Reevaluating dune scaling relations

In sand-bedded rivers, dunes dominate sediment transport and flow resistance. Dunes are also commonly preserved in fluvial deposits as cross-stratified units that record their size, shape and migration rates. Prediction of dune dimensions is therefore important for forecasting modern river channel dynamics as well as reconstructing past fluvial environments on Earth and other planets. Predictions are often made by assuming that the formative flow depth (h) sets dune dimensions with height scaling as 1/6h and length as 5h. Yet, there is a suite of other scaling relations that link dune dimensions to other variables like grain size, transport stage and Froude number. Here we present a new compilation of flow and dune dimension data to evaluate scaling relations. The data reveal approximately two orders of magnitude variation in dune height and length at any given flow depth. Dune heights in shallow flows (< 2.5 m), where strongly asymmetric dunes with high lee angles are common, are generally larger than 1/6h. Dunes in deeper channels (> 2.5 m) are often more symmetric, have lower lee angles, are relatively shorter in height than 1/6h and have a wider range of observed heights for a given depth. None of the scaling relations predict the observations exceptionally well, likely because of natural variability in dune dimensions and because they do not explicitly account for the apparent scaling break that occurs at 2.5 m. We propose new simple depth-scaling relations with added statistical uncertainty for the prediction of dune height and length from flow depth, as well as flow depth from dune height. We conclude that shallow and deep flow dunes exhibit different scaling due to a change in the dominant process controls as dunes get larger.