Probability of travel distances in gravel bedload transport: size
dependence
Kimberly Hill, Mark Meerschaert, and Leslie DellAngelo
Bedload transport -- where particles move intermittently in frequent
contact with the bed -- is the dominant mode for particle transport in
gravelbed rivers and streams. Modeling the movement of particles in
bedload
transport is extremely difficult, in part due to complicated fluid/particle
and particle/particle interactions. Furthermore, the particle movement
is
stochastic rather than deterministic, giving rise to a distribution of
transport behaviors under any particular set of conditions. Hence,
most
models for bedload transport applied in the field rely on average
transport
quantities. It is well-known that the apparent average behaviors of
quantities with heavy-tailed probability distribution functions are
dominated by extreme events and therefore vary over the time or
distance
over which data are obtained. In this talk, we investigate the
plausibility
of heavy-tailed transport behavior of particles in bedload transport
using
carefully controlled flume experiments and theoretical analysis. We
find
the distribution of travel distances of single-sized particles over a
slightly mixed bed follows an exponential, whose details depend on the
particle sizes. Based on these results and typical particle size
distribution functions in the field, we present a plausible link between
thin-tailed distributions of the movement of single-sized particles and
heavy-tailed distributions of the movement of a mixture of particles. In
such cases, the overall average step length is a poor predictor of the
actual travel distance of any individual particle.