Particle energy partitioning and transverse diffusion during rarefied travel on an experimental hillslope

Abstract

Abstract. Recent theoretical and experimental work (Furbish et al., 2020a, 2020b) indicates that rarefied particle motions on rough hillslope surfaces are controlled by the balance between gravitational heating of particles due to conversion of potential to kinetic energy and frictional cooling of the particles due to collisions with the surface. Here we elaborate how particle energy is partitioned between kinetic, rotational, and frictional forms during downslope travel using measurements of particle travel distances on a laboratory-scale hillslope, supplemented with high-speed imaging of drop-impact-rebound experiments. The drop-impact-rebound experiments indicate that particle shape has a dominant role in energy conversion during impact with a surface. Relative to spherical and natural rounded particles, angular particles give greater variability in rebound behavior resulting in more effective conversion of translational to rotational energy. The effects of particle shape on energy conversion are especially pronounced on a sloping sand-roughened surface. Angular particles travel shorter distances downslope than rounded particles though travel distance data for both groups are well fit by generalized Pareto distributions. Moreover, particle-surface collisions during downslope motion lead to a transverse random-walk behavior and transverse particle dispersion. Transverse spreading increases with surface slope as there is more available energy to be partitioned into the downslope or transverse directions during collision due to increased gravitational heating. Rounded particles exhibit greater transverse dispersion than angular particles, as less energy is lost during collision with the surface. Because the experimental surface is relatively smooth, this random-walk behavior represents a top-down control on the randomization of particle trajectories due to particle shape, which is in contrast to a bottom-up control on randomization of particle trajectories associated with motions over rough surfaces. Importantly, transverse particle diffusion during downslope motion may contribute to a cross-slope particle flux, and likely contributes to topographic smoothing of irregular hillslope surfaces such as scree slopes.

Rarefied particle motions on hillslopes – Part 4: Philosophy

“…In addition, Pierce and Hassan (2020a) modify the formulation of Ancey et al (2008) to couple erosion and deposition with the bed state n(t). This explicitly includes a stabilizing feedback where entrainment preferentially occurs with aggradation and deposition preferentially occurs with degradation (Sawai, 1987;Wong et al, 2007). This coupling ensures that the state n possesses a stable distribution with finite mean and variance.…”

Flume Experiments on the Erosive Energy of Bed Load Impacts on Rough and Planar Beds

“…It is reasonable to assume that a larger range of bed surface angles would disperse impact energies more than what we observed in these experiments. Relative to spherical particles, nonspherical shape of natural sediment increases variability in rebound behavior and impact energy (Williams & Furbish, 2021), and mixed mode impacts with an element of rolling or sliding are more likely for irregularly shaped particles (Schmeeckle et al, 2001). However, our two-dimensional observations of particles in motion did not allow us to separate the effects of sediment from the effects of the bed surface on the rebound trajectory.…”

Probabilistic description of bedload fluxes from the aggregate dynamics of individual grains

“…One option is to render slower-moving particles more likely to deposit, which can be viewed as making the dichotomous noise "state-dependent" (e.g., Laio et al, 2008;Bartlett and Porporato, 2018). This would preferentially cull slow-moving particles and positively skew the particle velocity distribution (Williams and Furbish, 2021), probably affecting the sediment flux.…”