RE-EXAMINATION OF THE SCOUR FACTOR PRINCIPLE IN MEANDER BENDS WITH HIGHLY ERODIBLE BANKS

Reduced-order numerical models of meandering river dynamics generally assume a point bar transverse bed slope that is primarily a function of planform curvature; the transverse slope dictates the flow depth at the outer bank. The linear relation between transverse bed slope and curvature is quantified with a coefficient of proportionality known as the scour factor. The relation is theoretically based on a mobile bed dynamic equilibrium that develops when bed processes occur at a much faster rate than bank processes. In streams whose banks consist of readily erodible noncohesive materials, this assumption may not be realistic. Analytical and simplified numerical methods are used to demonstrate modified near outer bank depths for the canonical case of fully developed flow in a constant radius bend with uniform sediment. A solution criterion for the bar transverse slope is developed that does not specify the dynamic equilibrium condition of vanishing bedload transport rate in the transverse direction; the solution depends on the migration rate itself. The results indicate that, under certain conditions, increasing migration rates forced by curvature will not monotonically increase as the radius of curvature decreases as suggested by reduced-order models. Furthermore, the shallowing can be exacerbated by physical limitations of the bend to maintain sediment mass balance when curvature becomes large. Substantial shallowing of outer bank depths owing to high migration rate and sediment mass balance limitations is shown to cause the migration rate versus radius of curvature relationship to undergo an inflection with a peak at low radius. This phenomenon is explored in the context of the classic observational relationships between channel migration rate and dimensionless radius (i.e., radius divided by channel width) that show a clear inflection at a dimensionless radius of about 2 in some natural channels. The present explanation relies on active migration and, thus, cannot explain complete stabilization of a bend at low radius; i.e., the analysis does not discount prior explanations regarding secondary flow weakening and outer bank flow separation at sharp bends. However, the current analysis does provide another potentially important factor in the shape of the migration rate versus radius relationship.