On the probability of occurrence of rogue waves

Abstract

<jats:p>&lt;p&gt;&lt;strong&gt;Abstract.&lt;/strong&gt; A number of extreme and rogue wave studies have been conducted theoretically, numerically, experimentally and based on field data in the last years, which have significantly advanced our knowledge of ocean waves. So far, however, consensus on the probability of occurrence of rogue waves has not been achieved. The present investigation is addressing this topic from the perspective of design needs. Probability of occurrence of extreme and rogue wave crests in deep water is here discussed based on higher order time simulations, experiments and hindcast data. Focus is given to occurrence of rogue waves in high sea states.&lt;/p&gt;</jats:p>

Modeling extreme wave heights from laboratory experiments with the nonlinear Schrödinger equation

“…The high-level agreement between However, the numerical simulations overestimate the experimental results particularly in the group of severe sea state for the reason that the NLS equation could not model wave breaking. This kind of limitation, which also the higherorder spectral method (HOSM) has, is observed in other studies as well (Bitner-Gregersen and Toffoli, 2012). Nevertheless, it still catches the main characteristics of the extreme waves and provides an important physical insight of their formation.…”

“…5g-i, the same conclusion can be drawn that the NLS equation still captures the main characteristics of extreme wave heights, particularly in the intermediate and end stages of the evolution process, and the pronounced deviation at the beginning stage can be explained in the same manner as before. It is also detected that the numerical simulation presents larger wave heights than the experiments, which definitely attribute to the energy dissipation such as wave breaking in reality (Bitner-Gregersen and Toffoli, 2012). In other words, to give an exact description of the tail of the exceedance probability, the influence of wave breaking must be considered.…”

Alternative environmental contours for structural reliability analysis

“…Rogue waves, sometimes also referred to as monster waves, freak waves, killer waves, abnormal waves or simply extreme waves, are waves with individual wave height exceeding twice the significant wave height, 3 and may occur in sea states that are not identified as extreme by the environmental contours of significant wave height and mean zero-crossing period. Such waves, even if not occurring in an extreme sea state, may impose extreme loads on marine structures, and have the potential to be dimensioning for the structural design.…”

Modulational instability and wave amplification in finite water depth

“…The occurrence of extreme waves (also known as freak or rogue waves) has an important role in many branches of physics and engineering (see, for example, Chabchoub et al, 2011;Onorato et al, 2013a, b;Chalikov, 2009;Babanin et al, 2011;Bitner-Gregersen and Toffoli, 2012;Toffoli et al, 2008b;Solli et al, 2007;Kibler et al, 2010;Bailung et al, 2011, among many others). Apart from a linear superposition of wave modes and the effect of currents on waves (caustic theory), the modulational instability of a plane wave to side band perturbations remains the most plausible mechanism for the formation of rogue waves in deep water (Zakharov and Ostrovsky, 2009;Osborne, 2010;Onorato et al, 2013b;Kharif et al, 2009), i.e.…”