Mathematics – Metric Geometry
Scientific paper
Feb 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010georl..3704401s&link_type=abstract
Geophysical Research Letters, Volume 37, Issue 4, CiteID L04401
Mathematics
Metric Geometry
1
Hydrology: Geomorphology: Hillslope (1625), Hydrology: Geomorphology: Fluvial (1625), Hydrology: Debris Flow And Landslides, Hydrology: Modeling (1952), Hydrology: Erosion
Scientific paper
A simple model of topographic ridge evolution is developed in which mass-wasting is treated as a vectorial erosion process. Channel incision drives backcutting as well as downcutting of the connected hillslope and the result is a mobile drainage divide that exhibits sustained horizontal and vertical motions mediated by asynchronous, asymmetric channel incision rates. The model resolves a ridge cross-section into coupled hillslope and channel links and the model equations are found to form a low-dimensional, non-linear dynamical system. For weak forcing of hillslope erosion the system converges to a stable, symmetric geometry, but for strong forcing a limit cycle arises and the divide oscillates back and forth over time. The lessons to draw from this model are that such low-dimensional dynamical behavior: (i) may explain the sinuous planform of interfluves; (ii) may form a key constituent of the high-dimensional dynamics of landscape evolution as a whole.
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