Stochastic Characteristics of Sediment Motions

The stochastic characteristics of the discrete movements of a sand grain under the action of flowing water are examined. Functional relationships between the step length (or rest duration) distributions and the probability of a sand grain making a specified number of steps (or rest durations) over a distance (or time) are derived and compared with the results from radioactive tracer experiments. A technique for determining the behavior of the density functions for step lengths and rest durations, involved the determination of the curvature of the autocorrelation function specially constructed from the step length and rest duration data.