Where do rivers grow? Path selection and growth in a harmonic field

TL;DR

This paper introduces a model where river streams grow by following local symmetry to maximize water flux, linking individual stream growth to the overall network structure.

Contribution

It applies a fracture mechanics-inspired criterion to model stream growth in a diffusion field, revealing how local environment dictates river network development.

Findings

Streams follow local symmetry to maximize flux

The growth law can reconstruct network history

Single-channel growth models characterize network structure

Abstract

River networks exhibit a complex ramified structure that has inspired decades of studies. Yet, 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 a stream will follow local symmetry in order to maximize the water flux and that its trajectory is defined by the local field in its vicinity. We also study the growth of a real network. We use this principle to construct the history of a network and to find a growth law associated with it. The 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.