Height of Sand Dunes in Open Channel Flows

Starting from the hydraulic model first proposed by Exner, equations have been deduced for maximum height of sand dunes in open channel flows using kinematic and dynamic approaches. The final result obtained by the dynamic approach is essentially similar to that obtained from the kinematic approach; the only difference is due to a term including Froude number in the dynamic approach. These equations are similar to the equation proposed by Yalin. In the analytical deduction from the Exner model, an assumption had to be made that the hydraulic resistance of the alluvial bed remains invariant with respect to velocity. This restricts the applicability of Yalin's equation to rather narrow limits. It was argued that the wide scatter on Yalin's diagram for dune heights can be explained as due to the inapplicability of this assumption. The prediction of dune height from Yalin's equation and from those proposed herein will also be affected by the inexactness of the bed load equation.