Alluvial Channel Geometry: Theory and Applications

The downstream hydraulic geometry of alluvial channels, in terms of bank-full width, average flow depth, mean flow velocity, and friction slope, is examined from a three-dimensional stability analysis of noncohesive particles under two-dimensional flows. Four governing equations (flow rate, resistance to flow, secondary flow, and particle mobility) are solved to analytically define the downstream hydraulic geometry of noncohesive alluvial channels as a function of water discharge, sediment size, Shields number, and streamline deviation angle. The exponents of hydraulic geometry relationships change with relative submergence. Four exponent diagrams illustrate the good agreement with several empirical regime equations found in the literature. The analytical formulations were tested with a comprehensive data set consisting of 835 field channels and 45 laboratory channels. The data set covers a wide range of flow conditions from meandering to braided, sand-bed and gravel-bed rivers with flow depths and channel widths varying by four orders of magnitude. Figures illustrate the results of the three-part analysis consisting of calibration, verification, and validation of the proposed hydraulic geometry equations. Field and laboratory observations are in very good agreement with the calculations of flow depth, channel width, mean flow velocity, and friction slope.