A theoretical formulation for modeling 3D wave and current interactions in estuaries

Based on the fundamental hydrodynamic equations, a theoretical model is proposed for describing wave and current interactions in estuaries. The following basic assumptions are made: (1) wave period is several orders smaller than that of the tidal currents, (2) tidal current is periodic ranging from semi-diurnal to diurnal, and (3) the estuarine bottom topography is slowly varying with characteristic length variation that is much greater than its wavelength. Two systems of equation are obtained, one for the tidal motion containing the action from the waves and the other for the waves including the effects of the tidal motions. These two systems of equations are coupled and have to be solved iteratively to give their complete interactions.