Impulse framework for unsteady flows reveals superdiffusive bed load transport

Abstract

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. Key Points Variability in hydrographs can be quantified using the dimensionless impulse. Sediment tracers display thin-tailed steps and heavy tailed waiting times. Sediment transport should be modeled as an asymmetric random walk. ©2013. American Geophysical Union. All Rights Reserved.