Bifurcation dynamics of natural drainage networks

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Abstract

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. © 2013 The Author(s) Published by the Royal Society. All rights reserved.

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CITATION STYLE

APA

Petroff, A. P., Devauchelle, O., Seybold, H., & Rothman, D. H. (2013). Bifurcation dynamics of natural drainage networks. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371(2004). https://doi.org/10.1098/rsta.2012.0365

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