Time Domain Simulation on Wave Shoaling and Breaking Based on HLGN Equations
Due to the decreasing of water depth near the islands and reefs,the nonlinearity of ocean waves is growing and the wave breaking occurs easily.The Green-Naghdi equations was initially developed for the simulation of evolution of nonlinear shallow water waves.After the development in this decade,the scope of the Green-Naghdi equations has been greatly expanded,despite the wave breaking resulting from the variation of topography has not yet been considered.Based on the high-level Green-Naghdi(HLGN)equations,the time domain simulation is performed on the wave shoaling and breaking of regular water waves propagating on an underwater slope in this work.Polynomial series are used in HLGN equations to describe the vertical structure of fluid velocity and the nonlinear free surface condition is accurately satisfied at the instantaneous water surface.In order to consider wave breaking,an eddy viscosity model related to local water depth is introduced.The numerical results are compared with available laboratory data.It is shown that the HLGN equations combined with the wave-breaking model not only accurately and efficiently simulate the propagation and evolution of water waves approaching the underwater slope,but also consider the wave breaking caused by wave shoaling.In this work,the sensitivity analysis is additionally performed on the characteristic parameters of the eddy viscosity breaking model.
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