Boussinesq modeling of waves, currents and sediment transport

New Boussinesq-type equations are derived for surface water wave propagation and currents in relatively shallow water regions. The new equations are fully nonlinear and accurate to O(mu2), with mu the indicator of wave dispersion. 1-D and 2-D computer models (FUNWAVE1D2.0 and FUNWAVE2D2.0) are developed based on the new Boussinesq equations for wave current modeling. The new Boussinesq models are based on a staggered grid system. The FUNWAVE2D2.0 model is also based on generalized curvilinear coordinate to fit complex nearshore geometries. Wave breaking introduced undertow currents are included in the dependent reference velocities automatically. The new equations retain vertical vorticity generated by wave breaking and bottom friction to the second order of dispersion. Wetting and drying algorithm is developed to model wave run up and run down and track shoreline change instantaneously. Phase resolving sediment transport is integrated into the Boussinesq wave current model to investigate nearshore morphological change due to wave and current forces (FUNSEDI1D1.0 and FUNSEDI2D1.0). A non-oscillatory Euler-WENO morphological scheme is developed to model the interaction between hydrodynamics and morphological change accurately and stably as compared to classical Lax-Wendroff schemes. 1-D vertical wave current bottom boundary layer models are developed to calculate the bottom shear stresses instantaneously. Classical sediment transport formulas are implemented and compared to investigate their performance for unsteady, transient flow as well as skewed and asymmetric waves introduced sediment transport in nearshore region. The model is applied to simulate DUCK'94 field measurement to investigate both accretional and erosional events of sand bar migration. The LIP11 lab experiment is also simulated to further test the performance of the model. The present sediment transport model can also be used to examine future transport formulas for unsteady flow system.