The geometric complexity of stream networks has been a source of fascination for centuries. However, a comprehensive understanding of ramification-the mechanism of branching by which such networks grow-remains elusive. Here we show that streams incised by groundwater seepage branch at a characteristic angle of 2π/5 = 72°. Our theory represents streams as a collection of paths growing and bifurcating in a diffusing field. Our observations of nearly 5,000 bifurcated streams growing in a 100 km 2 groundwater field on the Florida Panhandle yield a mean bifurcation angle of 71.9°± 0.8°. This good accord between theory and observation suggests that the network geometry is determined by the external flow field but not, as classical theories imply, by the flow within the streams themselves.river networks | network growth | Laplacian growth

International audienceWe investigate experimentally the statistical properties of bedload transport induced by a steady, uniform, and laminar flow. We focus chiefly on lateral transport. The analysis is restricted to experiments where the flow-induced shear stress is just above the threshold for sediment transport. We find that, in this regime, the concentration of moving particles is low enough to neglect interactions between themselves. We can therefore represent bedload as a thin layer of independent walkers travelling over the bed surface. In addition to their downstream motion, the particles show significant fluctuations of their cross-stream velocity, likely due to the roughness of the underlying sediment bed. This causes particles to disperse laterally. Based on thousands of individual trajectories, we show that this lateral spreading is the manifestation of a random walk. The experiments are entirely consistent with Fickian diffusion

A viscous fluid flowing over plastic grains spontaneously generates single-thread channels. With time, these laminar analogues of alluvial rivers reach a reproducible steady state, showing a well-defined width and cross section. In the absence of sediment transport, their shape conforms with the threshold hypothesis which states that, at equilibrium, the combined effects of gravity and flow-induced stress maintain the bed surface at the threshold of motion. This theory explains how the channel selects its size and slope for a given discharge. In this light, laboratory rivers illustrate the similarity between the avalanche angle of granular materials and Shields's criterion for sediment transport.