考虑环流横向输沙及河岸变形的平面二维扩展数学模型

Extended 2-D numerical model for alluvial river considering transverse transport of sediment and bank erosion due to secondary flow in river bends

本文考虑弯道环流输沙效应,在泥沙运动基本方程中增加了反映环流横向输沙附加项,对平面二维水沙数学模型的悬移质、推移质输沙方程和河床变形过程进行了扩展。借助土力学中关于边坡稳定性理论中的圆弧滑动法,并引入多杈树搜索方法,建立了适用于平面二维数学模型的河岸崩塌变形计算方法。经扩展后的平面二维水沙数学模型能模拟环流横向输沙及由其引起的河床冲淤和河岸变形,并应用该模型模拟了弯道发生、发展过程,计算结果与已有的认识是一致的。

An additional term reflecting the transverse sediment transport due to secondary flow in river bends is addd to the basic equation for plane 2-D flow and sediment movement to extent the existing mathematical model. In addition, an approach based on the soil mechanics is adopted to analyze the stability of the riverbank and integrated into the extended mathematical model, so that the mathematical model is capable to simulate the deformation of river bend due to both hydraulic erosion and slope failure. For numerical solving the governing equations for shallow water flow and sediment transport the finite volume method(FVM) and Riemann solver are applied. An example of its application is presented. It shows that this extended model is capable to simulate the generation and evolution of river bends.