A time-averaged approach to wave evolution from deep water to shallow water

Flow circulation and the field variation of wave height and setup are important data in coastal engineering practice. This dissertation presents a wave-averaged model for simulating wave transformation and associated mean flow circulation in coastal regions. It is intended for applications where interest centers on the evolution of wave-averaged parameters such as wave height, setup and wave-induced current, and where the resolution of wave phase is unnecessary.;An analysis technique used in turbulent shear flow is adapted to develop the governing equations for wave height, wave setup, and current. Variables are decomposed into a slowly varying mean flow and a fluctuating residual which includes both wave and turbulent components. Subsequently, the conservation equations of mass, momentum and energy are averaged over the wave groups and integrated over water depth. The time-averaging introduces apparent stresses representing the influence of wave fluctuations on the mean flow. Fourier approximation wave theory is employed to construct closure surfaces describing the apparent stresses as a function of wave height, water depth and wave period. The model is valid for both shoaling waves and surf zones. Both wave-current interaction and mean flow circulation are represented.;The governing equations are a quasi-linear hyperbolic system. Numerical solutions are based on the method of characteristics. In a one-dimensional space, this system has two families of characteristics: wave characteristics and energy characteristics. In a two-dimensional space, the system has three families of characteristics: flow characteristics, wave characteristics and energy characteristics. Corresponding to each family of characteristics, there are an infinity of characteristic surfaces and an infinity of compatibility equations. The numerical algorithm combines the compatibility equations integrated along several bi-characteristics. Open boundary conditions are constructed for typical inflow and outflow boundaries. Case studies demonstrate wave propagation in one and two spatial dimensions with non-reflecting boundary conditions.;Conceptual schemes for simulating wave reflection and sediment transport are suggested.