REEVALUATING DUNE DEPTH SCALING RELATIONS

Dunes formation, growth and migration dominate sediment dynamics and flow resistance in sand-bedded rivers. Dunes also leave characteristic signatures of their presence and evolution in the depositional record. An improved understanding of bedform dynamics is therefore necessary for more accurate paleo-reconstructions. We currently lack a comprehensible theory to explain why dunes grow to a certain height and rely on simple empirical relations based on inherently variable and scattered data that suggest that dune height and length increase with depth. Of these relations, one of the most commonly cited comes from Yalin (1964) who proposed that that height scales with 1/6 depth and length with 5 times the depth. Here, we evaluate dune scaling relations by examining published dune dimension data from over 20 flume and 20 field studies. The results show that there is a general trend of increasing dune height with the scale of the system that is particularly evident in the field data, however the relations are characterized by considerable scatter. Most data plot well above the 1/6 depth scaling and fall within a wide range of 1/2 and 1/25 depth. The fact that dunes do not exceed a height of 1/2 depth suggests that depth does play a limiting factor in bedform growth. Evidence also suggests that transport stage, defined as the non-dimensional Shields stress divided by its value at the threshold for sediment entrainment, is an important control on dune geometry that warrants further consideration. Dune aspect ratio (height/length) initially increases with transport stage but then declines as transport stage continues to increase. This bell-shape patterns appears to emerge as heights decline and dunes wash out during higher transport stages while lengths continue to grow longer. The results suggest that paleo-reconstructions based on height-depth relations should be based on the probability of getting a particular scaling with depth. This would also provide some estimate of the error associated with paleo-flow estimates. Examination of the mechanisms that control dune height and length in rivers is sorely needed.