Geometry of channel networks incised by subsurface flow
Abstract
When groundwater returns to the surface at springs, the material atthe surface may erode and channels may be incised. Over time,ramified networks can form. Alternatively, water flowing over landcan also incise channels. Networks formed by overland flow have beenmore widely studied, but, paradoxically, the geometric aspects ofgroundwater-fed networks, which depend only weakly on topography, maybe more straightforwardly understood from elementary fluid mechanics.Here we focus on two aspects of the geometry of growinggroundwater-fed networks: the direction in which channels advanceand the angle at which they branch. First, using a conventionaltwo-dimensional approximation of the groundwater flow, we remark thatthe direction taken by moving channel tips may be equivalentlyunderstood from the maintenance of local symmetry in the groundwaterfield, the maximization of flux to tips, or motion along thegroundwater streamline into tips. Next, we use these ideas toshow that a bifurcated tip that grows in the predicted directionsresults in a branching angle of 2 pi/5 = 72 degrees. Our studies of astream network on the Florida Panhandle that is unequivocally drivenby subsurface flow accords well with this prediction. We also presentthe results of an empirical study of branching angles throughout thecontiguous United States. Our results show that in humid climates,branching angles appear to asymptotically approach 72 degrees as theso-called aridity index--the ratio of rainfall rate to potentialevapotranspiration--increases. The tendency toward this angle foraridity indicies greater than one is evident over approximatelyone-half of the country, suggesting that groundwater may play asignificant role in channelization processes wherever climates aresufficiently humid.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2016
- Bibcode:
- 2016AGUFMEP52A..01R
- Keywords:
-
- 1804 Catchment;
- HYDROLOGYDE: 1825 Geomorphology: fluvial;
- HYDROLOGYDE: 1850 Overland flow;
- HYDROLOGYDE: 1861 Sedimentation;
- HYDROLOGY