Numerical modeling of erosional and depositional bank processes in migrating river bends with self-formed width: Morphodynamics of bar push and bank pull

Meandering rivers display active communication between bank erosion and bar deposition processes. How does this occur? How does the river select its width? To answer these questions, we implement a model for meander migration where both bank processes (erosion and deposition) are considered independently. Bank erosion is modeled as erosion of purely noncohesive bank material damped by natural slump block armoring; channel deposition is modeled via flow-retarded vegetal encroachment. Both processes are tied to a slope-dependent channel forming Shields number; banks with near-bank Shields number below this value undergo deposition, and those above it undergo erosion. Channel-forming Shields number must increase with slope, as dictated by available data and model performance. Straight channel modeling shows that a channel arrives at an equilibrium width from any initial condition. For the channel bend, the river always approaches an asymptotic state where width reduces slowly in time and where bank erosion and deposition occur at nearly equal rates. Before this state is reached, however, the river follows a phase-plane trajectory with four possible regimes: (a) both banks erode, (b) both banks deposit, (c) both banks migrate outward, but with a faster depositing bank (bar push), and (d) both banks migrate outward, but with a faster eroding bank (bank pull). The trajectory of migration on the phase plane depends on initial conditions and input parameters controlling the rate of depositional and erosional migration. All input parameters have specific physical meaning, and the potential to be measured in the field.