The elements and richness of particle diffusion during sediment transport at small timescales

Abstract

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. Copyright © 2016 John Wiley & Sons, Ltd.

Sand particle velocities over a subaqueous dune slope using high‐frequency image capturing

“…Particle activity fluctuates as particles respond to near-bed fluid turbulence, whilst particles simultaneously interact with the bed. Furthermore, sediment particles show diffusive and advective behaviour, which is reflected in the fluxes directed from areas of high entrainment to low entrainment (Furbish et al, 2017). A larger sampling area will decrease the relative effect of the magnitude of the fluctuations compared to the overall level of activity.…”

Luminescence as a Sediment Tracer and Provenance Tool

“…At scales smaller than landscape scale (less than tens of kilometers), the dynamics of individual processes have a control on sediment storage times. The extent of regeneration depends on probability distributions of resting times whose exact form is a function of the specific geomorphic process (Furbish et al, ). For example, a grain of sand travelling through a meandering river system may spend time between periods of in‐channel motion and long‐term storage in floodplain deposits.…”

“…of resting times whose exact form is a function of the specific geomorphic process (Furbish et al, 2017). For example, a grain of sand travelling through a meandering river system may spend time between periods of in-channel motion and long-term storage in floodplain deposits.…”

A Well‐Posed Alternative to the Hirano Active Layer Model for Rivers With Mixed‐Size Sediment

“…The variability in particle velocity, taken into consideration by the particle diffusivity, is a relevant process at this scale. At the global scale, sediment dispersion is governed by the rest time of sediment particles and the interaction between the bed surface and the sediment in transport (Furbish et al, ; Martin et al, , ; Pelosi et al, ; Voepel et al, ). Nikora et al () sets the limit time between the intermediate and global scales in t =15 d k / u * , where (m/s) is the shear velocity, τ b (N/m 2 ) is the bed shear stress, and ρ w (kg/m 3 ) is the water density.…”