植被山坡上考虑侵蚀的水流模型
Water flow model on vegetated hillslopes with erosion
AI总结：
研究植被山坡水流中水土和水植相互作用，构建耦合圣维南与海辛-罗斯方程的数学模型，用有限体积法和分数时间步长方案求解，经测试验证可定量评估植物覆盖对水动力学及土壤侵蚀的影响，有助于管理环境资源防灾。
摘要：
土壤-植物-大气连续体中的水循环，尤其是水引起的土壤侵蚀，是气候变化新时代的主要关注问题。本文旨在提供一个数学工具，研究植被覆盖土壤表面水流复杂过程中涉及的水-土和水-植物相互作用。数学模型由扩展的圣维南水流方程组与土壤侵蚀的海辛-罗斯方程耦合而成，对经典圣维南模型进行了修改以考虑土壤表面植物的存在。利用有限体积法进行空间离散化，分数时间步长方案离散时间变量和时间导数来构建模型解的数值近似。讨论并研究了该方案的几个与物理相关的性质。为验证模型和数值方法，进行了一系列定性和定量测试。每个数值实验都构建为目标水文环境的图像，如溃坝问题、山洪暴发、流域内水蚀等都是数值分析对象。结果表明植物覆盖极大地改变了水动力学和土壤侵蚀颗粒分布，且能定量评估这些影响。本文方法还可帮助管理环境资源以避免水灾害。
英文摘要：
The water circulation in the Soil-Plant-Atmosphere continuum and particularly the soil erosion induced by water are problems of main concern in the new era of climate change. The present paper aims to provide a mathematical tool to investigate the water-soil and water-plant interactions involved in the complex process of water flow on plant-covered soil surfaces. Basically, the mathematical model consists of an extended Saint-Venant system of equations for water flow coupled with Hairsine-Rose equations for soil erosion. The classical Saint-Venant model is thus modified in order to take into account the presence of plants on the soil surface. A numerical approximation of the solution of our model is built using a Finite Volume Method for the discretization in space and a fractional time-step scheme to discretize the time variable and resulting time derivatives. Several properties of the scheme with physical relevance are also discussed and investigated. In order to validate both the model and the numerical method, and to see if essence of the reality is adequately reflected, a series of qualitative and quantitative tests are performed. Given that the mathematical model is flexible enough to reflect the variability of the environmental variables such as soil structure, soil surface roughness, or plant cover structure, each numerical experiment is constructed as an image of a target hydrological context. The dam break problem, flash floods, water-induced soil erosion in a catchment basin are all subjects of numerical analysis. It is shown that the presence of the plant cover drastically modifies the water dynamics and the distribution of the soil eroded particles and one can quantitatively evaluate such effects. The methods described in the paper can also help one to manage the environmental resources in order to avoid the water induced disasters.
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