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Some theoretical advancements and improved conceptions in ocean wave shoaling and wave-current interactions

Understanding the free-surface flow regime in oceans, seas and other water basins is of high importance to various applications. These applications include: sea state forecasting, climate and weather research, oceanographic research, coastal and off-shore engineering, environmental modeling, ecological and ecosystem modeling and so on. Surface gravity waves, specifically, play a crucial role in both deep water and near-shore flows. Currently, surface wave forecasting models, which are adequate for large-scale domains, do not account for some important physical phenomena. The seminar will present progress in two significant physical processes of ocean surface waves. These processes will be nonlinear wave shoaling and the wave-current interactions.

In order to address an audience with various backgrounds, some basic concepts of wave propagation will be discussed, and the main mechanism for near-shore nonlinear energy transfer will be explained in a simplistic manner. An improved conception for wave shoaling, which can be contrary to what linear wave shoaling intuition would indicate, will be presented. Numerical solutions of simplistic nonlinear wave shoaling problems will be used for explaining the involved physical mechanisms.

The part on wave-current interactions will first discuss vertically-averaged currents. Advancements in modeling the interactions of waves with strong as well as faster changing vertically averaged currents will be presented. Second, vertically-structured currents will be investigated. In recent years the capability of circulation models has significantly improved reproducing the vertical variability of ocean flows. Further advancements have coupled forecasting models to circulation ones. Still, the wave-action equation used in forecasting models accounts only to vertically averaged currents requiring the averaging of the circulation models' results. A wave-action equation that overcome this shortcoming will be presented and discussed.