Flow resistance evaluation in gravel- and boulder- bed

The standard exponential and logarithmic flow resistance laws in shallow streams with gravel- and boulder- bed cannot be adapted. Field investigations suggest that the flow velocity near gravel bed is lower than that of the upper flow, similarly to the mixing layer flow. In this study, the newly mixing layer analogy is applied theoretically for deducing the flow resistance law by introducing the Reynolds number, Froude number, and shear velocity, which is respectively affected by flow regime, flow condition, and shear stress. Most field data located in 140 mountainous streams located at the Apennines in Italy are selected to calibrate and compared with other resistance laws of mountainous streams. The results show that the novel multivariable mixing layer law is characterized by the most closed-1 Nash-Sutcliffe efficiency index, lowest root mean square error and relative error. This mixing layer approach is based on an entirely different view of shallow gravel stream turbulence, which interprets the flow structure and improves the calculation accuracy.