冲积河流一维全沙数学模型的特征值

Eigenvalues of 1-D total sediment model for alluvial rivers

研究了冲积河流中显著河床变形对水流运动特性所产生的影响。根据双曲系统特征理论及奇异摄动理论,采用了渐进匹配展开方法,推导得到了一维全沙数学模型所构成的4阶拟线性双曲系统的4簇特征值。这4簇特征值表征了双曲波的传播速度。结果表明:这4簇特征值耦合了水流运动、泥沙输运及河床变形之间的相互作用。水流中扰动的传播特性随着不同程度河床变形的影响而发生变化,且扰动程度越大,这种影响也越显著。因此,当河床冲淤较为显著时,考虑河床冲淤对水流运动产生的影响是必要的。

Four families of eigenvalues were obtained for a fourth-order quasilinear hyperbolic system representing a one-dimensional total sediment mathematical model to investigate the effects of significant river bed deformation in alluvial rivers on the flow.The asymptotic mapping method was used with the characteristic and singular-perturbation theories.The four families of eigenvalues represent the speeds at which the four hyperbolic waves propagate.The results show that the interactions among the flow,sediment transport and bed deformation are coupled through the eigenvalues.The disturbance propagation in the flow is affected by the river bed deformation with the effect increasing as the disturbance increasing.Hence,the effects of riverbed deformation on the flows need to be considered when the river bed experiences significant deformation.