Stochastic properties of bed load transport

The fluctuation of bed-shear stress on moving bed load particle plays an important role in the particle velocity. Our theoretical model treated the instantaneous bed-shear stress as a log-normal distribution, and developed a theoretical model to calculate the spatially averaged particle velocity and its distribution. A series of experiments were conducted in an open channel flume to measure instantaneous bed load particle velocities using the image based bed load analyzer. The instantaneous bed load particle velocities were measured in both the streamwise and the transverse directions. A total of 26 experimental runs were performed, and over 1,000 instantaneous particle velocities in the horizontal plane were measured. Results showed that the bed load particle velocity relates to the instantaneous bed-shear stress, which satisfies a log-normal distribution. The spatially averaged streamwise mean velocity is a function of mean bed shear stress and particle size. The probability density function (PDF) of the streamwise particle velocity is an exponential function, and the PDF of transverse particle velocity is a normal distribution. Bed-shear stress affects both the particle velocity distribution and the peak intensity. At last, the measurements were used to verify a theoretical model for the particle velocity and its distribution. Reasonable agreements were found between model's predictions and the experimental measurements.