Drainage divides are critical organizational components of river networks and the degree to which they are primarily static or mobile has become a point of debate within the geosciences community. My collaborators and I have worked on both understanding some of the controls on drainage divide migration and developing metrics for estimating the current mobility of divides.
The timescale of drainage divide mobility compared to the response timescale of a profile to a change in drainage area is a critical component to consider in terms of how important the motion of drainage divide is for influencing our understanding of topography. A series of numerical experiments suggest that under most conditions the response of a drainage network to changes in drainage area are rapid compared to the rate at which divides move (e.g., Whipple et al., 2017).
There are a variety of metrics for assessing whether drainage divides may be mobile. Some of these metrics which are averaged over large sections of the drainage network (e.g., chi) are more diagnostic of future divide motion whereas those focused on the area near the divide (e.g., the "Gilbert Metrics") are more diagnostic of current divide motion. Comparison of the predictions of these different metrics can provide a variety of information about the host landscape (e.g., Forte & Whipple, 2018).