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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A new formulation of the spectral dissipation source term S ds for wind-wave modeling applications is investigated. This new form of S ds is based on a threshold behavior of deep-water wave-breaking onset associated with nonlinear wave-group modulation. It is expressed in terms of the azimuth-integrated spectral saturation, resulting in a nonlinear dependence of dissipation rates on the local wave spectrum. Validation of the saturation-based S ds is made against wave field parameters derived from observations of fetch-limited wind-wave evolution. Simulations of fetch-limited growth are made with a numerical model featuring an exact nonlinear form of the wave-wave-interactions source term S nl. For reference, the performance of this saturation-based S ds is compared with the performance of the wavedissipation source-term parameterization prescribed for the Wave Modeling Project (WAM) wind-wave model. Calculations of integral spectral parameters using the saturation-based model for S ds agree closely with fetch-limited observations. It is also shown that the saturation-based S ds can be readily adjusted to accommodate several commonly used parameterizations of the wind input source term S in. Also, this new form of S ds provides greater flexibility in controlling the shape of the wave spectrum in the short gravity-wave region.

The time-honored topic of fully developed wind seas pioneered by Pierson and Moskowitz is revisited to review the asymptotic evolution limits of integral spectral parameters used by the modeling community in the validation of wind-wave models. Discrepancies are investigated between benchmark asymptotic limits obtained by scaling integral spectral parameters using alternative wind speeds. Using state-of-the-art wind and wave modeling technology, uncertainties in the Pierson-Moskowitz limits due to inhomogeneities in the wind fields and contamination of the original data by crossing seas and swells are also investigated. The resulting reanalyzed database is used to investigate the optimal scaling wind parameter and to refine the levels of the full-development asymptotes of nondimensional integral wave spectral parameters used by the windwave modeling community. The results are also discussed in relation to recent advances in quantifying wavebreaking probability of wind seas. The results show that the parameterization of integral spectral parameters and the scaling of nondimensional asymptotes as a function of U 10 yields relations consistent with similarity theory. On the other hand, expressing integral spectral parameters and scaling nondimensional asymptotes as a function of u * or alternative proposed scaling wind speeds yields relations that do not conform to similarity requirements as convincingly. The reanalyzed spectra are used to investigate parameter values and shapes of analytical functions representing fully developed spectra. These results support an analytical form with a spectral tail proportional to f Ϫ4 .

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