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Modelling Swell High Frequency Spectral and Wave Breaking

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Final rept.

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My long-term goal was development of a self-consistent analytical, dynamical and statistical theory of weak and strong nonlinear interactions in ocean gravity waves. The theory should be supported by the extensive numerical simulations as well as by laboratory experiments and field observations. The theory will be used as a basis for development of approximate models of Snl, which can be used in a new generation of operational models for wave forecasting. Another goal is the development of the theory of wave breaking which will make it possible to find a well-justified estimate for the rate of energy dissipation due to this process. The level of nonlinearity in an ensemble of wind-driven ocean waves is relatively small. It makes it possible to apply for its statistical description the theory of weak turbulence. In the most simple case, it is the theory of kinetic Hasselmanns equation for spectra of the normalized wave action. The kinetic equation has a remarkable family of exact stationary Kolmogorov-type solutions. They are governed by two parameters fluxes of energy and momentum to the region of high wave numbers, and can be applied for description of energy spectra in the universal range behind the spectral peak. All Kolmogorov spectra have asymptotics Ewsimilar or equal w-4 after averaging in angle. The exact kinetic equation is too complicated to be used in the operational model of wave prediction. Thus, the development of its approximate models is an actual problem. The wave-breaking, which in most cases participate in the wave dynamics is a strongly nonlinear process, makes an important contribution to energy dissipation. So far, there is no reliable theory for this phenomenon. I combine in my work the analytical methods of mathematical physics with massive numerical simulation end construction of simple phenomenological models. All results are compared with laboratory experiments and field observations.

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  • Physical and Dynamic Oceanography
  • Numerical Mathematics

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