对于粉沙淤泥质河口和海岸，海底泥沙受潮流作用主要以悬沙形式输运。在这样的海区建港与疏浚航道，需要首先进行泥沙淤积问题的研究。本文采用潮流作用下不平衡方程式、挟沙能力公式和起动流速公式，建立了潮流作用下河口悬沙运动二维数学模型，在对二维悬沙不平衡输沙方程和海底变形方程进行离散时直接采用显式迎风格式，得到了较好的结果。在此基础上，将该模型应用于实际水域，结果表明，该数学模型能够模拟河口的悬沙运动规律和冲淤变化，对于水流较大的海域该模型有一定的应用价值。

A nonlinear dispersion relation is presented to model the nonlinear dispersion of waves over the whole range of possible water depths. It reduces the phase speed over-prediction of both Hedges' modified relation and Kirby and Dalrymple's modified relation in the region of 1 < kh <1.5 at small wave steepness and maintains the monotonicity in phase speed variation at large wave teepness. And it has a simple form. By use of the new nonlinear dispersion relation along with the mild slope equation taking into account weak nonlinearity, a mathematical model of wave transformation is developed and applied to laboratory data. The results show that the model with the new dispersion relation can predict the wave transformation over complicated bathymetry satisfactorily.

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.

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.