Generation and Limiters of Rogue Waves

Abstract

Rogue waves are abnormally high, with respect to the mean, waves in the ocean. Present understanding of their nature will be reviewed and discussed. Rogue waves can be due to quasi-linear superpositions of waves and nonlinear effects such as instabilities of wave trains. Both appear to be important and possible. Individual waves can be focused into a superposition due to either dispersive or directional features of wave fields. While probability of the former in oceanic conditions is very low, the directional focusing appears to be rare but regular events. Nonlinear wave fields should be separated into stable and unstable conditions, with different probability distributions for wave heights/crests. In stable conditions, wave statistics are determined by the quasi-linear focusing, whereas in unstable wave trains high transient wave events can occur. Their maximal height/steepness is determined by combined dynamics of the instability growth and the limiting wave breaking.