Open AccessThe physical basis for anomalous diffusion in bed load transport
Author(s) -
Martin Raleigh L.,
Jerolmack Douglas J.,
Schumer Rina
Publication year - 2012
Publication title -
journal of geophysical research: earth surface
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.67
H-Index - 298
eISSN - 2156-2202
pISSN - 0148-0227
DOI - 10.1029/2011jf002075
Subject(s) - bed load , anomalous diffusion , inertia , physics , mechanics , dispersion (optics) , diffusion , rest (music) , particle (ecology) , gaussian , scaling , fick's laws of diffusion , geology , statistical physics , sediment transport , sediment , classical mechanics , mathematics , geometry , geomorphology , knowledge management , oceanography , innovation diffusion , quantum mechanics , computer science , acoustics , optics , thermodynamics
Recent studies have observed deviation from normal (Fickian) diffusion in sediment tracer dispersion that violates the assumption of statistical convergence to a Gaussian. Nikora et al. (2002) hypothesized that particle motion at short time scales is superdiffusive because of inertia, while long‐time subdiffusion results from heavy‐tailed rest durations between particle motions. Here we test this hypothesis with laboratory experiments that trace the motion of individual gravels under near‐threshold intermittent bed load transport (0.027 < τ * < 0.087). Particle behavior consists of two independent states: a mobile phase, in which indeed we find superdiffusive behavior, and an immobile phase, in which gravels distrained from the fluid remain stationary for long durations. Correlated grain motion can account for some but not all of the superdiffusive behavior for the mobile phase; invoking heterogeneity of grain size provides a plausible explanation for the rest. Grains that become immobile appear to stay at rest until the bed scours down to an elevation that exposes them to the flow. The return time distribution for bed scour is similar to the distribution of rest durations, and both have power law tails. Results provide a physical basis for scaling regimes of anomalous dispersion and the time scales that separate these regimes.