Alluvial Roughness in Streams with Dunes: A Boundary-Layer Approach

Abstract

The motion of sediment and development of bed forms in natural rivers still constitute intriguing phenomena that always challenge engineers and researchers involved in a variety of problems including river hydraulics and other geophysical and environmental flows. Resistance to flow in alluvial streams has been widely investigated. Since the pioneer work of Exner [12] and, later, Einstein and Barbarossa [8], the profound effects of movable sediments on the flow structure have been recognized as relevant in order to determine the nature of flow resistance (Kennedy [21]; Yalin [40]; Vanoni [36]; Garcia and Parker [14]). This paper presents a simple methodology, based on energy balance, to compute 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. Then, boundary-layer theory is used in order to find an equivalent turbulent-wall-shear flow for the actual spatially-averaged flow over dunes and to derive a characteristic roughness length for the logarithmic velocity distribution above the dunes. The corresponding roughness function that also appears in the logarithmic velocity profile is also investigated and related to dimensionless sediment transport parameters. Alluvial roughness is found to be a function of a single parameter which includes the total Shields stress., a particle Reynolds number, and the ratio between flow depth and sediment diameter.