

Selfsimilarity of wind input terms and magic numbers
Date/Time: 17:30 07Aug2014
Abstract:
We study numerically solutions of Hasselmann equation for different wind input terms, including those used in operational wave prediction models, for limited fetch growth statement. Some of the wind input terms are well physically justified and some are not, but simulation results with first ones exhibit remarkable universal properties  selfsimilar behavior of total energy and frequency as a functions of the fetch distance, described by power laws obtained from selfsimilarity analysis of Hasselmann equation.
It is more remarkable that even for not so well physically justified wave input terms, we do observe absence of good selfsimilar behavior of the total energy and spectral peak frequency, but still can construct specific "magic" combinations of specific powers of total energy and peak frequency, obtained from selfsimilar analysis of Hasselmann equation for limited fetch waves growth, which are preserved with good accuracy along the fetch. We explain this "strange" coincidence as locally realized selfsimilar regimes in individual locations of the fetch. In summary, we observe the universality of the wind wave growth for wide spectrum of the wind input terms historically developed for Hasselmann equation, exhibiting itself in either direct manifestation in the form of selfsimilar laws of the total energy and peak frequency as function of fetch, or preservation of the specific combinations of the powers of theoretical selfsimilar solutions. In our opinion, the observed properties emphasize the key role of nonlinearity in the evolution of wave ocean surface. Attachments:
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