This paper presents a weakly nonlinear water wave model using a mild slope equation and a new aplicit formulation which takes into account dispersion of wave phase velocity,approximates Hedges'(1987) nonlinear dispersion relationship,and accords well with the original empirical formula.Comparison of the calculating results with those obstained from the experimental data and those obstained from linear wave theory showed that the present water wave model considering the dispersion of phase velocity is rational and in good agreement with experiment data.

Nonlinear effect is of importance to waves propagating from deep water to shallow water.The non-linearity of waves is widely discussed due to its high precision in application.But there are still some problems in dealing with the nonlinear waves in pratice.In this paper,a modified form of mild-slope equation with weakly nonlinear effect is derived by use of the nonlinear dispersion relation and the steady mild-slope equation containing energy dissipation.The modified form of mild-slope equation is convenient to solve nonlinear effect of waves.The model is tested against the laboratory measurement for the case of a submerged elliptical shoal on a slope beach given by Berkhoff et al.The present numerical results are also compared with those obtained through linear wave theory.Better agreement is obtained as the modified mild-slope equation is employed.And the modified mild-slope equation can reasonably simulate the weakly nonlinear effect of wave propagation from deep water to coast.

本文采用ADI法对莱州湾的潮流进行了数值模拟，在此基础上，计算了莱州湾沿岸养殖区排海废水在主要半日分潮作用下的空间分布状况，推算出对虾养殖废水对近海环境的影响周期。

A new nonlinear dispersion relation is given in this paper,which can overcome the limitation of the intermediate minimum value in the dispersion relation proposed by Kirby and alrymple(1986),and which has a better approximation to Hedges' empirical relation than the modified relations by edges(1987),Kirby and Dalrymple(1987) for shallow water.The new dispersion relation is simple in form, thus it can be used easily in practice.Meanwhile, a general explicit approximation to the new dispersion relation and other nonlinear dispersion relationa is given.By use of the explicit approximation to the new dispersion relation along with the mild slope equation taking into ccount weakly nonlinear effect, a mathematical model is obtained, and it is applied to laboratory ata.The results show that the model developed with the new dispersion relation predicts wave ransformation over complicated topography quite well.