Dunes depth-scaling in rivers: A reanalysis of flume and field data

Abstract:

The formation, growth and migration of dunes have important implications for sediment transport and flow resistance in many of the world’s sand-bedded rivers. The notion that dunes scale with depth is often cited as a definitive feature of these bedforms and suggests that depth exerts a major control on dune geometry and dynamics. Empirical relations often suggest that height scales as 1/6 depth and length as 5 times the depth. However, there is limited evidence for this scaling in the literature and no widely accepted theory to explain why dunes grow to a certain height. Here, we reexamine published dune dimension data from over 20 flume and 20 field studies to critically test the assumption that dunes are depth-scaled in rivers. The results, particularity in the field data, do show a general trend of increasing dune height with depth but these relations are subject to considerable scatter. Most data plot higher than the 1/6 depth scaling and fall within a wide range from 1/2 to 1/25 depth. Depth must exert some control on dune dynamics as few dunes have heights above 1/2 the depth, yet the scatter indicates that depth is not the only control on dune size. Transport stage, defined as the non-dimensional Shields stress divided by its value at the threshold for sediment entrainment, exerts a stronger control on dune dimensions. As transport stage increase, dunes grow in height but then decrease as the length grows. This pattern produces a bell-shaped plot of aspect ratio (height/length) as transport stage increases. Further investigation of the physical mechanisms that control dune height and length are sorely needed in order to better understand dune dynamics in natural systems.