An empirical model of subcritical bedform migration



The ability to predict bedform migration in rivers is critical for estimating bed material load, yet there is no relation for predicting bedform migration (downstream translation) that covers the full range of conditions under which subcritical bedforms develop. Here, the relation between bedform migration rates and transport stage is explored using a field and several flume data sets. Transport stage is defined as the non-dimensional Shields stress divided by its value at the threshold for sediment entrainment. Statistically significant positive correlations between both ripple and dune migration rates and transport stage are found. Stratification of the data by the flow depth to grain-size ratio improved the amount of variability in migration rates that was explained by transport stage to ca 70%. As transport stage increases for a given depth to grain-size ratio, migration rates increase. For a given transport stage, the migration rate increases as the flow depth to grain-size ratio gets smaller. In coarser sediment, bedforms move faster than in finer sediment at the same transport stage. Normalization of dune migration rates by the settling velocity of bed sediment partially collapses the data. Given the large amount of variability that arises from combining data sets from different sources, using different equipment, the partial collapse is remarkable and warrants further testing in the laboratory and field.