Flume Experiments to Constrain Bedload Adaptation Length

Spatially variable channel geometry in natural rivers produces nonuniform flow and spatial gradients in the shear stress field. The travel distance required for the flow to acquire the capacity bedload concentration and attain a new equilibrium bedload transport rate upon encountering a region of higher or lower shear stress is defined as the bedload adaptation length ($L_b$). Estimates of $L_b$ are used by some numerical morphodynamic models to account for nonequilibrium bedload transport in the computation of local transport rates. However, current methods for estimating this parameter are uncertain and often crude. The authors therefore conducted experiments designed to measure $L_b$ for a uniform sediment mixture in a laboratory flume. Instantaneous bedload transport rates were determined by counting passing sediment particles on digital imagery collected at variable distances downstream from a zero-transport boundary in a small flume. The flume was operated at three bed slopes in order to assess $L_b$ over a range of hydraulic conditions. Bedload adaptation length was found to be about $30\pm 8$ particle diameters at a relatively low excess dimensionless shear stress ($\theta -{\theta }_c=0.018$, where $\theta$ is the dimensionless shear stress and ${\theta }_c=0.0436$ is the critical dimensionless shear stress) and about $100\pm 30$ particle diameters at a moderate level of excess dimensionless shear stress ($\theta -{\theta }_c=0.032$). The experiments failed to resolve $L_b$ at higher shear stresses. These results support physically based models that cast $L_b$ as an increasing function of excess shear stress. They also suggest that $L_b$ may be small relative to the resolution of the numerical mesh used in many modeling applications. In such cases, model performance may be insensitive to the choice of any arbitrary small value of $L_b$.