigate the effects of higher-order wave interaction on the freak wave occurrence. The New Year Wave is used as the case study herein. Its crest is 18.5 m, a criterion applied to categorize the simulated wave trains. To efficiently simulate a wave train with complicated wave interactions, a 1D FFT method is suggested. It is pointed out that the high values of skewness and kurtosis excess of New Year Wave cannot be captured by the 2^nd-order model. The 2^nd-order model is more suitable for reproducing events of high crests. Extreme events need a higher-order wave model. This work extends the study by Prevosto and Bouffandeau (2002). With totally 75,000,000 waves simulated the occurrences of freak waves of crest > 18.5 m are compared among linear, 2^nd- and 3^rd-order wave models. The comparative study also includes the predictions by Forristall (2000), Prevesto (2000) and the one derived based on Mori and Janssen (2004). The simulation once again reveals the inadequacy of the 2^nd-order model to generate freak waves. The occurrence probability of freak waves under the 3^rd-order model is more than 6 times higher than that under the 2^nd-order.