Mathematical Model For The Evolution Of Sandy Beach Profiles

Sandy coasts are the classic types of the coasts, consisting of gravel,gritcobbles and other coarse particles. They are usually characterized by narrow berm and steep shore face. The sandy coasts are the ideal space for the marine fishery and attract lots of visitors from the world and hence contribute lots to the econmic developement. However, changes of the natural environment and the artificial destruction made the sandy coasts suffer from severe erosion in recent years. Therefore, research on the coastal sediment movement is of great value to guard againt the adverse coastal deformation and to the economic and social development.In order to model the coastal hydrodynamic and explore the interaction between the beach evolution and the topographical change, an efficient and process-based mathematical model for the evolution of sandy beach profiles has been established. The paper includes the following content:1. New numerical scheme for Boussinesq moduleBoussinesq-type wave models are attractive and effective to simulate wave propagation in the nearshore region as it can simulate lots of hydrodynamics, such as wave propagation.wave breaking, setup-down and the nonlinear motion of the fluid. Finite Difference Method(FDM) has been widely used for solving Boussinesq-type wave models due to its simplicity. However the disadvantage of the FDM scheme are obvious:First, the models tend to be unstable to high wavenumbers near the grid Nyquist limit. Numerical filters are usually needed to stabilize the wave model. Furthermore, moving wet-dry interface and wave breaking in Boussinesq models are treated by experience, as a result, it will introduce additional noisy source and brings uncertainty to the numerical data. A hybrid finite-difference(FDM) and finite-volume(FVM) numerical scheme is developed to solve one-dimensional Boussinesq equations in this study. The model can solve breaking and time-varying wet-dry interface well without the use of additional numerical filter, and the process of calculation is stable.2. Process-based mathematical model for the evolution of sandy beach profilesThe bottom shear stress is calculated by numerically solving the bottom boundary equation and then used to calculate the sand transport rate. The beach evolution is time marched by solving sand conservation equation using a high resolution scheme and the conservative filter is used to smooth the morphologic. The models mentioned above are effectively coupled to form a process-based mathematical model for the evolution of sandy beach profiles. Some nuemrical expriments are conducted to study the evolution of sandy beach profiles.