Abstract
During the last century, descriptions of sediment transport on the
surface of Earth have been mostly deterministic and strongly influenced
by concepts from continuum mechanics. The assumption that particle
motions on hillslopes and in rivers satisfy the continuum hypothesis has
provided an important foundation for this topic. Recent studies,
however, have recognized that bed load and hillslope sediment transport
conditions often are rarefied and do not satisfy continuum assumptions,
therein pointing to the need for new ways of describing particle motions
and transport. The problem of rarefied sediment transport is
probabilistic in nature, and emerging methods for describing particle
motions hark back to the pioneering work of Einstein (1938), who
conceptualized bed load transport as a probabilistic problem. Here we
provide a data set of particle travel distances and supplemental
high-speed videos of particle-surface collisions collected during
laboratory experiments to assess a theoretical formulation of the
probabilistic physics of rarefied particle motions and deposition on
rough hillslope surfaces. The formulation is based on a description of
the kinetic energy balance of a cohort of particles treated as a
rarefied granular gas, and a description of particle deposition that
depends on the energy state of the particles. Both laboratory and
field-based measurements are consistent with a generalized Pareto
distribution of travel distances and predicted variations in behavior
associated with the balance between gravitational heating and frictional
cooling by particle-surface collisions. These behaviors vary from a
truncated distribution associated with rapid thermal collapse to an
exponential distribution representing approximately isothermal
conditions to a heavy-tailed distribution associated with net heating of
particles. The transition to a heavy-tailed distribution likely involves
an increasing conversion of translational to rotational kinetic energy
leading to larger travel distances with decreasing effectiveness of
collisional friction. The analysis points to the need for further
clarity concerning how particle size and shape in concert with surface
roughness influence the extraction of particle energy and the likelihood
of deposition.