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Proc Natl Acad Sci U S A. 2015 Nov 17;112(46):14132-7. doi: 10.1073/pnas.1413883112. Epub 2015 Nov 2.

Path selection in the growth of rivers.

Author information

1
Lorenz Center, Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139; ycohen@mit.edu.
2
Institut de Physique du Globe, 75252 Paris Cedex 05, France;
3
Lorenz Center, Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139;
4
Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, 02-093, Warsaw, Poland.

Abstract

River networks exhibit a complex ramified structure that has inspired decades of studies. However, an understanding of the propagation of a single stream remains elusive. Here we invoke a criterion for path selection from fracture mechanics and apply it to the growth of streams in a diffusion field. We show that, as it cuts through the landscape, a stream maintains a symmetric groundwater flow around its tip. The local flow conditions therefore determine the growth of the drainage network. We use this principle to reconstruct the history of a network and to find a growth law associated with it. Our results show that the deterministic growth of a single channel based on its local environment can be used to characterize the structure of river networks.

KEYWORDS:

Loewner equation; fracture mechanics; harmonic growth; principle of local symmetry; river channels

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