Statistics of unidirectional wave groups with and without freak waves observed in the Norwegian Sea

The statistical properties of observed wave groups are essential for designing marine structures. However, the characteristics of group energy, length, and profiles remain unclear. This paper analyzes more than 1 million measured ocean unidirectional wave groups in deep water of the Norwegian Sea during a decade. By classifying wave groups into ordinary and extreme categories based on the presence of a freak wave, it is found that both the distributions of the non-dimensional group energy and group duration follow the Generalized extreme value functions. Moreover, the statistics of wave groups are significantly influenced by the spectral width, with wave steepness having negligible effects. The ratio of the average group duration between extreme and ordinary categories varies slightly from 1.4 to 1.8, although the energy of extreme wave groups can reach 3.0-4.5 times than that of ordinary wave groups. Furthermore, unlike the typical shape of a freak wave with a high wave crest or deep wave trough significantly larger than the surrounding waves, consecutive large waves resembling the "three sisters" are quite common in this location. However, NewWave theory generally underestimates the wave amplitudes surrounding a freak wave, leading to the predicted energy of the most likely extreme wave groups being only about 50-80% of the measured values. Finally, a new modified model is proposed to predict the average shapes of extreme wave groups. After testing numerous wave cases, the model accurately captures the mean morphology of extreme wave groups in the Norwegian Sea.