Improved Mild Slop Equation With Accurate Dispersion

Since mild-slop equation is fully dispersive and of high calculation efficiency, it becomes one of the mathematical models which are widely used for calculating waves in coastal and offshore region. However, most mild-slop equations are just suitable for regular waves, such as Berkhoff s (1972) elliptic mild-slope equations、Radder’s (1979) parabolic mild-slope equations and Copeland’s (1985) classical hyperbolic mild-slope equations. What’s more, Smith and Sprinks’s (1975) mild-slop equations are just suitable for narrow spectrum irregular waves. In summary, the above mild-slop equations are just linear models, and not suitable for irregular waves with any spectrum width.In order to resolve this problem, Zou Zhili and Jin Hong give a new wave model with accurate dispersion which is suitable for irregular waves. This model is fully dispersive and of third order nonlinearity. Compare to Boussinesq equations, this model sets no limit for applicable water depth, so it is suitable for arbitrary water depth. Compare to mild-slop equations, both models are full dispersion, but the new model is nonlinear, so it can simulate nonlinear effect of waves, and it is suitable for irregular waves.However, the new model just considers the wave refraction caused by variable water depth. Here we improve the new model by including the terms proportional to(?)h, while higher order terms such as ((?)h)2and (?)2h are ignored. This improved model can accurately simulate general variable water depth cases such as shoaling effect and wave reflection and so on. The new model is also fully dispersive and of third order nonlinearity, and suitable for irregular waves with any spectrum width.The one dimensional new model is verified by simulating wave propagation on plane beach. The good agreements between the numerical results and experimental data demonstrate that the improved model can accurately simulate general variable water depth cases such as shoaling effect and wave reflection and so on.The two dimensional new model is verified by simulating wave propagation on two kinds of elliptical shoals. The good agreements between the numerical results and experimental data demonstrate that the improved model is suitable for irregular waves with any spectrum width, and is suitable for general variable water depth cases.