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Parsing anomalous versus normal diffusive behavior of bedload sediment particles
Author(s) -
Fathel Siobhan,
Furbish David,
Schmeeckle Mark
Publication year - 2016
Publication title -
earth surface processes and landforms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.294
H-Index - 127
eISSN - 1096-9837
pISSN - 0197-9337
DOI - 10.1002/esp.3994
Subject(s) - bed load , brownian motion , anomalous diffusion , particle (ecology) , diffusion , random walk , range (aeronautics) , sediment transport , statistical physics , physics , geology , mechanics , sediment , geomorphology , materials science , mathematics , thermodynamics , statistics , computer science , knowledge management , oceanography , innovation diffusion , quantum mechanics , composite material
Abstract Bedload sediment transport is the basic physical ingredient of river evolution. Formulae exist for estimating transport rates, but the diffusive contribution to the sediment flux, and the associated spreading rate of tracer particles, are not clearly understood. The start‐and‐stop motions of sediment particles transported as bedload on a streambed mimic aspects of the Einstein–Smoluchowski description of the random‐walk motions of Brownian particles. Using this touchstone description, recent work suggests the presence of anomalous diffusion, where the particle spreading rate differs from the linear dependence with time of Brownian behavior. We demonstrate that conventional measures of particle spreading reveal different attributes of bedload particle behavior depending on details of the calculation. When we view particle motions over start‐and‐stop timescales obtained from high‐speed (250 Hz) imaging of coarse‐sand particles, high‐resolution measurements reveal ballistic‐like behavior at the shortest (10 −2 s) timescale, followed by apparent anomalous behavior due to correlated random walks in transition to normal diffusion (>10 −1 s) – similar to Brownian particle behavior but involving distinctly different physics. However, when treated as a ‘virtual plume’ over this timescale range, particles exhibit inhomogeneous diffusive behavior because both the mean and the variance of particle travel distances increase nonlinearly with increasing travel times, a behavior that is unrelated to anomalous diffusion or to Brownian‐like behavior. Our results indicate that care is needed in suggesting anomalous behavior when appealing to conventional measures of diffusion formulated for ideal particle systems. Copyright © 2016 John Wiley & Sons, Ltd.