多沙河流的波系结构Ⅱ:波系求解与应用

Wave hierarchies in alluvial rivers of heavy sediment load Ⅱ. Solution and application

通过波前展开及拉普拉斯变换方法,本文推导了多沙河流波系结构方程的解析解,其直观地将多沙河流中洪水演进、泥沙输运及河床冲淤过程中各变量的变化过程及相互作用关系通过数学表达式定量表出。该方法为研究河流水沙运动尤其是水沙运动与河床变形耦合机理提供了一个新思路和新途径。结合黄河下游典型高含沙洪水实测资料,运用本文获得的波系结构解析解对高含沙洪水异常运动现象成功地进行了模拟。进一步分析表明,含沙量变化对低阶波传播特性影响较大,水体中含沙量越高,波传播速度越快。因此一场洪水过程中后期高含沙洪水传播速度较快,逐步赶上前期低含沙洪水,产生流量叠加形成洪峰沿程增值。

Analytical solutions to the wave hierarchies in alluvial rivers of heavy sediment load are obtained by means of wave front expansion and integral transforms.The solutions facilitate and enrich the approaches to study the sediment-laden flow and its interactions with morphological changes,as variables such as flow depth,velocity,sediment concentration and the relationship between them can be quantitatively and explicitly expressed.Using the field data of a typical flood with high sediment concentration happened in the lower Yellow River,the flood propagation is simulated.The capability of using the analytic solutions to successfully describe the uncommon phenomena of discharge amplification is encouraging.Further investigation on the properties of the flood waves shows that,the post-phase flood with higher sediment concentration will propagate faster than the former-phase one with lower sediment concentration,resulting in a superimposed flood peak discharge.