A model for knickpoint migration in first- and second-order streams

We introduce a new theoretical framework for knickpoint migration in unventilated flows prevalent in channelized semicohesive first-and second-order streams characterized by a sequence of constrictions and expansions in the channel cross section. A key feature of the framework is the inclusion of shear-induced fluvial erosion due to flow suction at the nappe as the key mechanism driving migration. Channel surveys, water stage, time-lapse photography, and laser scans from Mud Creek, Iowa, USA, confirm this unventilated erosive mechanism and reveal a dual advective-diffusive mode of retreat. We treat the fluvial bed shear stress as being similar to the flow on the lee side of a submerged obstacle and derive a governing equation which is a generalized Burgers' equation. The equation is solved to successfully simulate knickpoints monitored in two sites (Iowa and Mississippi), and a modified Peclet number is used to analyze the advective-diffusive nature of the knickpoint migration.