Abstract
Abstract. 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.
Highlights
In three companion papers (Furbish et al, 2021a, b, c) we examine a theoretical formulation of the probabilistic physics of rarefied particle motions and deposition on rough hillslope surfaces
Recent efforts involve descriptions of (1) bed load particle motions and transport; (2) bed load tracer particle motions, including effects of particle–bed exchanges; (3) nonlocal sediment transport on hillslopes; (4) particle motions in soils, including tracer particles; and (5) rain splash transport (Appendix A). (We note that there is a parallel interest in describing the statistical physics of relatively dense granular materials, e.g., Bi et al, 2015.) this effort is a patchwork of approaches and methods, and to date it mostly has involved kinematic descriptions of sediment motions and transport with limited elucidation of the associated mechanics
We suggest that this example, details of which are provided in Furbish et al (2021a), offers a clear view of the value of a statistical mechanics approach involving the Fokker–Planck equation, highlighting the mechanistic yet probabilistic nature of the analysis
Summary
In three companion papers (Furbish et al, 2021a, b, c) we examine a theoretical formulation of the probabilistic physics of rarefied particle motions and deposition on rough hillslope surfaces. (We note that there is a parallel interest in describing the statistical physics of relatively dense granular materials, e.g., Bi et al, 2015.) this effort is a patchwork of approaches and methods, and to date it mostly has involved kinematic descriptions of sediment motions and transport with limited elucidation of the associated mechanics. We believe that it is important for the philosophical underpinning of this growing effort to be part of the conversation, adding to recent perspectives on bed load transport offered by Ancey (2020a, b). In several sections we provide historical background on the technical material covered
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