Experimental evidence of statistical ensemble behavior in bed load sediment transport

A high-resolution data set obtained from high-speed imaging of coarse sand particles transported as bed load allows us to confidently describe the forms and qualities of the ensemble distributions of particle velocities, accelerations, hop distances, and traveltimes. Autocorrelation functions of frame-averaged values (and the decay of these functions) support the idea that the forms of these distributions become time invariant within the 5 s imaging interval. Distributions of streamwise and cross-stream particle velocities are exponential, consistent with previous experiments and theory. Importantly, streamwise particle velocities possess a "light" tail, where the largest velocities are limited by near-bed fluid velocities. Distributions of streamwise and cross-stream particle accelerations are Laplace in form and are centered on zero, consistent with equilibrium transport conditions. The majority of particle hops, measured start to stop, involve short displacements, and streamwise hop distances possess a Weibull distribution. In contrast to previous work, the distribution of traveltimes is exponential, consistent with a fixed temporal disentrainment rate. The Weibull distribution of hop distances is consistent with a decreasing spatial disentrainment rate and is related to the exponential distribution of traveltimes. By taking into account the effects of experimental censorship associated with a finite sampling window, the relationship between streamwise hop distances and traveltimes, Lx-Tpα, likely involves an exponent of α2. These experimental results - an exponential distribution of traveltimes T_p and a Weibull distribution of hop distances L_x with shape parameter k < 1 - are consistent with a nonlinear relationship between these quantities with α > 1.