Numerical Simulation of Two-Dimensional Regular Wave Overtopping Flows over the Crest of a Trapezoidal Smooth Impermeable Sea Dike

The objectives of the current study are to develop a two-phase flow solver and to investigate the two-dimensional regular wave overtopping flow field over a sea dike. The solver is based on the Navier-Stokes equations and the classical Smagorinsky eddy-viscosity model. A coupled approach of wave generation and absorption is accomplished in the numerical wave flume, and the wave reflection from the work zone can be eliminated efficiently. Simulations of the wave run-up and breaking were performed to validate the effectiveness of the numerical wave flume. The influences of turbulent eddy viscosity and grid refinement on the simulations of the breaking waves are discussed. The flow features of wave overtopping over a sea dike are investigated systematically for both nonbreaking and breaking waves. The numerical results show that the layer thicknesses along the dike crest decay following an exponential rule, whereas the maximum velocities along the dike crest exhibit a mild increasing trend. Furthermore, a relationship between the overtopping discharges and the maximum velocities on the dike crest is obtained by regression analysis. With this correlation, the maximum overtopping velocity can be estimated from the overtopping discharge, which provides a practical approach for the risk assessment of a sea dike.