Chalikov D. V.
Numerical 2-D and 3-D models of surface waves allowed to simulate and prove most of the facts studied both experimentally and analytically. In addition, a detailed modelling discovers new regularities beyond the scope of traditional concepts. The results obtained mostly at Saint-Petersburg Branch of Oceanography Institute RAS are listed. The facts, which were never discussed in papers of other authors and never explained are described. These facts are mostly contradict general views. The results are based on accurate numerical models of potential liquid motion with a free surface. Harmonic waves quickly obtain bound modes and, on the average, turn into Stokes waves. The Fourier analysis of exact solutions shows that a real field is rather a superposition of Stokes waves with different amplitudes and phases, than the superposition of linear modes. Wave field is the result of superposition of unstable modes whose amplitudes fluctuate in time under the influence of reversible interactions. Development of extreme waves occurs over the time of the order of one wave period. Such fast evolution cannot be explained by the theory of modulational instability. Calculations of extreme wave probability, using a linear model, provide the results close to the calculations by a non-linear model. This is why the role of the nonlinearity in generation of extreme waves is evidently not very significant. When crest merging occurs, a quick nonlinear wave interaction takes place, which leads to a sharp increase of the resulting wave and further possibility of overturning. A jaggy character of 2-D wave spectrum with high resolution (presence of steady peaks and holes) is a typical result of direct wave modeling. The results of the numerical modeling significantly depend on the minor details of initial conditions. Therefore, the results confirmed statistically should be obtained by ensemble modeling. Such modeling, in particular, does not prove correctness of the Hasselmann’s theory.
