Untangling the Control of Channel Width on Lateral Migration Rates

Empirical and theoretical studies of alluvial river meandering planforms have indicated that channel width is a first-order controller of lateral migration rates. There is even a rule of thumb in fluvial geomorphology that alluvial meandering rivers typically laterally migrate at a rate of 1-2% of their channel width per year. However, the process of lateral migration is driven by a combination of boundary shear stress in excess of the critical shear stress for erosion of the cut bank and a deficiency of shear stress that enables sediment deposition on the point bar. As boundary shear stress is a function of the velocity profile away from the channel boundary, often approximated as the product of channel depth and slope, it is counterintuitive that channel width should be a strong controller of lateral migration rate. To address this knowledge gap, we first combine multiple global datasets of bank erosion rates to confirm that channel width does indeed correlate with lateral migration rates. Additionally, we find a width scale-dependence in the proportion of channel widths migrated per year with narrower channels migrating a greater proportion of their width per year than wider channels. To understand the mechanistic influence of channel width on lateral migration rates, we utilize Delft3D to model flow down a meandering river reach. We manipulate bathymetric data of a reach of the Merced River to stretch and compress the channel’s width while preserving the channel’s vertical bathymetry and gradient to isolate the control of channel width on the flow structure. Utilizing a Ray Isovel Model, we extract boundary shear stresses along the channel’s wetted perimeter within meander bends. Results show that the magnitude of boundary shear stress remains largely unaffected by channel width scaling. Furthermore, flow in narrower channels appears to exert a relatively higher stress at the cutbank than in wider channels. Our findings, in combination with hydraulic scaling relationships, suggest that the apparent control of channel width on lateral migration rates, while a useful tool, is an artifact of width-depth scaling. In this light, we reanalyze our global datasets to demonstrate that channel depth exerts a first order control on lateral migration rates, with average migration rates clustering around approximately 20% of channel depth per year.