The Formation of River Channels
The Formation of River Channels
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河道的形成
DOI：
--
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发表时间：
2007
影响因子：
1.9
通讯作者：
C. Oakley
中科院分区：
文献类型：
--
作者：
A. Fowler;N. Kopteva;C. Oakley
我们认为一个确定性的景观演变模型，通过在可侵蚀的基板上的坡面流的机制，使用圣维南方程的水力学与Exner方程的山坡侵蚀。在模型中的一个新奇是允许非零的推移质层厚度，这是必要的运输有限和分离有限的泥沙清除区分。人们早就知道，当山坡地形在地貌上是凹形的（即，曲率中心高于地面）。在本文中，我们展示了顺向槽流的有限振幅发展如何导致其深度h的形式为$h_t=h^{3/2}+（h^{3/2}）_{YY}$的演化方程，其中Y是横流空间变量。我们表明，解决方案的紧凑的支持存在，但尽管外观，爆破不会发生，因为相关的积分约束，通道方程承认一个独特的，显然是全球性的st.
We consider a deterministic model of landscape evolution through the mechanism of overland flow over an erodible substrate, using the St. Venant equations of hydraulics together with the Exner equation for hillslope erosion. A novelty in the model is the allowance for a nonzero bedload layer thickness, which is necessary to distinguish between transport limited and detachment limited sediment removal. It has long been known that transport limited uniform flow is unstable when the hillslope topography is geomorphologically concave (i.e., the center of curvature is above ground). In this paper, we show how finite amplitude development of the consequent channel flow leads to an evolution equation for its depth h of the form $h_t=h^{3/2}+(h^{3/2})_{YY}$, where Y is the cross‐stream space variable. We show that solutions of compact support exist but that, despite appearances, blow up does not occur because of an associated integral constraint, and the channel equation admits a unique and apparently globally st...