Preprints
https://doi.org/10.5194/esurf-2020-101
https://doi.org/10.5194/esurf-2020-101

  08 Dec 2020

08 Dec 2020

Review status: this preprint is currently under review for the journal ESurf.

Rarefied particle motions on hillslopes: 4. Philosophy

David Jon Furbish1 and Tyler H. Doane2,a David Jon Furbish and Tyler H. Doane
  • 1Department of Earth and Environmental Sciences, Vanderbilt University, Nashville, Tennessee, USA
  • 2Department of Geosciences, University of Arizona, Tucson, Arizona, USA
  • acurrently at: Department of Earth and Atmospheric Sciences, Indiana University, Bloomington, Indiana, USA

Abstract. Theoretical and experimental work (Furbish et al., 2020a, 2020b, 2020c) 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 and time scales. 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.

David Jon Furbish and Tyler H. Doane

 
Status: open (until 01 Feb 2021)
Status: open (until 01 Feb 2021)
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David Jon Furbish and Tyler H. Doane

David Jon Furbish and Tyler H. Doane

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