Optimization Of Dispersive Nonlinear Shallow Water Wave Model And Its Application To Wave Induced Currents

water waves, which should be taken into account in design of coastal structures and simulation of nearshore pollutants transportation, are an important dynamical factor in ocean areas. When propagating towards shore line, water waves transform due to variation of topography, such as refraction, diffraction, shoaling, reflection, nonlinear interaction and breaking which induce long period currents. A type of dispersive nonlinear wave model, Boussinesq-type equation, which is able to describe these phenomena, has been studied and applied widely to coastal engineering. In order to improve the properties of this type of equations, higher order terms or more unknowns are introduced in these type of equations. While difficulties arise for obtaining the numerical solutions. Higher order numerical schemes used for these high accuracy equations bring numerical instability and need more computational efforts. On the other hand, Boussinesq-type equation is a phase resolved wave model and is capable of simulating wave currents interaction. So it is a good choice to study wave induced currents in nearshore areas by using this type of equations. In this study, we pay more attention to these two aspects.In order to improve the properties of lower order Boussinesq-type equation, especially the nonlinearity, we started from the three dimensional Euler equation for water waves, derived a set of Boussinesq-type equation with five free parameters by modifying the reference velocities. The properties of the equation are analyzed theoretically by Stokes type analysis method and the free parameters are determined by optimization of overall errors. Both theoretical analysis and numerical test show that optimization of free parameters indeed improve the linear and nonlinear properties of the equations, while there is still limited effect of improvement.To further improve the nonlinearity of lower order Boussinesq-type equation, we rederived a set of Boussinesq-type equation by assuming thatε=O(μ). Then the method of Schaffer and Madsen for improving the linear properties is generalized and used to improve the nonlinearity of the above equation. A new set of lower order Boussinesq-type equation with improving nonlinearity is obtained. Results of theoretical analysis and numerical tests show that comparing with the original equation and Wei et al. equation, the accuracy of nonlinear properties of new equations is improved significantly.Forth order predictor corrector scheme is applied to solve the new equations numerically. Internal wave maker, sponge layer boundary and slot method are introduced to establish the numerical model. The stability of the numerical scheme is analyzed by Von Neumann method. Four sets of numerical tests are carried out to validate the numerical model. Results show that the numerical model in this section is stable, reliable and accurate.For employing the numerical model above to study wave propagation and wave breaking induced currents in surf zone, wave breaker model, subgrid turbulence and bottom friction model are introduced in the numerical model. Then three tests are given to test the ability of numerical model to simulate wave breaking and the following induced currents. Results indicate that the numerical model can be used to simulate wave breaking correctly. Finally, the numerical model is used to study the effects of topography on wave induced currents. Results show that variations of topography in along shore direction affects greatly the distribution, strength and growth of wave induced currents.