Distribution of crest heights in sea states with abnormal waves

Abstract

The short-term statistical representation of wave crests in sea states with abnormal waves is discussed on the basis of comparison with the crest statistics in lower sea states. The analyzed set of field data was collected during a storm in the North Sea. Some typical properties of the reported abnormal waves and the associated sea states that have been described in Guedes Soares et al. [Guedes Soares C, Cherneva Z, Antão E. Characteristics of abnormal waves in North Sea storm sea states. Appl Ocean Res 2003;25:337–44] are reviewed and additional relations are derived here. To describe the observed crest height distributions, the model of Forristall [Forristall G. Wave crest distributions: Observations and second-order theory. J Phys Oceanogr 2000;30:1931–43] has been applied. Nonlinear effects to second order are taken into account by means of the mean wave steepness and the Ursell number. Although the model is found to be generally adequate for sea states with less severe conditions, the largest crests in the highest sea states, and especially those with abnormal waves present, are permanently underestimated. It could be concluded that the abnormal waves do not conform to the underlying population of waves in the associated sea states.