| Coastal and offshore areas are extremely dynamic regions. Near-shore wave-current field affects the layout and design of hydraulic constructions and is of great importance to nearshore sediment transport and pollutant transport.In this paper, the 2-D Second-Order Fully Non-linear Boussinesq Equation numerical model and the near-shore wave-induced current mathematical model is developed in un-staggered grid with finite difference method.First, simple analysis of the deduction and the characters of the 2-D Second-Order Fully Non-linear Boussinesq Equation are put forward. Under un-staggered grid, the 2-D Second-Order Fully Non-linear Boussinesq mathematical model are simulated. Compared with the modeled results, analysis about the influence on the results of different precision level of nonlinearity and the mild slope hypothesis in non-linear terms are given. The mixing 4-order Adams-Bashforth-Moulton is used for time difference terms. Source function for wave generation and sponge layer boundary condition are used since here they are able to damp wave energy and possible wave reflection.Comparing with the experiments'results, the 2-D Second-Order Fully Non-linear Boussinesq Equation model has good reliability; the influence of different precision level of nonlinearity and the mild slope hypothesis in non-linear terms is not so obvious. Then, vegetation term is added into the wave model to simulate the affection on the wave that the vegetation damping brings. Comparing with the experiment information, the numerical results prove the reliability of the vegetation model.Second, breaking term,bottom friction term and subgrid turbulent mixing term are added to the wave model to simulate the breaking phenomenon. The regular wave-induced longshore current is caculated under the circular shoal terrain and the action of regular wave with various grade,wave height,wave period, and the results are in good agreement with experiment results.
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