Modeling the hydraulic roughness of a movable flatbed in a sand channel while considering the effects of water temperature

The prediction of the flow resistance (usually quantified as the hydraulic roughness) of a movable flatbed is a key issue affecting the calculation accuracy of flood levels in river training projects. Bedload motion on a movable flatbed causes additional energy loss and increases hydraulic roughness. Several theoretical and empirical predictors for characterizing this phenomenon have been proposed, but the accuracy and physical basis of these models should be improved. In this study, the total energy dissipation rate is separated into two components: the energy dissipation rate due to grain drag and the additional energy dissipation rate due to bedload motion. Following the energy dissipation rate balance equation, a new predictor was proposed for movable flatbed flows. The water temperature was empirically coupled with the fluid viscosity and its associated physical variables. A new empirical relation between two dimensionless flow‒sediment combination variables was established to demarcate the various bedform transitions induced by the water temperature. The new predictor was compared with other predictors, and the prediction results were compared to the measured data. The error metric showed that the new predictor provided the highest accuracy, with ∼88.5% of the 826 data points falling within the ±30% error band. The new predictor suggested that the additional drag is nonlinearly proportional to the grain drag, and the scale factor between these two parameters is related to five flow‒sediment variables. In addition, the ability of the new predictor to quantify water temperature effects was examined. The predicted resistance exhibited three change modes with increasing water temperature, and the results suitably agreed with the measurements. The effect of the water temperature on the resistance of a movable flatbed is jointly controlled by the suspension number and roughness Reynolds number. This study provides an effective predictor that can be used by decision makers for modeling the hydraulic roughness of a movable flatbed. • A new predictor to estimate the hydraulic roughness of a movable flatbed is proposed based on energy division method. • Additional resistance due to bedload motion is nonlinearly related to grain drag. • The effect of water temperature is quantitatively encapsulated in the new predictor. • The optimized predictor has significant advantages over the four conventional predictors.