Skip to Main Content
Skip Nav Destination

Hidden order emerges in stream networks

7 January 2013

A groundwater flow model reveals that merging tributaries have an affinity for the angle 2π/5.

The Grand Canyon in the US is but one example of a landscape shaped over geologic time scales by flow. In all corners of Earth, as water drains toward oceans and seas, it carves channels such as the ones shown in this topographical map of a stream network near Bristol, Florida. Typically, channels are carved out by erosion due to a combination of surface runoff and groundwater seepage. As MIT researchers led by Daniel Rothman have now discovered, the groundwater seepage contribution leaves behind a very specific, and seemingly universal, geomorphological signature. The researchers looked specifically at the case in which a growing channel bifurcates into two branches. (Geologically, channels grow in the upstream direction, so such a bifurcation manifests as the convergence of two tributaries in the downstream direction.) Calculating groundwater fluxes near a model bifurcation, the MIT team found that the branches grow straight only if they form an angle of 2π/5 radians, or 72°. If the angle is any larger, seepage erosion works to bend the branches inward; if the angle is smaller, erosion bends the branches apart. The Bristol tributary network—believed to have been formed exclusively by groundwater seepage—provided an ideal test of the model. Indeed, the angles of the network's nearly 5000 branches are well fit by a Gaussian distribution, with a mean of 71.9° ± 0.8°. (O. Devauchelle, A. P. Petroff, H. F. Seybold, D. H. Rothman, Proc. Natl. Acad. Sci. USA 109, 20832, 2012.)—Ashley G. Smart

Close Modal

or Create an Account

Close Modal
Close Modal