Connecting grain motion to large-scale fluctuations in bed load transport: The role of collective dynamics

Abstract:

Bed load transport is a notoriously unpredictable process. A primary component of this unpredictability arises from stochastic fluctuations which require non-trivial averaging. This averaging must be informed by the length and time scales of the fluctuations, and a rigorous method for arriving at the proper averaging scales must link grain scale motion to macroscopic transport. A statistical mechanical framework has been suggested by Furbish and colleagues to accomplish this goal. This model assumes that grain motion is independent of other particles. Experiments show that this is not the case, and that bed load fluctuations possess length and time scales larger than any hydrodynamic scaling. This indicates that fluctuations in grain motion are correlated; as hydrodynamics cannot explain this behavior, we posit that its origins lie in the granular dynamics of bed load transport. Evidence to support this view can be found in the work of Ancey and colleagues where they show that, upon approaching the threshold of motion: intermittency of transport grows, dynamics of grain motion slow down, and collective entrainment occurs. These behaviors are hallmarks of a disordered system approaching a jamming transition, or the point where motion ceases. This points to the utility of using the jamming framework to study transport near threshold. We seek to use this framework to document the occurrence and understand the origins of the collective entrainment of grains. This is done using a 2D experiment with spherical particles driven by a turbulent flow where collisions are a significant driver of entrainment due to the momentum transfer that occurs when saltating particles collide with the bed. We characterize the collective particle motion observed in the system using the Χ₄${\mathrm{ }}_{}$susceptibility. This measure uses the variance of the displacement of a population of sediment in the system to characterize the timescales at which a subset of grains move collectively relative to the rest of the system. We find evidence that the correlation scales of collective particle dynamics change with the driving rate. These observations elucidate the granular contributions to stochastic bed load transport, and demonstrate how the requisite averaging time for bed load measurements increases rapidly on approach to the threshold of motion.