Alluvial Resistance and Sediment Transport for Flows over Dunes

The motion of sediment and development of bed forms in natural rivers still constitute intriguing phenomena encountered in a variety of problems including river hydraulics and other geophysical and environmental flows. Since the pioneer work of Einstein and, later, Einstein and Barbarossa, the profound effects of movable sediments on the flow fields have been recognized very important in order to determine the nature of resistance. This paper presents the results of a simple methodology, based on energy balance, for computing the components of the total shear stress (grain and form-drag) acting on a uniform, two-dimensional flow over fully developed dunes. The method considers mainly an analysis of spatially-averaged (over several dune wavelengths) shear stress distributions. The corresponding roughness function that appears in the logarithmic velocity profile is also investigated and related to dimensionless numbers of the sediment transport phenomenon. Different regimes indicating the nature of the total resistance, mainly for different scales of the flows, are identified. Then, the characteristic roughness length for the logarithmic velocity distribution is derived from the roughness function and applied, in turn, to the boundary-layer-type total friction coefficients. Finally, an alternative expression for the dimensionless bedload transport due to fully-developed, two dimensional dunes, including a wide range of alluvial streams, is presented.