Form Resistance in Gravel Channels with Mobile Beds

Abstract

Form resistance, which includes pressure drag on bed forms and pressure and viscous drag on bed particles in transport, is shown to be a major component of hydraulic roughness in steady, quasi‐uniform, two‐dimensional turbulent flow over mobile gravel beds. Dimensionless form shear stress exceeds dimensionless particle shear stress for values of about three times critical Shields stress in subcritical flow, and five times in supercritical flow. Theoretical analysis provides a physical basis for expressing friction factor as a function of particle friction factor, estimated by the Keulegan equation, and the ratio of form to particle shear stress, termed relative form shear stress. Dimensional reasoning and empirical modeling of flume data demonstrate that relative form shear stress depends on Shields stress and relative roughness in subcritical and upper supercritical flow regimes, and on relative roughness alone in the lower supercritical regime. In particular, for given Shields stress and increasing relative roughness, relative form shear stress increases in subcritical flow because of bed form influences but decreases in supercritical flow owing to transport rate effects. Predictive relations for relative form shear stress allow an explicit solution of the depth‐discharge problem for mobile gravel beds.