Stochastic Model for Sand Dispersion

The movement of sand particles is expressed in terms of steps and rest periods. The longitudinal dispersion of sand particles along the bed of an alluvial channel is formulated in a general one-dimensional stochastic model. Three different methods are suggested for determining the three parameters in the stochastic model. Experimental results indicate that the step lengths follow a gamma distribution and that the rest periods follow an exponential distribution. Statistical analysis of bed configuration indicates the movement of sand particles along an alluvial bed should be closely related to the statistical properties of the bed configuration. The results of longitudinal dispersion experiments compare favorably with predictions based on the stochastic model.