Algorithm for Resistance to Flow and Transport in Sand-Bed Channels

Abstract

An algorithm is developed that relates depth to discharge and determines bed- and suspended-load transport for the entire range of bed forms found in sand-bed channels; equilibrium-state geometry of lower flow regime bedforms is also predicted. Grain shear stress and form resistance are differentiated using a drag coefficient closure and a two-segment logarithmic velocity profile. A Meyer-Peter-type formulation is used to compute sand transport in the bed-load layer and for computing suspended sand transport, McLean’s procedure of 1991 and 1992 is adopted. A bed-form classification scheme is developed that uses a particle size parameter and the transport strength to predict bed-form type; it correctly identifies 73% of the 1,192 mostly flume-scale calibration data sets. For 194 sets of dune-transition bed-form calibration data, a modified version of van Rijn’s 1984 bed-form geometry predictor yields a geometric average predicted to observed height ratio of 1.00. After calibration, the algorithm produces overall geometric averages of predicted to observed depth and predicted to observed transport of 1.00. For a verification data set of 855 observations, mostly from rivers and canals, the overall geometric averages of predicted to observed depth and transport are 0.87 and 1.14.