Determination of Skin Friction Factor in Gravel Bed Rivers: Considering the Effect of Large-Scale Topographic Forms in Non-Uniform Flows

Determination of skin friction factor has been a controversial topic, particularly in gravel-bed rivers where total flow resistance is influenced by the existence of small-scale skin roughness and large-scale topographic forms. The accuracy of existing models predicting skin friction factors in conditions where small-scale skin roughness and large-scale topographic forms exist is very low. The objective of this study is to develop a modified model that improves the accuracy of the determination of skin friction factors in gravel-bed rivers. To this end, 100 velocity profile data obtained from eight gravel-bed rivers were utilized to develop an analytical method that considers the momentum thickness of the boundary layer and its deviation in large-scale topographic bedforms in a 1D force-balance model. The results show that the accuracy of the skin friction factors is enhanced when (1) the model is in the form of an exponential function of energy slope, and (2) the deviation of momentum thickness is considered in the model. The proposed model results in high accuracy of the predicted skin friction factors for energy slopes between 0.001 and 0.1, which exist in most gravel-bed rivers with different morphologies. Additionally, this study model was used to modify the classic Einstein–Strickler equation. The modified equation resulted in improved accuracy of the predicted skin friction factors in non-uniform flow conditions even when velocity profiles and energy slope were not available