Experimental Support of Statistical Mechanics Theory of Bed Load Sediment Motions Using High-Speed Imagery

Abstract:

Bed load particles move as a complex mixture of rolling, sliding, and small saltating motions on the stream bed. We track particle motions from start to stop using high speed imagery of coarse sand particles in flume experiments. This work utilizes a rich data set to provide foundational support for a statistical mechanics approach to bed load transport. The streamwise and cross-stream particle accelerations form Laplacian-like distributions, centered on zero, such that the positive and negative accelerations are balanced, which is consistent with equilibrium transport conditions wherein the mean particle acceleration must equal zero. Measurements from the imagery are censored by the window size and the sampling time, wherein particle `hops' are only measured if they both start and stop in the field of view (spatial censorship) and during the analyzed period of time (temporal censorship). We focus on the former, by considering data from complete particle hops in different sampling windows. Although all hop data are censored, we find that with a decreasing window size, longer hop distances and travel times are preferentially censored from the data. Furthermore, this suggests the streamwise hop distances scale with travel times to the second power, rather than previous estimates of a 5/3 power relationship. Data from a new experiment, with a higher particle activity, suggest similar forms of the instantaneous velocities and hops compared to lower activity data. Furthermore, the relationship between the streamwise hop distance and travel times appears to scale with the second power. Data from this new experiment will provide further insight concerning the nature of bed load transport from coupled measurements of particle transport and near-bed fluid velocities, which will ultimately inform statistically expected sediment behaviors.