Scaling of alluvial bedforms using the Backwater Number

Abstract:

The backwater number (Bw), defined as the characteristic flow depth divided by the characteric slope and bedform wavelength, is found to strongly determine the evolution of said alluvial bedform. When Bw > 1, deposition and erosion derived from changes in flow depth that produce accelerations akin to a kinematic wave. When Bw < 1, shear stress is determined by changes in slope, which produces diffusional evolution. We conduct a survey of Bw for 41 alluvial bedform studies ranging in scale from dunes to river deltas, from both field and experimental studies. For field-scale measurements, we find that dunes have Bw > 140, braid bars range between 13 and 37, meanders wavelengths range between 13 and 18, river mouth processes range between 8 and 30, and delta avulsions cluster around 1, as predicted by theory. Importantly, Bw >> 1 for field-scale alluvial bedforms appears to be a rule. Further, bedforms that are traditionally simple to recreate in physical experiments have strong overlap between lab and field scales, while experimental meanders and river mouth processes, which have been difficult to recreate in the lab, have much smaller Bw in the lab than in the field. We present the theory of backwater scaling as a method for estimating sedimentary dimensions, and propose a potential solution to the difficulties of Bw scaling in the laboratory.