The influence of roughness structure on flow resistance on steep slopes

There is no standard flow resistance equation for the determination of mean flow velocity in mountain streams. The reason lies in the morphology of mountain streams, i.e. steep slopes, large roughness elements, bed forms and water depths of the same order of magnitude as the bed material size. Logarithmic, Froude and power-law approaches to determine flow resistance are discussed with respect to the roughness parameter which is usually a characteristic grain size. As a result of the irregular nature of gravel-bed profiles it is shown that the structure of these stream beds cannot be described sufficiently by a characteristic percentile of the grain size distribution. Statistical properties of a series of bed profiles are investigated in order to quantify the effect of roughness on flow resistance. The standard deviation of the bed elevations is introduced as characteristic roughness length and its applicability is verified by the analysis of experimental data. Based on this roughness parameter, an approach for the determination of flow resistance is derived which allows for spatial averaging of the flow field. Conclusions concerning the influence of bed forms on flow resistance are drawn with the use of the concept of the "at-a-site" hydraulic geometry.