Longitudinal Dispersion of Bed-Material Particles

The movement of sediment particles is expressed in terms of steps and rest periods. A set of difference equations based on the Aris moment transformation and used previously for the longitudinal dispersion of suspended particles is modified to find the distribution functions of step length and rest period of tracer particles moving along an alluvial bed for a given flow condition. This study indicates that the rest periods follow an exponential distribution function and the step lengths follow a gamma distribution function. The comparison between the numerical solution of Aris' moment equations and Yang's general one-dimensional stochastic model indicates that both models lead to the same solution for the same condition.