title: Path selection in the growth of rivers.
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.
authors.affiliation: Lorenz Center, Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139; ycohen@mit.edu.
authors.forename: Yossi
authors.initials: Y
authors.lastname: Cohen
authors.affiliation: Institut de Physique du Globe, 75252 Paris Cedex 05, France;
authors.forename: Olivier
authors.initials: O
authors.lastname: Devauchelle
authors.affiliation: Lorenz Center, Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139;
authors.forename: Hansjörg F
authors.initials: HF
authors.lastname: Seybold
authors.affiliation: Lorenz Center, Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139;
authors.forename: Robert S
authors.initials: RS
authors.lastname: Yi
authors.affiliation: Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, 02-093, Warsaw, Poland.
authors.forename: Piotr
authors.initials: P
authors.lastname: Szymczak
authors.affiliation: Lorenz Center, Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139;
authors.forename: Daniel H
authors.initials: DH
authors.lastname: Rothman
keywords: Loewner equation; fracture mechanics; harmonic growth; principle of local symmetry; river channels