The nonlinear energy transfer through the wave spectrum is studied on the basis of the previously obtained explicit equation for matrix elements of a four-wave kinetic integral. The equation describes the evolution of a system of gravity waves at the surface of a sea of finite depth with a uniform distribution of broken ice over the sea surface. Particular attention is paid to the analytical part of the algorithm of the calculation of the kinetic integral. This part differs from the standard algorithm by a set of prominent features of the dispersion relation for wave oscillations in the ice-covered water. The kinetic integral for the system under consideration is calculated, and the results are compared with the results obtained for the ice-free water.

The objective of this paper is to perform a theoretically justified parameterization of the dissipation function for wind waves in the spectral form. To solve the problem, the similarity method was used: similarity statements are formulated; dimensionless characteristics of the system are introduced; and general phenomenological representation of the dissipation function for wind waves DIS(S) is constructed. The only additional assumption is that this presentation is valid in a local approximation in the wave spectrum S. Physical analysis of the general representation allows us to reduce the dissipation function to the form DIS(S) ∝ S 2. The further systematic formulation of the final representation of phenomenological function DIS(S) is performed by joining numerous previous results of the author. The physical meaning of the accepted parameterization parameters is analysed, and the correspondence of the parameterization with the new experimental facts found in this field for the last 5-10 years is shown. The previous numerical results are presented that illustrate a successful application of the constructed dissipation function. A regular theoretical justification of the revealed phenomenological representation of DIS(S) is based on the well-known Hasselmann's approach[1]. This theory was modified by the system of postulates resulting in the dissipation mechanism realized due to turbulence in the upper water layer. Physically it means the eddy viscosity mechanism of wind wave dissipation. The final theoretical representation of the dissipation function corresponds to the phenomenological formulation: DIS(S) ∝ S 2. This fact provides the physical justification of the phenomenological approach proposed.

Based on different modifications of the source function in the WAM(C4) wind-wave model, a large series of verification calculations aimed at increasing the quality of the numerical model (with respect to the parameters of accuracy and performance) is performed. We propose a methodology allowing us to solve the following fundamental and practical problems of numerical modeling: (1) determining the minimum interval of verification of numerical wind-wave models, (2) finding a criterion for choosing the best model out of all models subjected to verification, and (3) formulating the accuracy requirement for specifying the input field necessary for the given accuracy of wind-wave field calculations. Particularly, we have found that (a) the minimum term of verification calculations for numerical wind-wave models is three months; (b) according to our criterion, the proposed modification of the WAM model impartially is “essentially preferable” to the original model; and (c) the relative errors (yielded by the proposed version of the WAM model) in the calculated wave heights ρH _s and average periods ρT _m for different levels of the relative error of the input wind-wave field ρW make it possible to solve the third problem mentioned above.

In this paper, a detailed statistical analysis of the wind and wave fields in the Indian Ocean (IO) for the period of 1998-2009 was performed based on using the wind fields taken from the site of the National Centers for Environmental Prediction and the National Oceanic and Atmospheric Administration (NCEP/NOAA) [1] and on the numerical wind-wave model WAM [2] modified with the source function proposed in [3]. The primary analysis of the fields includes mapping the wind and wave fields, as well as their energy fields, calculated with different scales of space-time averaging; the subsequent zoning of the IO area; and assessing the seasonal interannual variability of all the fields and their 12-years trends. Further analysis is carried out taking into account the zoning. This analysis includes a construction of the time series obtained with different scales of space-time averaging for all the fields, a spectral analysis of these series, finding and analyzing the spatial and temporal distribution of extrema of the wind and wave fields (accounting for the their sharing in the zones), and making histograms of the wind and wave fields and calculating their first four statistical moments (in the zones and in the ocean as a whole). The results allow us to evaluate a large set of statistical characteristics of the wind and wave fields in the IO area, scales of their variability, their long-term trends, and the features of distribution for these statistical characteristics in the ocean area as well.

Wind waves are considered as an intermediate small-scale dynamic process at the air-sea interface, which modulates radically middle-scale dynamic processes of the boundary layers in water and air. It is shown that with the aim of a quantitative description of the impact said, one can use the numerical wind wave models which are added with the blocks of the dynamic atmosphere boundary layer (DABL) and the dynamic water upper layer (DWUL). A mathematical formalization for the problem of energy and momentum transfer from the wind to the upper ocean is given on the basis of the well known mathematical representations for mechanisms of a wind wave spectrum evolution. The problem is solved quantitatively by means of introducing special system parameters: the relative rate of the wave energy input, I _RE , and the relative rate of the wave energy dissipation, D _RE . For two simple wave-origin situations, the certain estimations for values of I _RE and D _RE are found, and the examples of calculating an impact of a wind sea on the characteristics of both the boundary layer of atmosphere and the water upper layer are given. The results obtained permit to state that the models of wind waves of the new (fifth) generation, which are added with the blocks of the DABL and the DWUL, could be an essential chain of the general model describing the ocean-atmosphere circulation.