Numerical simulation of freak wave generation in random oceanic sea states described by JONSWAP spectrum is carried out based on the modified four-order nonlinear Schrödinger (mNLS) equation in deep water. By comparison of the variation of each term modulus in mNLS equation and the power spectra for freak wave occurrences, it can be concluded that nonlinear focusing of some components with approximate frequencies to the dominant frequency is one possible mechanism of freak waves. Effects of the relevant parameters on freak wave formation are also discussed.
With the development of ocean exploitation, people have recently encountered freak waves more and more, and the most famous example is no other than the so-called New Year wave which hit the Draupner platform in January 1, 1995. It is usually thought that a freak wave is an extraordinarily large wave with its height exceeding twice significant height in a wave train and has potentially devastating effects on coastal or offshore structures and ships, so its mechanism has attracted many oceanographers' attention. Various mechanisms have been proposed to explain the formation of freak waves subject to some special conditions (Kharif and Pelinovsky, 2003), such as spatio-temporal focusing of wave groups, geometrical focusing of water waves and wave-current interaction in the linear theory; and nonlinear-dispersive focusing of wave trains for the Korteweg-de Vries equation in shallow water and nonlinear modulation instability of wave trains for the nonlinear Schrödinger (NLS) equation in deep water in the nonlinear theory. Since the investigation of freak waves on the basis of experimental data still has certain difficulties such as the selection of measured points in situ and the instrumental detection by buoys (Pelinovsky et al., 2003), numerical experiments have been developed greatly. At present the model based on the famous cubic NLS equation (CSE) which describes the nonlinear evolution of deep-water wave trains is robust to investigate freak wave phenomenon.
