明渠水流泥沙运动水深平均及力矩方程的理论和验证

首次提出了水流泥沙运动水深平均及其力矩方程的概念 ,并从理论上推导出这套方程组。提出水流泥沙运动力矩方程的目的有两个 ,一是在不增加空间维数的情况下可以有效地恢复水流泥沙因子沿水深分布信息 ,克服目前普遍使用的水深平均方程过多地忽略沿水深分布信息的缺点 ;二是增强模型的模拟能力。针对这两个目的是否能真正得到体现 ,分别从理论和实验室资料两个方面对新推导的力矩方程进行了全面的检验。理论验证结果表明 ,一维的力矩方程除了能模拟水深平均的流速和含沙量 ,还能够较好地模拟水流泥沙因子沿水深分布信息 ,这充分说明了一维力矩方程的二维特性。为了检验力矩方程的模拟能力 ,特别选取了一些极端的水流泥沙运动实验 ,如清水冲刷、点源加沙和深槽回淤等。模拟结果表明 ,力矩方程对于这些极端的水沙运动具有较好的模拟能力

Depth-Averaged and Moment Equations for Flow and Suspended Sediment Transport

In current numerical models for flow and sediment transport, the equations widely used are depth averaged equations which are obtained at the price of sacrificing the information along depth. In this paper, a set of totally new equations, moment equations, describing suspended sediment transport in flows have been derived. The significant characteristics of these new equations are that the equations can recover sufficient information of flow and sediment factors along the flow depth without increasing spatial dimension. Functionally, 1 D moment equations are equivalent to 2 D vertical depth averaged ones, whereas 2 D moment equations are equivalent to 3 D models. The theoretical verifications show that the proposed 1 D moment model can reasonably simulate the depth profiles for both velocity and sediment concentration. The comparisons between the simulated and laboratory data indicate that the model has a good ability to simulate some extreme channel bed variations, such as clear water scouring, siltation of deep channel, and point added sediment, which most current models couldn't properly simulate.