Anomalous waves and rogue events are closely associated with irregularities and unexpected events occurring at various levels of physics, such as in optics, in oceans and in the atmosphere. Mathematical modeling of rogue waves is a highly actual field of research, which has evolved over the last decades into a specialized part of mathematical physics. The applications of the mathematical models for rogue events is directly relevant to technology development for prediction of rogue ocean waves, and for signal processing in quantum units. In this survey, a comprehensive perspective of the most recent developments in methods for representing rogue waves is given, along with discussion of the devised and forms and solutions. The standard nonlinear Schrödinger equation, the Hirota equation, the MMT equation and further to other models are discussed, and their properties highlighted. This survey shows that the most recent advancement in modeling rogue waves give models which can be used to establish methods for prediction of rogue waves at open seas, which is important for the safety and activity of marine vessels and installations. The study further puts emphasis on the difference between the methods, and how the resulting models form a basis for representing rogue waves in various forms, solitary or with a wave-background. This review has also a pedagogic component directed towards students and interested non-experts, and forms a complete survey of the most conventional and emerging methods published until recently

The main goal of the paper is to compare the effects of the wave spectrum, computed using the Discrete Interaction Approximation (DIA) and the Webb–Resio–Tracy (WRT) methods, on statistical wave properties such as skewness and kurtosis. The statistical properties are obtained by integrating the three-dimensional free-surface Euler equations with a high-order spectral method combined with a phenomenological filter to account for the energy dissipation due to breaking waves. In addition, we investigate the minimum spatial domain size required to obtain meaningful statistical wave properties. The numerical simulations are performed over a physical domain of size 4.13 km × 4.13 km. The results indicate that statistical properties must be computed over an area of at least 4 km2. The results also suggest that selecting a more computationally expensive WRT method does not affect the statistical values to a great extent. The most noticeable effect is due to the energy dissipation filter that is applied. It is concluded that selecting the WRT or the DIA algorithm for computing the wave spectrum needed for the numerical simulations does not lead to major differences in the statistical wave properties. However, more accurate energy dissipation mechanisms due to wave breaking are needed.

Wave breaking is one of the most important yet poorly understood water wave phenomena. It is via wave breaking that waves dissipate most of their energy and the occurrence of wave breaking directly influences several environmental processes, from ocean-atmosphere gas exchanges to beach morphodynamics. Large breaking waves also represent a major threat for navigation and for the survivability of offshore structures. This paper provides a systematic search for intermediate to deep water breaking waves with particular focus on the elusive occurrence of plunging breakers. Using modern remote sensing and deep learning techniques, we identify and track the evolution of over four thousand unique wave breaking events using video data collected from La Jument lighthouse during ten North Atlantic winter storms. Out of all identified breaking waves (Nb=4683), ≈22% were dominant breaking waves, that is, waves that have speeds within [0.77cp, 1.43cp], where cp is the peak wave speed. Correlations between the occurrence rate of dominant breaking waves (that is, waves per area and time per peak wave period) and wave steepness and wave age were observed. As expected, the number of identified plunging waves was small and six waves of all detected breaking waves, or 0.13%, could undoubtedly be considered as plunging waves. Two waves were also identified as unusually large, or rogue waves. Although afflicted by several technical issues, the data presented here provides a good indication that the probability of occurrence of plunging waves should be better incorporated into the design of offshore structures, particularly the ones that aim to harvest energy in offshore environments.