Improvement Of Accurate Dispersion Nonlinear Mild Slope Equations

Zou Zhili and Jin Hong presented a gentle slope equation wave model with accurate dispersion and third-order nonlinearity which is suitable for irregular waves. And on this basis, Zhang Le presented a new wave model which considered the wave refraction caused by slowly-varying water depth. In this paper, we improved the new model to make it suitable for rapidly-varying water depth such as multiple sand bars.In order to verify the effect of underwater slope entry, this paper simulated wave propagation on plane beach by using the one-dimensional varying-water depth wave model. The good agreements between the numerical results and experimental data demonstrated that the improved model could accurately simulate the shoaling effect and the wave reflection which caused by varying water depth.In order to verify the accuracy of nonlinear equations, the propagation over shallow embankment terrain waves were simulated in this paper. Numerical results of wave surface elevation by using the fourth-order nonlinear equation were in good agreement with the BouN4D4 numerical results and the experimental data, which showed that the improved equation with precise and highly accurate nonlinear dispersive. In addition, the paper also verified the applicability of the improved equation by varying slopes.In order to verify the effect of rapidly-varying entry, the one dimensional new model was applied to simulate wave propagation and deformation over multiple sand bars. The comparison showed that the overall numerical results were in good agreement with the experimental results. Then the effect of sand bars on wave reflection coefficient was studied.In order to discuss the impact of numerical difference scheme, this paper used the Runge-Kutta scheme to recalculate the cases in the range of appropriate slopes. The comparison showed that the calculation by using the Rung-Kutta was better than the calculation by using the Frog Leap.