Abstract
Abstract. Abrasion of sedimentary particles in fluvial and eolian environments is widely associated with collisions encountered by the particle. Although the physics of abrasion is complex, purely geometric models recover the course of mass and shape evolution of individual particles in low- and middle-energy environments (in the absence of fragmentation) remarkably well. In this paper, we introduce the first model for the collision-driven collective mass evolution of sedimentary particles. The model utilizes results of the individual, geometric abrasion theory as a collision kernel; following techniques adopted in the statistical theory of coagulation and fragmentation, the corresponding Fokker–Planck equation is derived. Our model uncovers a startling fundamental feature of collective particle size dynamics: collisional abrasion may, depending on the energy level, either focus size distributions, thus enhancing the effects of size-selective transport, or it may act in the opposite direction by dispersing the distribution.
Highlights
1.1 Geological observationsProbably the most fundamental observation on pebbles is that they appear to be segregated both by size and shape and it is broadly accepted that the dynamics is driven by two physical processes: transport and abrasion
The most fundamental observation on pebbles is that they appear to be segregated both by size and shape and it is broadly accepted that the dynamics is driven by two physical processes: transport and abrasion
10 By implementing these two assumptions into the statistical model based on the collision kernel (1), we take the first step towards establishing the statistical theory of collective size and shape evolution of sedimentary particles
Summary
The most fundamental observation on pebbles is that they appear to be segregated both by size and shape and it is broadly accepted that the dynamics is driven by two physical processes: transport and abrasion. One of the most remarkable accounts of pebble size and shape distribution is provided by Carr (Carr, 1969) based on the measurement of approximately a hundred thousand pebbles on Chesil Beach, Dorset, England In summarizing his results, Carr provides mean values and sample variations for maximal pebble size and pebble axis ratios along lines orthogonal to the 10 beach. A detailed account of the interaction of abrasion and transport is given 15 by Landon (Landon, 1930) who investigated the beaches on the west shore of Lake Michigan He attributes size and shape variation to a mixture of abrasion and transport. These large rocks could be interpreted as outliers emerging spontaneously in a pebble size distribution on which collisional abrasion certainly has strong impact in upper reaches of rivers. 30 As we can see, a complex picture emerges from geological observations which suggest that the interaction of transport and abrasion may be far from trivial, raising the need to consider both processes (transport and abrasion) simultaneously when trying to explain geological observations on sedimentary particles
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