Collaborative Research: CMG: Mathematical Theory and Modeling of Wave-Current Interaction

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This project develops a multi-scale, fluctuation-averaged, asymptotic theory for the evolution and interaction of currents and surface gravity waves, typical of stratified coastal shelf waters. The theory will provide a picture of how waves, currents, and materials interact on large spatio-temporal scales. The theory will also yield a practical three-dimensional model with which shelf dynamics may be computationally simulated without the necessity of resolving features of the flow on the short space and time scales typical of the primary gravity-wave oscillations. The model aims to improve on the current computationally intensive near-shore small-scale circulation codes, while being founded more rigorously than large-scale models that attempt to parameterize wave effects through ad hoc closure hypotheses.The long term goal of this line of research is the creation of a realistic numerical simulator the geoscience community can use to study geophysical problems typical of the coastal and shelf environments: wave/current climatology; the evolution and transport of sea floor beds; the transport of pollutants; the dispersal or retention of living populations; the circulation of heat and ocean water constituents; the intrusion of a fresh water river plume into the ocean; and the dynamics of man-made structures.