Impulse framework for unsteady flows reveals superdiffusive bed load transport

Authors

  • Colin B. Phillips,

    Corresponding author
    1. Department of Earth and Environmental Science, University of Pennsylvania, Philadephia, Pennsylvania, USA
    • Corresponding author: C. B. Phillips, Department of Earth and Environmental Science, University of Pennsylvania, Philadephia, Pennsylvania, 19104, USA. (colinp@sas.upenn.edu)

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  • Raleigh L. Martin,

    1. Department of Earth and Environmental Science, University of Pennsylvania, Philadephia, Pennsylvania, USA
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  • Douglas J. Jerolmack

    1. Department of Earth and Environmental Science, University of Pennsylvania, Philadephia, Pennsylvania, USA
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Abstract

[1] Sediment transport is an intrinsically stochastic process, and measurement of bed load in the environment is further complicated by the unsteady nature of river flooding. Here we present a methodology for analyzing sediment tracer data with unsteady forcing. We define a dimensionless impulse by integrating the cumulative excess shear velocity for the duration of measurement, normalized by grain size. We analyze the dispersion of a plume of cobble tracers in a very flashy stream over two years. The mean and variance of transport distance collapse onto well-defined linear and power-law relations, respectively, when plotted against cumulative dimensionless impulse. Data suggest that the asymptotic limit of bed load tracer dispersion is superdiffusive, in line with a broad class of geophysical flows exhibiting strong directional asymmetry (advection), thin-tailed step lengths and heavy-tailed waiting times. The impulse framework justifies the use of quasi-steady flow approximations for long-term river evolution modeling.

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