Particle-scale Diffusion during Rarefied Transport as a Probabilistic Mechanics Problem
Williams, Sarah
0000-0002-8779-6712
:
2024-06-17
Abstract
As dynamic sculptors of landscapes, rivers present an interesting opportunity to explore how sediment transport at the particle scale informs macro-scale bedform evolution. Observations of river bedload transport rates are prone to large fluctuations about deterministically expected values, indicating that prevailing continuum-like formulations of bedload transport may be ill-equipped for describing the rarefied transport of moving particles at low concentrations. Though a fundamental behavior observed across many rarefied particle systems, lateral diffusion and associated two-dimensional particle motions are such particle-scale behaviors that are frequently overlooked or oversimplified when observing bedload sediment transport through a continuum lens. Herein I use a probabilistic approach to examine how collisional energy exchanges at the particle-scale inform two dimensional spreading behaviors in order to build a more physically grounded description of bedload diffusion. I present two sets of experiments aimed at elucidating the mechanics of two-dimensional particle diffusion in terms of particle angularity and surface roughness. Using high speed imaging of particles in a static bath and a laminar flume, I explore how energy redistribution during collisions forces particles to reorient stochastically in two dimensions during each moment of transport. I focus particularly on the mechanistic origins of particle-scale diffusion in terms of energy evolution for a single particle and within a particle ensemble to demonstrate how stochastic interpretations of variables best capture these random particle motions. In the final content chapter, I draw from several of the concepts within the two previous experimental chapters to elaborate how particle-scale dynamics result in fundamentally stochastic behaviors from the particle scale to the bedform scale for even the “tamest” of transport scenarios, i.e. rain splash transport. I present a series of rain splash simulations and deterministic stability analyses to illustrate how uncertainty at the particle scale informs actual realizations of transport rates. Such an appreciation of the inherently stochastic elements of transport and resulting variability between individual realizations about expected values as demonstrated herein is largely lacking in the geomorphological literature until recently.