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This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered.The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, non-linear interactions in deep water; 4, white-capping dissipation; 5, non-linear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments. Keywords

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Wind-sea generation was observed during two experiments off the coast of North Carolina. One event with offshore winds of 9-11 m s Ϫ1 directed 20°from shore normal was observed with eight directional stations recording simultaneously and spanning a fetch from 4 to 83 km. An opposing swell of 1-m height and 10-s period was also present. The wind-sea part of the wave spectrum conforms to established growth curves for significant wave height and peak period, except at inner-shelf stations where a large alongshore wind-sea component was observed. At these short fetches, the mean wave direction m was observed to change abruptly across the wind-sea spectral peak, from alongshore at lower frequencies to downwind at higher frequencies. Waves from another event with offshore winds of 6-14 m s Ϫ1 directed 20°-30°from shore normal were observed with two instrument arrays. A significant amount of low-frequency wave energy was observed to propagate alongshore from the region where the wind was strongest. These measurements are used to assess the performance of some widely used parameterizations in wave models. The modeled transition of m across the wind-sea spectrum is smoother than that in the observations and is reproduced very differently by different parameterizations, giving insights into the appropriate level of dissipation. Calculations with the full Boltzmann integral of quartet wave-wave interactions reveal that the discrete interaction approximation parameterization for these interactions is reasonably accurate at the peak of the wind sea but overpredicts the directional spread at high frequencies. This error is well compensated by parameterizations of the wind input source term that have a narrow directional distribution. Observations also highlight deficiencies in some parameterizations of wave dissipation processes in mixed swell-wind-sea conditions.

Goda, Y. et al. (1993): Intercomparison of extremal wave analysis methods using numerically simulated data, Proc.: Case studies of extreme wave analysis-a comparative analysis-, Proc. WAVES 93 Conf., Vol.2, pp.978-992. Yamaguchi, M. and Y. Hatada (1997): An extremal analysis system and its application to the estimation of extremes of meteorological and oceanographic elements around the coasts of Japan, Proc. WAVES 97 Conf., Vol.2, pp.932-946.