Reach-averaged flow resistance in gravel-bed streams

Previous studies about flow resistance in gravel-bed streams mostly use the log-law form and establish the relationship between the friction factor and the relative flow depth based on field data. However, most established relations do not perform very well when applied to shallow water zones with relatively large roughness. In order to clarify the hydraulic variables defined in the single cross-section, and find the reasons that reflect the instability of flow and uneven boundaries of the river, the concepts of hydraulic variables, such as hydraulic radius, are re-defined in the river reach in the paper. The form drag in the river reach is solved based on a reach-averaged flow resistance model which is developed by force balance analyzing of the water body in the given river reach. The reach-averaged form drag relation is then formulated by incorporating the Einstein flow parameter and a newly derived roughness parameter defined in the river reach. A large number of field data (12 datasets, 780 field measurements) is applied to calibrate and validate the form drag relation. The relation is found to give better agreement with the field data in predicting flow velocity in comparison with existing flow resistance equations. A unique feature of the reach-averaged resistance relation is that it can apply to both deep and shallow water zones, which can be treated as a bridge to link the flow hydraulics in plain rivers and mountain streams.