Novel Internal Wave Paradigm Strongly Nonlinear Scale Separated Interactions
RENSSELAER POLYTECHNIC INST TROY NY DEPT OF MATHEMATICAL SCIENCES
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My long-term goal is to understand and predict spectral energy density of internal waves in the ocean, and the effects of internal waves on oceanic large scale motions. First-Principle theory of strongly nonlinear wave-wave interactions for internal waves. Present study is based on the extension of the wave turbulence theory to the internal waves in the ocean. In particular, we attempt to go beyond traditional wave turbulence assumptions of weak nonlinearity and resonant interactions. This study is characterized by strong synergy with the work by Dr. Kurt Polzin WHOI. We have derived an extension of the traditional kinetic equation for internal waves that takes into account not only resonant, but near resonant interactions. This derivation is based on the Dyson-Wild diagrammatic technique. The rational for inclusion of the near-resonant interactions is the following kinetic equation shows that the amplitude of the waves do tend to change as a result of wave-wave interactions. Thus the life time of the waves is necessarily finite. Consequently waves can not be strictly resonant, as strict resonances appears only for the waves with infinite lifetime.
- Physical and Dynamic Oceanography
- Numerical Mathematics