title: Bifurcation dynamics of natural drainage networks.
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.
authors.affiliation: Lorenz Center and Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, , Cambridge, MA, USA.
authors.forename: Alexander P
authors.initials: AP
authors.lastname: Petroff
authors.forename: Olivier
authors.initials: O
authors.lastname: Devauchelle
authors.forename: Hansjörg
authors.initials: H
authors.lastname: Seybold
authors.forename: Daniel H
authors.initials: DH
authors.lastname: Rothman
mesh_terms: D004322:Drainage; D060587:Groundwater; D008962:Models, Theoretical; D045483:Rivers; D014867:Water
chemical_list: D014867:Water
keywords: Laplacian growth; network growth; potential flow