ITR/AP(DMS): Numerical Studies of the Nonlinear Interaction Between Turbulent Air Flow and Sea Surface Waves, with Application to Ocean Surface Wave Turbulence

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The proposed project develops a numerical model for turbulent airflow over nonlinearly evolving water surfaces that overcomes the limitations of previous studies. Efficient computational algorithms for modeling airflow, efficient hydrodynamic methods to evolve the sea surface boundary, and parallel computing techniques will be combined to make statistical analyses of realistic problems in both two and three dimensions possible. Scientific visualization methods will be applied to analyze results and to improve understanding of the nonlinear interactions between wind and waves that are important for sea surface growth and dissipation. Studies will be performed to determine the conditions under which "decoupling" the interacting complex systems into airflow-only or hydrodynamic-only simulations is possible by including appropriate forcing terms; the form of these forcing terms, when applicable, will be compared with existing empirical and analytical models to clarify the important physical processes. Decoupled hydrodynamic-only simulations will be pursued to investigate wave-wave energy transfer effects in larger scale problems than those possible in the coupled air-water model, and resulting forms of the equilibrium sea surface spectrum will be obtained. Commonly applied approximate hydrodynamic models will also be considered to assess their performance, and wave spectra obtained from numerical studies will be extrapolated using applicable approximate models to include breaking-wave effects not captured in the full numerical simulations. Results of the project will be significant for studies of the global climate, sea wave forecasting, and interpretation of direct and remotely sensed oceanographic data. More generally, project results will clarify important physical effects that can occur in a system of coupled nonlinear turbulent systems. The generation of sea surface waves by winds is one of the fundamental air-sea interaction processes that affect the global climate. Although this topic has been studied extensively through both physical modeling and experimental measurements, understanding of the physics involved remains limited due to the nonlinear phenomena implicit in both airflow and sea surface wave evolution. Numerical simulations offer a means to improve understanding of the complex interactions of this problem, but only recently have computing resources improved to make sufficiently large scale simulations possible. The proposed project represents an interdisciplinary collaboration between applied mathematics and engineering researchers. Educational efforts also comprise a principal objective of the project, including graduate and undergraduate education and research. All participants in the project will gain information technology (IT) experience through algorithm and code development. Project results will be communicated to the external community through conference and journal publications and through use of the world-wide-web; project web resources will also be used in classes taught by the research team to introduce students to scientific applications of IT research.