TY - JOUR
T1 - The elements and richness of particle diffusion during sediment transport at small timescales
AU - Furbish, David Jon
AU - Fathel, Siobhan L.
AU - Schmeeckle, Mark
AU - Jerolmack, Douglas J.
AU - Schumer, Rina
N1 - Funding Information:
This paper is dedicated to Peter K. Haff. We appreciate discussions with Peter and with Raleigh Martin, and we acknowledge support by the US National Science Foundation (EAR-0405119, EAR-0744934, EAR-1226076 and EAR-1420831 to DJF, and EAR-1226288 to MWS), the US Army Research Office – Division of Earth Materials and Processes (64455EV to DJJ) and the Desert Research Institute (Maki Endowment in Hydrologic Sciences to RS). We appreciate recommendations of the Associate Editor and two anonymous reviewers for improving an earlier draft.
Publisher Copyright:
Copyright © 2016 John Wiley & Sons, Ltd.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - The ideas of advection and diffusion of sediment particles are probabilistic constructs that emerge when the Master equation, a precise, probabilistic description of particle conservation, is approximated as a Fokker–Planck equation. The diffusive term approximates nonlocal transport. It ‘looks’ upstream and downstream for variations in particle activity and velocities, whose effects modify the advective term. High-resolution measurements of bedload particle motions indicate that the mean squared displacement of tracer particles, when treated as a virtual plume, primarily reflects a nonlinear increase in the variance in hop distances with increasing travel time, manifest as apparent anomalous diffusion. In contrast, an ensemble calculation of the mean squared displacement involving paired coordinate positions independent of starting time indicates a transition from correlated random walks to normal (Fickian) diffusion. This normal behavior also is reflected in the particle velocity autocorrelation function. Spatial variations in particle entrainment produce a flux from sites of high entrainment toward sites of low entrainment. In the case of rain splash transport, this leads to topographic roughening, where differential rain splash beneath the canopy of a desert shrub contributes to the growth of a soil mound beneath the shrub. With uniform entrainment, rain splash transport, often described as a diffusive process, actually represents an advective particle flux that is proportional to the land surface slope. Particle diffusion during both bedload and rain splash transport involves motions that mostly are patchy, intermittent and rarefied. The probabilistic framework of the Master equation reveals that continuous formulations of the flux and its divergence (the Exner equation) represent statistically expected behavior, analogous to Reynolds-averaged conditions. Key topics meriting clarification include the mechanical basis of particle diffusion, effects of rarefied conditions involving patchy, intermittent motions, and effects of rest times on diffusion of tracer particles and particle-borne substances.
AB - The ideas of advection and diffusion of sediment particles are probabilistic constructs that emerge when the Master equation, a precise, probabilistic description of particle conservation, is approximated as a Fokker–Planck equation. The diffusive term approximates nonlocal transport. It ‘looks’ upstream and downstream for variations in particle activity and velocities, whose effects modify the advective term. High-resolution measurements of bedload particle motions indicate that the mean squared displacement of tracer particles, when treated as a virtual plume, primarily reflects a nonlinear increase in the variance in hop distances with increasing travel time, manifest as apparent anomalous diffusion. In contrast, an ensemble calculation of the mean squared displacement involving paired coordinate positions independent of starting time indicates a transition from correlated random walks to normal (Fickian) diffusion. This normal behavior also is reflected in the particle velocity autocorrelation function. Spatial variations in particle entrainment produce a flux from sites of high entrainment toward sites of low entrainment. In the case of rain splash transport, this leads to topographic roughening, where differential rain splash beneath the canopy of a desert shrub contributes to the growth of a soil mound beneath the shrub. With uniform entrainment, rain splash transport, often described as a diffusive process, actually represents an advective particle flux that is proportional to the land surface slope. Particle diffusion during both bedload and rain splash transport involves motions that mostly are patchy, intermittent and rarefied. The probabilistic framework of the Master equation reveals that continuous formulations of the flux and its divergence (the Exner equation) represent statistically expected behavior, analogous to Reynolds-averaged conditions. Key topics meriting clarification include the mechanical basis of particle diffusion, effects of rarefied conditions involving patchy, intermittent motions, and effects of rest times on diffusion of tracer particles and particle-borne substances.
KW - Exner equation
KW - master equation
KW - particle diffusion
KW - sediment transport
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U2 - 10.1002/esp.4084
DO - 10.1002/esp.4084
M3 - Article
AN - SCOPUS:85007247424
SN - 0197-9337
VL - 42
SP - 214
EP - 237
JO - Earth Surface Processes and Landforms
JF - Earth Surface Processes and Landforms
IS - 1
ER -