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建立了集中水流作用下均质土壤坡面上细沟侵蚀动态模拟数学模型。模型包括根据质量守恒原理推导而得到的变沟宽水流连续性方程和泥沙运移方程;根据动量守恒方程推得到的水流动力学方程;由紊流冲击分布概率来确定的土壤剥离方程;过量泥沙采用沉积的一阶沉积方程。模型还考虑了沟床形态、水流动力、土壤侵蚀与泥沙沉积形成相互依赖的反馈环,具有表达细沟的空间变化和时间演变的能力。给出了利用有限元方法对水动力学方程及泥沙运移连续方程进行顺序求解的数值计算公式以及模型数值求解的具体步骤。
A dynamic simulation mathematical model of rill erosion on homogeneous soil slope under concentrated water flow was established. The model includes the equation of continuity of water flow and the equation of sediment transport derived from the principle of conservation of mass, the equation of water flow derived from the equation of momentum conservation, the equation of soil detachment determined by the probability of turbulence impact distribution, Sediment sediment deposition using the first-order equation. The model also takes into account the feedback loop of the formation of ditches, water flow, soil erosion and sediment deposition, which has the ability to express the spatial variation and time evolution of the rill. The numerical formulas for solving the equations of hydrodynamics and the continuous equations of sediment transport using the finite element method are given and the specific steps of numerical solution are given.