Transport Scaling of Dune Dimensions in Shallow Flows

Dune dimensions in sand-bedded rivers are often thought to scale with flow depth (h), with height (H) scaling as 1/6h and length (L) as 5h, even though substantial scatter about the relations has been observed. Transport stage has been shown to affect bedform geometry, but this control is often ignored in favor of depth scaling relations. Here, we use a series of flume experiments to systematically test controls on dune dimensions and variability. Experiments involved three sets of runs under five constant transport stages, ranging threshold to washout conditions, at three different flow depths. The mobile bed was repeatedly scanned during a 10-hr equilibrium period to derive mean values and quantify the variability. The results show that dune-depth scaling is not consistent because of a transport stage effect. Dune height increases with transport stage until a point when H decreases. Length remains nearly constant with transport stage until further increases in transport stage leads to lengthening. In general, dunes grow higher when significant bedload transport occurs but become flatter and longer in the presence of substantial suspension. Ultimately, dunes scale with transport stage, which is a function of slope, grain size, and h. The results are used to derive transport stage relations to guide predictions of dune dimensions in rivers and reconstructions of paleoflows based on dimensions estimated from cross strata. The relations incorporate the nonlinear response of dune dimensions with transport stage and provide metrics of uncertainty to include in predictions.