Steepness of Sedimentary Dunes

A family of curves is determined for the prediction of the steepness of dunes generated by rivers and open channel flows by using field and laboratory data from various sources. The dune steepness appears to be determined by two dimensionless variables: the ratio of the existing bed shear stress to the shear stress inducing the inception of sediment transport, and the ratio of the flow depth to the grain size of sediment. It has been found that with the increment of the former variable the dune steepness first increases, then reaches its maximum value and then progressively decreases as to vanish asymptotically. The increment of the second variable causes only the increment of the dune steepness up to a certain upper limit. The curves forming the family are normalized as to merge into a single curve which is formulated in an exponential form.