An analytical treatment of channel-morphology relations
Waite R. Osterkamp, Leonard J. Lane, George R. Foster · USGS professional paper · 1983
For a specified flow rate, the properties of channel width, mean depth, mean flow velocity, gradient, and roughness often are related to discharge by empirically developed power functions.Equations were derived that provide an analytical, or semitheoretical, basis for the empirical relations.The equations, which were calibrated and tested using field data, differ from previously derived power functions by incorporating variable exponents dependent on the shear-stress distribution along the channel section.Variable exponents permit the consideration of the entire range of natural channel geometries, including those of very wide braided channels that otherwise could not be described adequately by power functions.The derivation of these exponents is based on the continuity equation, the Manning equation, and an assumed equation for shear-stress distribution expressed in terms of channel width-depth ratio.By this approach, width-depth ratios are employed as surrogates for the channel sediment characteristics and the shearstress distribution.The equations were calibrated using channel data from the western half of the United States.The calibrated power equations were tested using data from relatively stable channels of the United States-in Ohio and southern Missouri-New Guinea, and Australia.Stable channels with steady discharge characteristics were selected for the testing to approximate the steady-state discharges assumed by the derivations.Results of the calibration and tests lead to generalizations concerning channel dynamics.