Freak wave

The processes that lead to the appearance of an extreme wave are not unique: one extreme wave may occur due to different mechanisms than another extreme wave. This gives challenges in the study of extreme waves, which are also called ’freak’ waves, or ’rogue’ waves when they satisfy certain conditions on the wave height compared to (the average of) neighbouring waves. After a freak wave with 18.5 m crest height hit the Draupner oil platform in the North sea on 1 January 1995, the investigation in the topic of freak wave has become more intense. It has been widely recognized that freak waves in the ocean are an important cause of accidents, and that they occur more frequent than expected. It is therefore important to understand the freak wave appearance. This dissertation is intended to understand the development of irregular waves into freak waves, restricting ourselves to waves travelling in one horizontal direction, corresponding to long-crested waves in the ocean. It contains new concepts that can explain the mechanism that can lead to a freak wave. The mechanism for freak wave appearance that is investigated is that of phase coherence: the more coherent the phases of waves contributing to the freak wave, the higher the crest of the freak wave will be. A freak wave for which all waves contribute to the highest possible crest is the so-called maximal wave. Although this concept is used in hydrodynamic laboratories to generate high waves in a tank, much higher than can be achieved with a single stroke of the wave flap, it is extremely unlikely to occur in the real open seas so that the occurrence of freak waves in a random wave field has to be investigated. It turns out that the more flexible notion of pseudo-maximal wave as a description of an extreme wave with less coherent phase is more applicable for extreme wave occurrence in the ocean. Even less restrictive, a weak pseudo-maximal wave that only takes into account the most energy carrying waves can be used to describe an extreme wave as well. These proposed concepts are based on linear wave theory, while nonlinear contributions are added by the Stokes correction. By understanding that an extreme wave may occur as a consequence of linear coherence, a linear prediction method based on minimizing the total wave phase can estimate the time and position of an extreme wave. A further contribution of this dissertation investigates the local energy propagation that leads to a freak wave. A freak wave is mostly developed from a localised wave group that contains a considerable amount of energy that evolves into successive states with even higher coherence. The wavelet transformation is used effectively for identifying the spectral energy distribution of the group events and its evolution. The local energy of waves in a wave group interact and build a larger amplitude. This interaction is based on local dispersive effects within the wave group. A high correlation between the local coherence and the wave amplitude showed that the local coherence can be a good indicator of the appearance of freak waves.