Bifurcation dynamics of natural drainage networks
Bifurcation dynamics of natural drainage networks
复制标题
自然排水网络的分叉动力学
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
D. Rothman
中科院分区：
文献类型：
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作者：
A. Petroff;O. Devauchelle;H. Seybold;D. Rothman
当水侵蚀地貌时，溪流形成并使地表水流通道化。随着时间的推移，溪流变成了高度分叉的网络，可以延伸到一块大陆。在这里，我们结合物理推理、数学分析和实地观察来了解网络增长的一个基本特征：不断增长的溪流的分叉。我们提出了一个确定性的分叉规则，该分叉规则源于网络中尖端的位置与地下水位的局部形状之间的关系。接下来，我们证明，当一条河流分叉时，溪流和支流之间的竞争选择了一个特殊的分叉角α=2π/5。我们通过测量一个千米尺度的地下水供水网络中的数千个分叉角来证实这一预测。除了提供对河流网络增长的洞察之外，这一结果还将河流网络呈现为一个经典数学问题的物理表现：谐波场中的界面增长。在最后的章节中，我们结合这些结果来开发和探索一个单参数的网络增长模型。该模型预测了对数螺线的发展。我们在千米尺度的网络中发现了类似的特征。
As water erodes a landscape, streams form and channellize the surficial flow. In time, streams become highly ramified networks that can extend over a continent. Here, we combine physical reasoning, mathematical analysis and field observations to understand a basic feature of network growth: the bifurcation of a growing stream. We suggest a deterministic bifurcation rule arising from a relationship between the position of the tip in the network and the local shape of the water table. Next, we show that, when a stream bifurcates, competition between the stream and branches selects a special bifurcation angle α=2π/5. We confirm this prediction by measuring several thousand bifurcation angles in a kilometre-scale network fed by groundwater. In addition to providing insight into the growth of river networks, this result presents river networks as a physical manifestation of a classical mathematical problem: interface growth in a harmonic field. In the final sections, we combine these results to develop and explore a one-parameter model of network growth. The model predicts the development of logarithmic spirals. We find similar features in the kilometre-scale network.