| In the coastal area, defined as the region between the shoreline and some offshore limit where the depth can no longer influence the waves, complex behavior of waves is anticipated due to various physical effects such as turbulence, wave-structure interaction, wave-current interaction, wave breaking and fluid-density variations. For modeling of nearshore hydrodynamics, many numerical models have been developed so far, but many of such effects are not yet considered appropriately.;In this dissertation, depth-integrated numerical models used in long wave simulation are developed for better understanding of complicated hydrodynamics at the nearshore. First, a non-dispersive shallow water equation model and dispersive Boussinesq model are two-way coupled. The fundamental purpose of the coupling effort is to develop the capability to seamlessly model long wave evolution from deep to shallow water with fine scale resolution, without the loss of locally important physics. Second, a set of depth-integrated equations describing combined wave-current flows are derived mathematically and discretized numerically. To account for the effect of turbulent interaction between waves and underlying currents with arbitrary profile, new additional stresses are introduced, which represent radiation stress of waves over the ambient current field. Finally, a numerical model for gravity waves propagating over variable density fluids is developed by allowing horizontal and vertical variation of fluid density. Throughout the derivation, density change effects appear as correction terms while the internal wave effects on the free surface waves in a two-layer system are accounted for through direct inclusion of the internal wave velocity component. For each of the studied topics, numerical tests are performed to support accuracy and applicability. Consequently, we have developed a comprehensive tool for numerical simulation of complex nearshore hydrodynamics. |
