基于最小可用能耗率原理的河流水沙数学模型

本文把河流视为具有能量紊动黏性热耗散结构的开放系统，根据耗散结构的熵和能耗理论，提出了保持冲积河流稳定的最小可用能耗率原理和公式。该原理全面地反映了河道输水输沙的能耗特性，在数学上完整地表达了冲积河流河床演变的基本原理——自动调整作用原理。应用该原理的公式封闭河床演变方程组，建立了冲积河流河道输水输沙优化的数学模型，根据该模型的计算结果分析了黄河下游河道输水输沙的规律，并解释了河床演变的各种现象。应用该模型计算了黄河下游各河段输水输沙优化的临界指标，并提出了有利于改善小浪底水库调水调沙运用的建议，为小浪底水库调水调沙提供参考。

Mathematical model for flow and sediment in alluvial river based on minimum rate of available energy dissipation principle

The river is regarded as an open system with structure of thermal energy dissipation due to turbulence and viscosity. On this basis, the theory of dissipation structure is applied to deduce the principle of minimum rate of available energy dissipation for maintaining the stability of the alluvial river. According to this principle, the energy dissipation characteristics of flow and sediment transport can be comprehensively described and the basic principle of riverbed evolution i.e. automatic regulation principle is fully expressed. The formula deduced is applied to close the equations describing the evolution of riverbed and establish the mathematical model expressing the optimized transport of water and sediment in alluvial river. The model is applied to calculate the critical indexes of optimized transport of water and sediment in the lower reaches of Yellow River and a recommendation on improving the dispatch of water and sediment in Xiaolangdi Reservoir is suggested accordingly.