Oscillatory motion of drainage divides

Abstract

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.