Oscillatory motion of drainage divides

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. Citation: Stark, C. P. (2010), Oscillatory motion of drainage divides, Geophys. Res. Lett., 37, L04401, doi:10.1029/2009GL040851.