Rarefied particle motions on hillslopes - Part 4: Philosophy

Theoretical and experimental work (Furbish et al., 2021a, b, c) indicates that the travel distances of rarefied particle motions on rough hillslope surfaces are described by a generalized Pareto distribution. The form of this distribution varies with the balance between gravitational heating due to conversion of potential to kinetic energy and frictional cooling by particle-surface collisions. The generalized Pareto distribution in this problem is a maximum entropy distribution constrained by a fixed energetic "cost"- the total cumulative energy extracted by collisional friction per unit kinetic energy available during particle motions. The analyses leading to these results provide an ideal case study for highlighting three key elements of a statistical mechanics framework for describing sediment particle motions and transport: the merits of probabilistic versus deterministic descriptions of sediment motions, the implications of rarefied versus continuum transport conditions, and the consequences of increasing uncertainty in descriptions of sediment motions and transport that accompany increasing length scales and timescales. We use the analyses of particle energy extraction, the spatial evolution of particle energy states, and the maximum entropy method applied to the generalized Pareto distribution as examples to illustrate the mechanistic yet probabilistic nature of the approach. These examples highlight the idea that the endeavor is not simply about adopting theory or methods of statistical mechanics "off the shelf"but rather involves appealing to the style of thinking of statistical mechanics while tailoring the analysis to the process and scale of interest. Under rarefied conditions, descriptions of the particle flux and its divergence pertain to ensemble conditions involving a distribution of possible outcomes, each realization being compatible with the controlling factors. When these factors change over time, individual outcomes reflect a legacy of earlier conditions that depends on the rate of change in the controlling factors relative to the intermittency of particle motions. The implication is that landform configurations and associated particle fluxes reflect an inherent variability ("weather") that is just as important as the expected ("climate") conditions in characterizing system behavior. © Copyright:Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

The variability of antidune morphodynamics on steep slopes

Steep streams on rough beds are generally characterised by supercritical flow conditions under which antidunes can develop and migrate over time. In this paper, we present flume experiments that we conducted to investigate the variability of antidune geometry and migration celerity, a variability observed even under steady-state conditions. Quantifying this variability is important for river morphodynamics, hydraulics and paleohydraulics. We imposed moderate to intense bedload transport rates at the flume inlet to assess their effects on antidune morphodynamics for near-constant values of the mean bed slope. The bed elevation profile was monitored for each experiment with high spatial and temporal resolution. Upstream migrating antidunes were observed along most of the flume length. Considering single values for wavelength and celerity was not sufficient to describe the antidune behaviour in these experiments. By using spectral analysis, we identified the variability ranges of bedform shape and celerity. Interestingly, migration celerity increased with increasing antidune wavelength; the opposite trend was reported for dunes in other studies. Antidunes were more uniform and migrated faster for higher sediment feeding rates. Scaling the spectra made it possible to find a general dimensionless relationship between antidune wavelength and celerity. This framework provides a novel method for estimating the mean bedload transport rate in the presence of upstream migrating antidunes

Rarefied particle motions on hillslopes - Part 3: Entropy

Theoretical and experimental work (Furbish et al., 2021a, b) indicates that the travel distances of rarefied particle motions on rough hillslope surfaces are described by a generalized Pareto distribution. The form of this distribution varies with the balance between gravitational heating, due to conversion of potential to kinetic energy, and frictional cooling, due to particle-surface collisions; it varies from a bounded form associated with rapid thermal collapse to an exponential form representing isothermal conditions to a heavy-tailed form associated with net heating of particles. The generalized Pareto distribution in this problem is a maximum entropy distribution constrained by a fixed energetic "cost"- the total cumulative energy extracted by collisional friction per unit kinetic energy available during particle motions. That is, among all possible accessible microstates - the many different ways to arrange a great number of particles into distance states where each arrangement satisfies the same fixed total energetic cost - the generalized Pareto distribution represents the most probable arrangement. Because this idea applies equally to the accessible microstates associated with net cooling, isothermal conditions and net heating, the fixed energetic cost provides a unifying interpretation for these distinctive behaviors, including the abrupt transition in the form of the generalized Pareto distribution in crossing isothermal conditions. The analysis therefore represents a novel generalization of an energy-based constraint in using the maximum entropy method to infer non-exponential distributions of particle motions. Moreover, the energetic costs of individual particle motions follow an extreme-value distribution that is heavy-tailed for net cooling and light-tailed for net heating. The relative contribution of different travel distances to the total energetic cost is reflected by the product of the travel distance distribution and the cost of individual particle motions - effectively a frequency-magnitude product. © Copyright:Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Particle motion of bed-load sediment moving over a smooth bed

The continuous motion of bed load moving particle over a smooth bed was experimentally studied. Particle motion was filmed by a CCD camera and an ad hoc Image Processing software was applied to track particles. The streamwise components of instantaneous particle velocity and mean particle velocity within each trajectory were quantified. Statistical properties of particle trajectories were investigated for three different hydrodynamic conditions. A clear dependence of the statistical moments of particle velocity on shear velocity was observed. The probability density function of the instantaneous streamwise velocity is well fitted by a Normal or a Gamma distribution, depending whether or not one single motion mode (sliding, rolling, saltation) prevails on the other ones. Finally, the correspondence between the autocorrelation time scale of instantaneous velocity and the bursting time scale was identified as a footprint of the hydrodynamic properties of the turbulent flow field on particle motion

The incipient motion of sediment in a channel with model emergent vegetation

In a bare channel (without vegetation), the incipient velocity for sediment motion, U[subscript crit], has historically been related to the mean bed shear stress ([bar over τ]) o or friction velocity (U[subscript ∗] = √[bar over τ]/ρ). More recent studies, however, suggest turbulence also plays a role. This paper examines whether the onset of sediment motion in a vegetated channel is correlated with U[subscript ∗], or turbulence (k[subscript τ). Images collected with a digital camera were interrogated with a particle-tracking code to measure sediment transport for different vegetation density and channel velocity. The trend in sediment transport with channel velocity was used to identify U[subscript crit] for each stem density. The values of k[subscript τ and U[subscript ∗] were estimated at Ucrit. However, none of these parameters produced a constant threshold across all stem density and bare bed. We construct a new metric representing the peak turbulent velocities impinging on the bed that produces a constant threshold value for all cases