Statistical properties of a directional wave field: direct simulations of the Euler equations and second-order theory

• Main Authors: Toffoli, Alessandro, Bitner-Gregersen, Elzbieta, Onorato, Miguel
• Other Authors: Swinburne University of Technology
• Format: Conference Object
• Language: unknown
• Published: American Society of Mechanical Engineers 2008
• Subjects: Arctic
• Online Access: http://hdl.handle.net/1959.3/151883; http://www.asmeconferences.org/omae08/

It is well established that modulational instability enhances the occurrence of extreme events in long crested wave fields. As a result, the statistical properties of random waves deviate from the second-order predictions often used for engineering applications. Recent studies, however, has shown that the effects related to the modulational instability reduce if coexisting directional wave components are considered. Here, direct numerical simulations of the Euler equations are used to investigate whether modulational instability may produce significant deviations from second-order statistical properties of surface gravity waves when short crestness (i.e., directionality) is accounted for. Simulations of unidirectional wave fields are also presented for a comparison. Although the directional effects are not investigated comprehensively due to the computational burden, the results demonstrates that directionality can drastically reduce the effects of the modulational instability when a large directional spreading (e.g. wind sea) is considered. In this respect, the result will also show that the distribution proposed by Forristall (J. Phys. Ocean., 30, 2000) provides a good estimate of the simulated crest height also at low probability levels. It will be shown, furthermore, that second-order theory also provides a good estimate of the probability distribution of wave troughs.