一维水沙数学模型基于特征的耦合分析

Characteristic analysis on the coupling mechanism of 1-D mathematical models for sediment-laden flows

推导了冲积河流一维水沙数学模型的特征值。基于连续介质假设,推导得到了河床冲淤层质量和动量守恒方程,建立了特征耦合的水沙数学模型。基于奇异摄动理论,通过渐进展开方法求得了模型所构成的双曲系统的特征值。其四个特征值耦合了水流运动、泥沙输运及河床变形的相互作用。根据双曲系统特征理论,分析了水流运动与河床变形的相互作用。结果表明,四个特征值中只有两个会对河床变形产生较大影响,且不同流态下河床变形受不同特征值作用,扰动向上游或下游传播。在过渡区域,河床变形同时受两个特征值作用而变形较快,并同时向上下游传播。

Eigenvalues of the 1-D mathematic model for alluvial rivers are derived,and mass and momentum equations of active bed layer are obtained using the assumption of continuum theory.A characteristic coupling model for sediment-laden flows is developed with a characteristic analysis on the fourth-order hyperbolic system used by the model.By the singular perturbation theory,four families of asymptotic solutions are obtained for the four eigenvalues,i.e.the speeds of the four dynamic waves that mutually interact.Two of the eigenvalues play a significant role on bed deformation,while the remaining two have weak effect.There exists a transition region of alluvial river in which bedform disturbance propagates in both the upstream and downstream directions.