任意梯形断面溃坝洪水最大流量解析解

摘要

利用特征变换,将Saint-venant方程组变成特征线方程组,即不变量形式.本文对弧形断面和任意梯形断面不变量中的被积函数用级数展开再积分,得到了Riemann不变量的初等表达式;进一步,获得了弧形断面和任意梯形断面无因次水深方程;最后,导出了任意梯形和弧形断面溃坝洪水最大流速和最大流量解析解.本文方法可用来预报任意梯形和弧形断面溃坝洪水最大流速和最大流量.%By using characteristic transformation,Saint-venant equations are reduced to the equations of characteristic lines expressed by Riemann invariants.Expanding integral function of Riemann invariants for the case of arc and arbitrary trapezoidal cross-sections in Taylor's series and integrating it,the elementary function expressions of Riemann invariants are obtained.Further,equations of dimensionless water depth in arbitrary trapezoidal and arc cross-section channels are acquired.Finally,analytical solutions to the maximum velocity and discharge of dam-breaking flood are suggested.The method in this paper can be used for predicting the maximum velocity and maximum discharge of dam-breaking flood in arbitrary trapezoidal and arc cross-section channels.