本文在水平无旋及 Boussinesq假设之下 ,导出了水面变化与水平速度场耦合方程组 ,以及相应的压力与垂向速度解析表示式。通过数值方法求得水面变化及某一特定水深的水平速度分布之后 ,压力分布及其余水深的速度分布即可由简单计算得到。由色散关系式可知 ,不同水深的长波色散关系在 0 (ε)近似之下是等同的。粘性的存在会使波高随时间的增加而衰减 ,但粘性与底斜率的耦合又可能使波高增长 ,形成不稳定 ;计算及分析说明 ,当同向流增大时 ,波速增大 ,波长增大 ,波高会增加 ;而水深减少 ,使波速减少 ,波长缩短 ,振幅增加。 In this paper, under the horizontal non-rotating and Boussinesq assumption, the coupled equations of water surface velocity and horizontal velocity field are derived, and the analytical expressions of pressure and vertical velocity are deduced. After obtaining the horizontal velocity distribution of water surface changes and a specific water depth by numerical method, the pressure distribution and the velocity distribution of the remaining water depths can be easily calculated. From the chromatic dispersion relation we can see that the long wave dispersion relation of different water depths is equal under the approximation of 0 (ε). Viscous existence will make the wave height decay with the increase of time, but the coupling of viscosity and bottom slope may make the wave height increase and form instability. Computation and analysis show that when the co-current increases, the wave velocity increases and the wavelength increases , The wave height will increase; while the water depth decreases, the wave speed decreases, the wavelength shortens and the amplitude increases.