Backwater number scaling of alluvial bed forms

The backwater number, B w , compares the backwater length scale to the length scale of alluvial bed forms. We derive theory to show that B w plays an important role in determining the behavior and scaling of morphodynamic systems. When B w ≫ 1, spatial patterns in deposition and erosion derive from flow accelerations associated with changes in flow depth, and bed evolution is akin to a kinematic wave. When B w ≪ 1, the spatial pattern of shear stress is determined by variations in energy slope, and alluvial beds experience topographic dispersion. This theory is confirmed using a numerical model and data compiled from the literature. We present a data set of B w for bed forms ranging from dunes to river deltas, including field and experimental measurements. For field‐scale measurements, we find that dunes have B w > 49, braid bars exist in the range B w = [7.1,17], meanders have a range B w = [7.1,18], and river mouth deposition ranges over B w = [7.4,29]. Further, alluvial morphologies that are easily recreated in the laboratory (dunes and avulsions) have overlapping field and laboratory B w ranges. In contrast, alluvial forms that have traditionally been difficult to recreate (meanders and river mouth processes) have field B w that are difficult to match in laboratory settings. Large experimental Froude numbers are shown to reduce experimental B w and incite diffusional behavior. Finally, we demonstrate the utility of B w scaling for estimating fundamental scales in sedimentary systems.