Expected Shape of Extreme Waves in Storm Seas

The theoretical expected structure of large nonlinear waves can be described, using the Gram-Charlier approximations of Jensen et al. (1995) and Jensen (1996, 2005), and the quasi-deterministic model of Fedele & Arena (2005). The second-order narrow-band approximation offers a simpler alternative to these models, as recently suggested in Tayfun & Fedele (2006). Herein, this latter alternative is elaborated further, deriving theoretical expressions for predicting the expected shape of large waves, conditional on somewhat more general constraints than those previously considered. The theoretical results are verified favorably with oceanic measurements gathered at deep and transitional water depths in the North Sea. Some comparisons of the present model with those of Jensen et al. (1995) and Fedele & Arena (2005) are also given, showing that all three models do in fact reasonably well in representing the expected profile of large waves in storm seas.